%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW470+5 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:37:06 AM UTC 2025
% Result : Theorem 6.92s 7.14s
% Output : Proof 7.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 55
% Syntax : Number of formulae : 143 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 570 ( 129 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 717 ( 323 ~; 250 |; 31 &)
% ( 74 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of FOOLs : 33 ( 33 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 11 con; 0-7 aty)
% Number of variables : 595 ( 502 !; 46 ?; 595 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(tptp_fun_S_21_type,type,
tptp_fun_S_21: ( $i * $i * $i * $i * $i ) > $i ).
tff(x_a_type,type,
x_a: $i ).
tff(b_type,type,
b: $i ).
tff(fNot_type,type,
fNot: $i ).
tff(combb_type,type,
combb: ( $i * $i * $i ) > $i ).
tff(state_type,type,
state: $i ).
tff(bool_type,type,
bool: $i ).
tff(fun_type,type,
fun: ( $i * $i ) > $i ).
tff(p_type,type,
p: $i ).
tff(fconj_type,type,
fconj: $i ).
tff(combs_type,type,
combs: ( $i * $i * $i ) > $i ).
tff(combc_type,type,
combc: ( $i * $i * $i ) > $i ).
tff(g_type,type,
g: $i ).
tff(c_type,type,
c: $i ).
tff(fFalse_type,type,
fFalse: $i ).
tff(combk_type,type,
combk: ( $i * $i ) > $i ).
tff(tptp_fun_Z_1_22_type,type,
tptp_fun_Z_1_22: ( $i * $i * $i * $i * $i ) > $i ).
tff(ti_type,type,
ti: ( $i * $i ) > $i ).
tff(bot_bot_type,type,
bot_bot: $i > $i ).
tff(bot_type,type,
bot: $i > $o ).
tff(hoare_1008221573triple_type,type,
hoare_1008221573triple: $i > $i ).
tff(hoare_509422987triple_type,type,
hoare_509422987triple: $i > $i ).
tff(com_type,type,
com: $i ).
tff(collect_type,type,
collect: $i > $i ).
tff(member_type,type,
member: $i > $i ).
tff(tptp_fun_S_1_23_type,type,
tptp_fun_S_1_23: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(insert_type,type,
insert: $i > $i ).
tff(hoare_122391849derivs_type,type,
hoare_122391849derivs: $i > $i ).
tff(1,plain,
( bot(bool)
<=> bot(bool) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
tff(3,plain,
bot(bool),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X_b: $i] :
refl(( ( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) )
<=> ( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) )
<=> ! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) )
<=> ! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [X_b: $i] :
rewrite(( ( bot(X_b)
=> ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) )
<=> ( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X_b: $i] :
( bot(X_b)
=> ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) )
<=> ! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X_b: $i] :
( bot(X_b)
=> ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).
tff(10,plain,
! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) )
| ~ bot(bool)
| ( ti(bool,bot_bot(bool)) = bot_bot(bool) ) )
<=> ( ~ ! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) )
| ~ bot(bool)
| ( ti(bool,bot_bot(bool)) = bot_bot(bool) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) )
| ~ bot(bool)
| ( ti(bool,bot_bot(bool)) = bot_bot(bool) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X_b: $i] :
( ~ bot(X_b)
| ( ti(X_b,bot_bot(X_b)) = bot_bot(X_b) ) )
| ~ bot(bool)
| ( ti(bool,bot_bot(bool)) = bot_bot(bool) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
ti(bool,bot_bot(bool)) = bot_bot(bool),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
bot_bot(bool) = ti(bool,bot_bot(bool)),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
^ [X_b: $i,X_c: $i] :
refl(( ( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
<=> ( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
<=> ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [X_b: $i,X_c: $i] :
rewrite(( ( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
<=> ( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
<=> ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
<=> ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
<=> ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [X_b: $i,X_c: $i] :
rewrite(( ( bot(X_c)
=> ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
<=> ( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [X_b: $i,X_c: $i] :
( bot(X_c)
=> ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
<=> ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [X_b: $i,X_c: $i] :
( bot(X_c)
=> ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_bot__fun__def) ).
tff(28,plain,
! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
| ~ bot(bool)
| ! [X_2: $i] : ( hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),X_2) = bot_bot(bool) ) )
<=> ( ~ ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
| ~ bot(bool)
| ! [X_2: $i] : ( hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),X_2) = bot_bot(bool) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
| ~ bot(bool)
| ! [X_2: $i] : ( hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),X_2) = bot_bot(bool) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [X_b: $i,X_c: $i] :
( ~ bot(X_c)
| ! [X_2: $i] : ( hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ) )
| ~ bot(bool)
| ! [X_2: $i] : ( hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),X_2) = bot_bot(bool) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X_2: $i] : ( hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),X_2) = bot_bot(bool) ),
inference(unit_resolution,[status(thm)],[34,31,3]) ).
tff(36,plain,
( ~ ! [X_2: $i] : ( hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),X_2) = bot_bot(bool) )
| ( hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))) = bot_bot(bool) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))) = bot_bot(bool),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
^ [X_b: $i] :
refl(( ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) )
<=> ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X_b: $i] : ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) )
<=> ! [X_b: $i] : ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X_b: $i] : ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) )
<=> ! [X_b: $i] : ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [X_b: $i] : ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_empty__def) ).
