TSTP Solution File: SWW569_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW569_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 : Fri May 19 12:25:05 EDT 2023
% Result : Theorem 64.52s 51.20s
% Output : Refutation 65.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 148
% Syntax : Number of formulae : 253 ( 67 unt; 45 typ; 0 def)
% Number of atoms : 7470 ( 140 equ; 0 cnn)
% Maximal formula atoms : 274 ( 35 avg)
% Number of connectives : 19023 ( 90 ~; 3 |; 43 &;18653 @)
% ( 12 <=>; 222 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 14 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 21 con; 0-6 aty)
% Number of variables : 1136 ( 0 ^;1087 !; 23 ?;1136 :)
% ( 26 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(char_type,type,
char: $tType ).
thf(ty_type,type,
ty: $tType ).
thf(val_type,type,
val: $tType ).
thf(hconf_type,type,
hconf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > $o ) ).
thf(lconf_type,type,
lconf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ val ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > $o ) ).
thf(fAcc_type,type,
fAcc:
!>[TA: $tType] : ( ( exp @ TA ) > ( list @ char ) > ( list @ char ) > ( exp @ TA ) ) ).
thf(tryCatch_type,type,
tryCatch:
!>[TA: $tType] : ( ( exp @ TA ) > ( list @ char ) > TA > ( exp @ TA ) > ( exp @ TA ) ) ).
thf(while_type,type,
while:
!>[TA: $tType] : ( ( exp @ TA ) > ( exp @ TA ) > ( exp @ TA ) ) ).
thf(throw_type,type,
throw:
!>[TA: $tType] : ( ( exp @ TA ) > ( exp @ TA ) ) ).
thf(wf_J_mdecl_type,type,
wf_J_mdecl: fun @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) ).
thf(map_add_type,type,
map_add:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( option @ TA ) ) > ( fun @ TB @ ( option @ TA ) ) > ( fun @ TB @ ( option @ TA ) ) ) ).
thf(hext_type,type,
hext: ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > $o ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_curry_type,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ ( product_prod @ TC @ TB ) @ TA ) > TC > TB > TA ) ).
thf(produc1605651328_split_type,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_prod_rec_type,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(red_type,type,
red: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) ).
thf(hp_type,type,
hp: ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ).
thf(transitive_rtrancl_type,type,
transitive_rtrancl:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).
thf(has_field_type,type,
has_field:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( list @ char ) > ( list @ char ) > ty > ( list @ char ) > $o ) ).
thf(widen_type,type,
widen:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ty > ty > $o ) ).
thf(typeSa976492716_sconf_type,type,
typeSa976492716_sconf: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) > $o ).
thf(is_refT_type,type,
is_refT: ty > $o ).
thf(class_type,type,
class: ( list @ char ) > ty ).
thf(nt_type,type,
nt: ty ).
thf(wf_prog_type,type,
wf_prog:
!>[TA: $tType] : ( ( fun @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) @ bool ) ) ) > ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > $o ) ).
thf(wTrt_type,type,
wTrt: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > ( exp @ ( list @ char ) ) > ty > $o ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(d_type,type,
d: list @ char ).
thf(e_type,type,
e: fun @ ( list @ char ) @ ( option @ ty ) ).
thf(f_type,type,
f: list @ char ).
thf(p_type,type,
p: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ).
thf(t_type,type,
t: ty ).
thf(e_a_type,type,
e_a: exp @ ( list @ char ) ).
thf(ea_type,type,
ea: exp @ ( list @ char ) ).
thf(h_a_type,type,
h_a: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ).
thf(ha_type,type,
ha: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ).
thf(l_a_type,type,
l_a: fun @ ( list @ char ) @ ( option @ val ) ).
thf(la_type,type,
la: fun @ ( list @ char ) @ ( option @ val ) ).
thf(77,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ ( hp @ F ) @ B @ G @ A )
=> ( ( typeSa976492716_sconf @ C @ B @ F )
=> ( typeSa976492716_sconf @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_red__preserves__sconf) ).
