TSTP Solution File: SWW470+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW470+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:58:48 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 92
% Syntax : Number of formulae : 174 ( 51 unt; 39 typ; 0 def)
% Number of atoms : 641 ( 119 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 855 ( 385 ~; 297 |; 46 &)
% ( 85 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 36 ( 36 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 27 >; 25 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 12 con; 0-6 aty)
% Number of variables : 566 ( 461 !; 56 ?; 566 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_state_bool_type,type,
hAPP_state_bool: ( $i * $i ) > $i ).
tff(tptp_fun_S_20_type,type,
tptp_fun_S_20: ( $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(cOMBB_160679318_state_type,type,
cOMBB_160679318_state: $i > $i ).
tff(fNot_type,type,
fNot: $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(cOMBB_1355796797bool_a_type,type,
cOMBB_1355796797bool_a: $i > $i ).
tff(cOMBB_188601460_state_type,type,
cOMBB_188601460_state: $i > $i ).
tff(fconj_type,type,
fconj: $i ).
tff(cOMBB_145932198bool_a_type,type,
cOMBB_145932198bool_a: $i > $i ).
tff(cOMBS_1378840469l_bool_type,type,
cOMBS_1378840469l_bool: $i ).
tff(cOMBC_892787026e_bool_type,type,
cOMBC_892787026e_bool: $i ).
tff(g_type,type,
g: $i ).
tff(c_type,type,
c: $i ).
tff(cOMBK_1458035955bool_a_type,type,
cOMBK_1458035955bool_a: $i > $i ).
tff(cOMBK_bool_state_type,type,
cOMBK_bool_state: $i > $i ).
tff(fFalse_type,type,
fFalse: $i ).
tff(hAPP_a2036067514e_bool_type,type,
hAPP_a2036067514e_bool: ( $i * $i ) > $i ).
tff(tptp_fun_Z_1_21_type,type,
tptp_fun_Z_1_21: ( $i * $i * $i * $i ) > $i ).
tff(hAPP_H1927961489a_bool_type,type,
hAPP_H1927961489a_bool: ( $i * $i ) > $i ).
tff(hoare_1050552211iple_a_type,type,
hoare_1050552211iple_a: ( $i * $i * $i ) > $i ).
tff(cOMBK_1150238960iple_a_type,type,
cOMBK_1150238960iple_a: $i > $i ).
tff(is_bool_type,type,
is_bool: $i > $o ).
tff(collec1266446174iple_a_type,type,
collec1266446174iple_a: $i > $i ).
tff(hAPP_f1753944735l_bool_type,type,
hAPP_f1753944735l_bool: ( $i * $i ) > $i ).
tff(hAPP_H1926610125l_bool_type,type,
hAPP_H1926610125l_bool: ( $i * $i ) > $i ).
tff(member564727580iple_a_type,type,
member564727580iple_a: $i ).
tff(bot_bo1687970473a_bool_type,type,
bot_bo1687970473a_bool: $i ).
tff(hAPP_f1400872321a_bool_type,type,
hAPP_f1400872321a_bool: ( $i * $i ) > $i ).
tff(hAPP_H1816261935a_bool_type,type,
hAPP_H1816261935a_bool: ( $i * $i ) > $i ).
tff(insert1871499715iple_a_type,type,
insert1871499715iple_a: $i ).
tff(tptp_fun_S_1_22_type,type,
tptp_fun_S_1_22: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(hoare_472868247rivs_a_type,type,
hoare_472868247rivs_a: $i > $i ).
tff(1,plain,
^ [P: $i,Q: $i] :
refl(
( ( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) )
<=> ( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) )
<=> ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) )
<=> ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [P: $i,Q: $i] :
rewrite(
( ( is_bool(P)
=> ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) )
<=> ( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [P: $i,Q: $i] :
( is_bool(P)
=> ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) )
<=> ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [P: $i,Q: $i] :
( is_bool(P)
=> ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__) ).