tff(42,plain,
! [X_b: $i] : ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X_b: $i] : ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X_b: $i] : ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [X_b: $i] : ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) )
| ( bot_bot(fun(hoare_509422987triple(x_a),bool)) = hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
bot_bot(fun(hoare_509422987triple(x_a),bool)) = hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)) = bot_bot(fun(hoare_509422987triple(x_a),bool)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [X_b: $i,Pa: $i] :
refl(( ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) )
<=> ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [X_b: $i,Pa: $i] : ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) )
<=> ! [X_b: $i,Pa: $i] : ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X_b: $i,Pa: $i] : ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) )
<=> ! [X_b: $i,Pa: $i] : ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [X_b: $i,Pa: $i] : ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
tff(52,plain,
! [X_b: $i,Pa: $i] : ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X_b: $i,Pa: $i] : ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X_b: $i,Pa: $i] : ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [X_b: $i,Pa: $i] : ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa) )
| ( hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)) = ti(fun(hoare_509422987triple(x_a),bool),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)) = ti(fun(hoare_509422987triple(x_a),bool),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
ti(fun(hoare_509422987triple(x_a),bool),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)) = hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),collect(hoare_509422987triple(x_a)),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
^ [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] :
refl(( ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) )
<=> ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) )
<=> ! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) )
<=> ! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
tff(62,plain,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ~ ! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) )
| ( ti(fun(hoare_509422987triple(x_a),bool),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)) = hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
ti(fun(hoare_509422987triple(x_a),bool),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)) = hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse) = ti(fun(hoare_509422987triple(x_a),bool),hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse) = bot_bot(fun(hoare_509422987triple(x_a),bool)),
inference(transitivity,[status(thm)],[67,57,47]) ).
tff(69,plain,
hAPP(hoare_509422987triple(x_a),bool,hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))) = hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
^ [X_b: $i,X_a: $i,P: $i,Q: $i] :
refl(( ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) )
<=> ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) )
<=> ! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) )
<=> ! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(74,plain,
! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) )
| ( hAPP(hoare_509422987triple(x_a),bool,hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))) = ti(bool,fFalse) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
hAPP(hoare_509422987triple(x_a),bool,hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))) = ti(bool,fFalse),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
ti(bool,fFalse) = hAPP(hoare_509422987triple(x_a),bool,hAPP(bool,fun(hoare_509422987triple(x_a),bool),combk(bool,hoare_509422987triple(x_a)),fFalse),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) )
| ( hAPP(state,bool,hAPP(bool,fun(state,bool),combk(bool,state),fFalse),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)) = ti(bool,fFalse) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
hAPP(state,bool,hAPP(bool,fun(state,bool),combk(bool,state),fFalse),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)) = ti(bool,fFalse),
inference(unit_resolution,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [X_c: $i,X_a: $i,B_1_1: $i,B_2: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2) )
| ( ti(fun(state,bool),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)) = hAPP(bool,fun(state,bool),combk(bool,state),fFalse) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
ti(fun(state,bool),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)) = hAPP(bool,fun(state,bool),combk(bool,state),fFalse),
inference(unit_resolution,[status(thm)],[82,64]) ).
tff(84,plain,
( ~ ! [X_b: $i,X_a: $i,P: $i,Q: $i] : ( hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) )
| ( hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)) = ti(fun(state,bool),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)) = ti(fun(state,bool),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),
inference(unit_resolution,[status(thm)],[84,76]) ).
tff(86,plain,
hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)) = hAPP(bool,fun(state,bool),combk(bool,state),fFalse),
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,plain,
hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)) = hAPP(state,bool,hAPP(bool,fun(state,bool),combk(bool,state),fFalse),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)) = ti(bool,bot_bot(bool)),
inference(transitivity,[status(thm)],[87,81,79,69,37,18]) ).
tff(89,plain,
( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
<=> hBOOL(ti(bool,bot_bot(bool))) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( hBOOL(ti(bool,bot_bot(bool)))
<=> hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))) ),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
( ~ hBOOL(ti(bool,bot_bot(bool)))
<=> ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))) = ti(bool,bot_bot(bool)),
inference(transitivity,[status(thm)],[37,18]) ).
tff(93,plain,
( hBOOL(hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))
<=> hBOOL(ti(bool,bot_bot(bool))) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ~ hBOOL(hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))
<=> ~ hBOOL(ti(bool,bot_bot(bool))) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
^ [X_b: $i,X_2: $i] :
refl(( ( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) )
<=> ( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) ) )),
inference(bind,[status(th)],[]) ).
tff(96,plain,
( ! [X_b: $i,X_2: $i] :
( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) )
<=> ! [X_b: $i,X_2: $i] :
( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [X_b: $i,X_2: $i] :
( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) )
<=> ! [X_b: $i,X_2: $i] :
( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,axiom,
! [X_b: $i,X_2: $i] :
( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_bot__empty__eq) ).