thf(347,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ ( hp @ F ) @ B @ G @ A )
=> ( ( typeSa976492716_sconf @ C @ B @ F )
=> ( typeSa976492716_sconf @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(16,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: exp @ TA,D: exp @ TA] :
( ( ( while @ TA @ D @ C )
= ( while @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_exp_Osimps_I13_J) ).
thf(159,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: exp @ TA,D: exp @ TA] :
( ( ( ( while @ TA @ D @ C )
= ( while @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( while @ TA @ D @ C )
= ( while @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_prod__induct5) ).
thf(273,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_prod__cases3) ).
thf(276,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(64,axiom,
! [A: list @ char] :
( ( wTrt @ p @ ha @ e @ ea @ ( class @ A ) )
=> ( ( has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ f @ t @ d )
=> ? [B: ty] :
( ( wTrt @ p @ h_a @ e @ ( fAcc @ ( list @ char ) @ e_a @ f @ d ) @ B )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ B @ t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_calculation) ).
thf(308,plain,
! [A: list @ char] :
( ( wTrt @ p @ ha @ e @ ea @ ( class @ A ) )
=> ( ( has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ f @ t @ d )
=> ? [B: ty] :
( ( wTrt @ p @ h_a @ e @ ( fAcc @ ( list @ char ) @ e_a @ f @ d ) @ B )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ B @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Pair__eq) ).
thf(142,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ ( list @ char ) @ ( option @ ty ),C: fun @ ( list @ char ) @ ( option @ val ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ E @ D @ C @ B )
=> ( ( hext @ D @ A )
=> ( lconf @ TA @ E @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_lconf__hext) ).
thf(153,plain,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ ( list @ char ) @ ( option @ ty ),C: fun @ ( list @ char ) @ ( option @ val ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ E @ D @ C @ B )
=> ( ( hext @ D @ A )
=> ( lconf @ TA @ E @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [TA: $tType,A: exp @ TA,B: TA,C: list @ char,D: exp @ TA,E: exp @ TA,F: exp @ TA] :
( ( while @ TA @ F @ E )
!= ( tryCatch @ TA @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_exp_Osimps_I222_J) ).
thf(185,plain,
! [TA: $tType,A: exp @ TA,B: TA,C: list @ char,D: exp @ TA,E: exp @ TA,F: exp @ TA] :
( ( while @ TA @ F @ E )
!= ( tryCatch @ TA @ D @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_prod__induct4) ).
thf(320,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(43,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: list @ char,D: list @ char,E: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ ( throw @ ( list @ char ) @ E ) @ D @ C ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ B ) ) @ ( red @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_red__reds_OFAccThrow) ).
thf(257,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: list @ char,D: list @ char,E: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ ( throw @ ( list @ char ) @ E ) @ D @ C ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ B ) ) @ ( red @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(94,axiom,
! [TA: $tType,A: list @ char,B: list @ char,C: exp @ TA,D: exp @ TA,E: exp @ TA] :
( ( while @ TA @ E @ D )
!= ( fAcc @ TA @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_exp_Osimps_I165_J) ).
thf(389,plain,
! [TA: $tType,A: list @ char,B: list @ char,C: exp @ TA,D: exp @ TA,E: exp @ TA] :
( ( while @ TA @ E @ D )
!= ( fAcc @ TA @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(87,axiom,
! [A: exp @ ( list @ char ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),D: exp @ ( list @ char ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),F: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ E ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ D ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ B ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( while @ ( list @ char ) @ F @ A ) @ E ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ D ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_WhileRedsThrow) ).
thf(372,plain,
! [A: exp @ ( list @ char ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),D: exp @ ( list @ char ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),F: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ E ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ D ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ B ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( while @ ( list @ char ) @ F @ A ) @ E ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ D ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(81,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: fun @ ( list @ char ) @ ( option @ val ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: exp @ ( list @ char ),G: fun @ ( list @ char ) @ ( option @ val ),H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ I @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ H @ G ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ E @ D ) ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ H @ B @ I @ A )
=> ( ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ H @ G @ B )
=> ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ E @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_red__preserves__lconf) ).