tff(7,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(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/sandbox/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_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) )
| ~ is_bool(fFalse)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse ) )
<=> ( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) )
| ~ is_bool(fFalse)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) )
| ~ is_bool(fFalse)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) )
| ~ is_bool(fFalse)
| ( hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse,
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
fFalse = hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
^ [P: $i,Q: $i] :
refl(
( ( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) )
<=> ( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) )
<=> ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) )
<=> ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [P: $i,Q: $i] :
rewrite(
( ( is_bool(P)
=> ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) )
<=> ( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [P: $i,Q: $i] :
( is_bool(P)
=> ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) )
<=> ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [P: $i,Q: $i] :
( is_bool(P)
=> ( hAPP_state_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(25,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) )
| ~ is_bool(fFalse)
| ( hAPP_state_bool(cOMBK_bool_state(fFalse),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse ) )
<=> ( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) )
| ~ is_bool(fFalse)
| ( hAPP_state_bool(cOMBK_bool_state(fFalse),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) )
| ~ is_bool(fFalse)
| ( hAPP_state_bool(cOMBK_bool_state(fFalse),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ) )
| ~ is_bool(fFalse)
| ( hAPP_state_bool(cOMBK_bool_state(fFalse),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
hAPP_state_bool(cOMBK_bool_state(fFalse),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = fFalse,
inference(unit_resolution,[status(thm)],[31,13,28]) ).
tff(33,plain,
^ [P: $i,Q: $i] :
refl(
( ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P )
<=> ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P )
<=> ! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P )
<=> ! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
! [P: $i,Q: $i] : ( hAPP_a2036067514e_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(37,plain,
! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P )
| ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = cOMBK_bool_state(fFalse) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = cOMBK_bool_state(fFalse),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = hAPP_state_bool(cOMBK_bool_state(fFalse),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),
inference(transitivity,[status(thm)],[42,32,18]) ).
tff(44,plain,
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
<=> hBOOL(hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( hBOOL(hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
<=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ~ hBOOL(hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
<=> ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
^ [Pa: $i] :
refl(
( ( collec1266446174iple_a(Pa) = Pa )
<=> ( collec1266446174iple_a(Pa) = Pa ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [Pa: $i] : ( collec1266446174iple_a(Pa) = Pa )
<=> ! [Pa: $i] : ( collec1266446174iple_a(Pa) = Pa ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [Pa: $i] : ( collec1266446174iple_a(Pa) = Pa )
<=> ! [Pa: $i] : ( collec1266446174iple_a(Pa) = Pa ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
! [Pa: $i] : ( collec1266446174iple_a(Pa) = Pa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Collect__def) ).
tff(51,plain,
! [Pa: $i] : ( collec1266446174iple_a(Pa) = Pa ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [Pa: $i] : ( collec1266446174iple_a(Pa) = Pa ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Pa: $i] : ( collec1266446174iple_a(Pa) = Pa ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [Pa: $i] : ( collec1266446174iple_a(Pa) = Pa )
| ( collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) = cOMBK_1150238960iple_a(fFalse) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) = cOMBK_1150238960iple_a(fFalse),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))) = hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
<=> hBOOL(hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ~ hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
<=> ~ hBOOL(hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
^ [X_2: $i] :
refl(
( ( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) )
<=> ( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) )
<=> ! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
^ [X_2: $i] :
rewrite(
( ( hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),bot_bo1687970473a_bool)) )
<=> ( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),bot_bo1687970473a_bool)) )
<=> ! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),bot_bo1687970473a_bool)) )
<=> ! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),bot_bo1687970473a_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),bot_bo1687970473a_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_bot__empty__eq) ).
tff(65,plain,
! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),bot_bo1687970473a_bool)) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ),
inference(modus_ponens,[status(thm)],[65,62]) ).
tff(67,plain,
! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( ~ ! [X_2: $i] :
( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),X_2))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) )
| ( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
^ [A_3: $i,A: $i] :
refl(
( ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) )
<=> ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) )
<=> ! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
^ [A_3: $i,A: $i] :
rewrite(
( ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != bot_bo1687970473a_bool )
<=> ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != bot_bo1687970473a_bool )
<=> ! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != bot_bo1687970473a_bool )
<=> ! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != bot_bo1687970473a_bool ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != bot_bo1687970473a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_insert__not__empty) ).