tff(99,plain,
! [X_b: $i,X_2: $i] :
( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X_b: $i,X_2: $i] :
( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [X_b: $i,X_2: $i] :
( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
( ~ ! [X_b: $i,X_2: $i] :
( hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))
<=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))) )
| ( hBOOL(hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))
<=> hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( hBOOL(hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))
<=> hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))) ),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
^ [X_b: $i,A_4: $i] :
refl(( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool))))
<=> ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool)))) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [X_b: $i,A_4: $i] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool))))
<=> ! [X_b: $i,A_4: $i] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool)))) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [X_b: $i,A_4: $i] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool))))
<=> ! [X_b: $i,A_4: $i] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,axiom,
! [X_b: $i,A_4: $i] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_emptyE) ).
tff(108,plain,
! [X_b: $i,A_4: $i] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool)))),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [X_b: $i,A_4: $i] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool)))),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [X_b: $i,A_4: $i] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool)))),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
( ~ ! [X_b: $i,A_4: $i] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ ( hBOOL(hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))
<=> hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))) )
| ~ hBOOL(hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))
| hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))) ),
inference(tautology,[status(thm)],[]) ).
tff(114,plain,
( ~ ( hBOOL(hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))
<=> hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))) )
| ~ hBOOL(hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))) ),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
~ hBOOL(hAPP(hoare_509422987triple(x_a),bool,bot_bot(fun(hoare_509422987triple(x_a),bool)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b))))),
inference(unit_resolution,[status(thm)],[114,103]) ).
tff(116,plain,
~ hBOOL(ti(bool,bot_bot(bool))),
inference(modus_ponens,[status(thm)],[115,94]) ).
tff(117,plain,
~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))),
inference(modus_ponens,[status(thm)],[116,91]) ).
tff(118,plain,
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
<=> ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,axiom,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(120,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
^ [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
refl(( ( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
<=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
<=> ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
^ [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
rewrite(( ( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
<=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(124,plain,
( ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
<=> ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
( ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
<=> ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[124,122]) ).
tff(126,plain,
^ [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
rewrite(( ( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
& ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
<=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
& ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
<=> ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) )
<=> ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
^ [X_b: $i,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(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S))
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)) )
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)) ) )
<=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ))),
( ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S))
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)) )
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)) ) )
<=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) )),
( ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S))
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)) )
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)) ) ) )
<=> ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) )),
rewrite(( ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) )
<=> ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) )),
( ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S))
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)) )
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)) ) ) )
<=> ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) ))),
( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S))
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)) )
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)) ) ) )
<=> ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) )),
( ( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S))
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)) )
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)) ) ) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) )
<=> ( ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) ) )),
rewrite(( ( ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) )
<=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) ) )),
( ( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S))
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)) )
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)) ) ) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) )
<=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S))
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)) )
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)) ) ) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) )
<=> ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,axiom,
! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( ! [Z_1: $i,S: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S))
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)) )
=> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)) ) ) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_conseq) ).
tff(132,plain,
! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ! [Z_1: $i,S: $i] :
( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
& ! [S_1: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
& ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
& ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[134,127]) ).
tff(136,plain,
! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[135,125]) ).
tff(137,plain,
( ( ~ ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
| hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),P_1),c),Q_2)),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),P_1,Z_2),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))) ) ) ) ) )
<=> ( ~ ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
| hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),P_1),c),Q_2)),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),P_1,Z_2),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
| hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),P_1),c),Q_2)),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),P_1,Z_2),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [X_b: $i,Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,tptp_fun_Z_1_22(Pa,Ca,Ga,Q_1,X_b)),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,Pa,Ca,Ga,Q_1,X_b)))
| ~ hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),tptp_fun_S_21(Pa,Ca,Ga,Q_1,X_b))) ) ) ) ) )
| hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),P_1),c),Q_2)),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),P_1,Z_2),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
~ ( ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),P_1),c),Q_2)),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),P_1,Z_2),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))) ) ) ) ),
inference(unit_resolution,[status(thm)],[139,136,120]) ).
tff(141,plain,
( ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [P_1: $i,Q_2: $i] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),P_1),c),Q_2)),bot_bot(fun(hoare_509422987triple(x_a),bool)))))
| ~ ( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ ! [Z_2: $i] :
( hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),Q_2,Z_2),tptp_fun_S_1_23(Q_2,P_1,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)))
| ~ hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),P_1,Z_2),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))) ) ) )
| hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))) ),
inference(tautology,[status(thm)],[]) ).
tff(142,plain,
hBOOL(hAPP(state,bool,hAPP(x_a,fun(state,bool),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),tptp_fun_Z_1_22(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a)),tptp_fun_S_21(hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse)),c,g,hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)),x_a))),
inference(unit_resolution,[status(thm)],[141,140]) ).
tff(143,plain,
$false,
inference(unit_resolution,[status(thm)],[142,117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWW470+5 : TPTP v9.0.0. Released v5.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 11:47:37 EDT 2025
% 0.13/0.34 % CPUTime :
% 6.92/7.14 % SZS status Theorem
% 6.92/7.14 % SZS output start Proof
% See solution above
% 7.08/7.30 % E exiting
%------------------------------------------------------------------------------