thf(357,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: fun @ ( list @ char ) @ ( option @ val ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: exp @ ( list @ char ),G: fun @ ( list @ char ) @ ( option @ val ),H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ I @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ H @ G ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ E @ D ) ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ H @ B @ I @ A )
=> ( ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ H @ G @ B )
=> ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ E @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_prod__cases5) ).
thf(284,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(100,axiom,
! [A: ty,B: list @ char,C: list @ char,D: exp @ ( list @ char ),E: fun @ ( list @ char ) @ ( option @ ty ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ G @ F @ E @ ( fAcc @ ( list @ char ) @ D @ C @ B ) @ A )
=> ( ! [H: list @ char] :
( ( wTrt @ G @ F @ E @ D @ ( class @ H ) )
=> ~ ( has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ G @ H @ C @ A @ B ) )
=> ( wTrt @ G @ F @ E @ D @ nt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_WTrt__elim__cases_I7_J) ).
thf(416,plain,
! [A: ty,B: list @ char,C: list @ char,D: exp @ ( list @ char ),E: fun @ ( list @ char ) @ ( option @ ty ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ G @ F @ E @ ( fAcc @ ( list @ char ) @ D @ C @ B ) @ A )
=> ( ! [H: list @ char] :
( ( wTrt @ G @ F @ E @ D @ ( class @ H ) )
=> ~ ( has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ G @ H @ C @ A @ B ) )
=> ( wTrt @ G @ F @ E @ D @ nt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(33,axiom,
! [A: ty,B: exp @ ( list @ char ),C: fun @ ( list @ char ) @ ( option @ ty ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ E @ D @ C @ ( throw @ ( list @ char ) @ B ) @ A )
=> ~ ! [F: ty] :
( ( wTrt @ E @ D @ C @ B @ F )
=> ~ ( is_refT @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_WTrt__elim__cases_I4_J) ).
thf(228,plain,
! [A: ty,B: exp @ ( list @ char ),C: fun @ ( list @ char ) @ ( option @ ty ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ E @ D @ C @ ( throw @ ( list @ char ) @ B ) @ A )
=> ~ ! [F: ty] :
( ( wTrt @ E @ D @ C @ B @ F )
=> ~ ( is_refT @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_prod__induct3) ).
thf(289,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(28,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ C @ B )
=> ( ( hext @ B @ A )
=> ( hext @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_hext__trans) ).
thf(216,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ C @ B )
=> ( ( hext @ B @ A )
=> ( hext @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_split__paired__All) ).
thf(376,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_prod__induct6) ).
thf(253,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(36,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: fun @ ( list @ char ) @ ( option @ val ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: exp @ ( list @ char ),G: fun @ ( list @ char ) @ ( option @ val ),H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ I @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ H @ G ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ E @ D ) ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ H @ B @ I @ A )
=> ( ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ H )
=> ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_red__preserves__hconf) ).
thf(238,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: fun @ ( list @ char ) @ ( option @ val ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: exp @ ( list @ char ),G: fun @ ( list @ char ) @ ( option @ val ),H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ I @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ H @ G ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ E @ D ) ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ H @ B @ I @ A )
=> ( ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ H )
=> ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(5,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: TA,D: list @ char,E: exp @ TA] :
( ( tryCatch @ TA @ E @ D @ C @ B )
!= ( throw @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_exp_Osimps_I225_J) ).
thf(121,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: TA,D: list @ char,E: exp @ TA] :
( ( tryCatch @ TA @ E @ D @ C @ B )
!= ( throw @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
<=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_pred__equals__eq2) ).
thf(397,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ! [C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(30,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: exp @ TA] :
( ( throw @ TA @ C )
!= ( while @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_exp_Osimps_I221_J) ).