tff(77,plain,
! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != bot_bo1687970473a_bool ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ),
inference(modus_ponens,[status(thm)],[77,74]) ).
tff(79,plain,
! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ~ ! [A_3: $i,A: $i] : ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) )
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))) != collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
^ [A_3: $i,A: $i] :
refl(
( ( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) )
<=> ( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) )
<=> ! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) )
<=> ! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
^ [A_3: $i,A: $i] :
rewrite(
( ( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
=> ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) )
<=> ( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [A_3: $i,A: $i] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
=> ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) )
<=> ! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [A_3: $i,A: $i] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
=> ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_insert__absorb) ).
tff(89,plain,
! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) )
| ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))) = collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ) )
<=> ( ~ ! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) )
| ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))) = collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ~ ! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) )
| ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))) = collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [A_3: $i,A: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A ) )
| ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))))
| ( hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))) = collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))),
inference(unit_resolution,[status(thm)],[95,92,82]) ).
tff(97,plain,
( ~ ( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) )
| ~ hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) ),
inference(tautology,[status(thm)],]) ).
tff(98,plain,
( ~ ( hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))) )
| ~ hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ),
inference(unit_resolution,[status(thm)],[97,96]) ).
tff(99,plain,
~ hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))),
inference(unit_resolution,[status(thm)],[98,70]) ).
tff(100,plain,
~ hBOOL(hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))),
inference(modus_ponens,[status(thm)],[99,58]) ).
tff(101,plain,
~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))),
inference(modus_ponens,[status(thm)],[100,46]) ).
tff(102,plain,
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool)))
<=> ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))))) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool)))
<=> ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool))) ),
inference(rewrite,[status(thm)],]) ).
tff(104,axiom,
~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(105,plain,
~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool))),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))))),
inference(modus_ponens,[status(thm)],[105,102]) ).
tff(107,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
refl(
( ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(108,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
rewrite(
( ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
rewrite(
( ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(113,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
rewrite(
( ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
rewrite(
( ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) )
<=> ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) )
<=> ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) )
<=> ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Z_1: $i,S: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [P_1: $i,Q_2: $i] :
rewrite(
( ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) )
<=> ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ))),
( ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) )
<=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) )),
( ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) ) )
<=> ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) )),
rewrite(
( ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) )
<=> ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) )),
( ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) ) )
<=> ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ))),
( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) ) )
<=> ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) )),
( ( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) ) )
=> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))) )
<=> ( ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) )
=> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))) ) )),
rewrite(
( ( ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) )
=> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))) )
<=> ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ) )),
( ( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) ) )
=> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))) )
<=> ( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) ) )
=> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))) )
<=> ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,axiom,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) ) )
=> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_conseq) ).
tff(122,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool)))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
& ! [S_1: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[123,117]) ).
tff(125,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[125,115]) ).
tff(127,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[126,113]) ).
tff(128,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[127,111]) ).
tff(129,plain,
( ( ~ ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
| hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,c,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ) ) ) ) )
<=> ( ~ ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
| hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,c,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ~ ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
| hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,c,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( ~ ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_20(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_1_21(Pa,Ca,Ga,Q_1)),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(Pa,Ca,Ga,Q_1))) ) ) ) ) )
| hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,c,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,c,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ) ) ) ),
inference(unit_resolution,[status(thm)],[131,128,106]) ).
tff(133,plain,
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,c,Q_2)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),tptp_fun_S_1_22(Q_2,P_1,cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ) ) )
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))) ),
inference(tautology,[status(thm)],]) ).
tff(134,plain,
hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),tptp_fun_Z_1_21(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),tptp_fun_S_20(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b))))),
inference(unit_resolution,[status(thm)],[133,132]) ).
tff(135,plain,
$false,
inference(unit_resolution,[status(thm)],[134,101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW470+1 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 17:33:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------