thf(221,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: exp @ TA] :
( ( throw @ TA @ C )
!= ( while @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(58,axiom,
wTrt @ p @ ha @ e @ ( fAcc @ ( list @ char ) @ ea @ f @ d ) @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_FAccRed_I4_J) ).
thf(293,plain,
wTrt @ p @ ha @ e @ ( fAcc @ ( list @ char ) @ ea @ f @ d ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(9,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA] :
( ( ( throw @ TA @ B )
= ( throw @ TA @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_exp_Osimps_I14_J) ).
thf(133,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA] :
( ( ( ( throw @ TA @ B )
= ( throw @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( throw @ TA @ B )
= ( throw @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(38,axiom,
! [A: fun @ ( list @ char ) @ ( option @ val ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: fun @ ( list @ char ) @ ( option @ val ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ val ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ G @ F ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ D @ C ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ B ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ G @ ( map_add @ ( list @ char ) @ val @ A @ F ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ D @ ( map_add @ ( list @ char ) @ val @ A @ C ) ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Red__lcl__add) ).
thf(243,plain,
! [A: fun @ ( list @ char ) @ ( option @ val ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: fun @ ( list @ char ) @ ( option @ val ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ val ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ G @ F ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ D @ C ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ B ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ G @ ( map_add @ ( list @ char ) @ val @ A @ F ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ D @ ( map_add @ ( list @ char ) @ val @ A @ C ) ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(46,axiom,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA] :
( ( fAcc @ TA @ D @ C @ B )
!= ( throw @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_exp_Osimps_I166_J) ).
thf(265,plain,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA] :
( ( fAcc @ TA @ D @ C @ B )
!= ( throw @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_prod_Oexhaust) ).
thf(206,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ D ) @ C ) )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ B )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ I @ J ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ I ) @ J ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ G ) @ H ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_converse__rtrancl__induct2) ).
thf(233,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ D ) @ C ) )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ B )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ I @ J ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ I ) @ J ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ G ) @ H ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_prod__cases6) ).
thf(380,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Pair__inject) ).
thf(201,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(84,axiom,
wTrt @ p @ ha @ e @ ( fAcc @ ( list @ char ) @ ea @ f @ d ) @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_wt) ).
thf(366,plain,
wTrt @ p @ ha @ e @ ( fAcc @ ( list @ char ) @ ea @ f @ d ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(71,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: fun @ ( list @ char ) @ ( option @ val ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: exp @ ( list @ char ),E: fun @ ( list @ char ) @ ( option @ val ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ F @ E ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ D @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ C @ B ) ) ) @ ( red @ A ) )
=> ( hext @ F @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_red__hext__incr) ).
thf(334,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: fun @ ( list @ char ) @ ( option @ val ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: exp @ ( list @ char ),E: fun @ ( list @ char ) @ ( option @ val ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ F @ E ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ D @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ C @ B ) ) ) @ ( red @ A ) )
=> ( hext @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(61,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ B @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ B @ ( transitive_rtrancl @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_r__into__rtrancl) ).
thf(302,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ B @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ B @ ( transitive_rtrancl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(78,axiom,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_converse__rtrancl__into__rtrancl) ).
thf(349,plain,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ TC @ A @ B @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_curry__def) ).
thf(392,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ TC @ A @ B @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(60,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ ( transitive_rtrancl @ TA @ A ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_rtranclE) ).
thf(297,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ ( transitive_rtrancl @ TA @ A ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(49,axiom,
wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wf_J_mdecl @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_assms) ).
thf(275,plain,
wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wf_J_mdecl @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(83,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ ( transitive_rtrancl @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_converse__rtranclE) ).
thf(361,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ ( transitive_rtrancl @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(70,axiom,
! [TA: $tType,A: list @ char,B: list @ char,C: exp @ TA,D: list @ char,E: list @ char,F: exp @ TA] :
( ( ( fAcc @ TA @ F @ E @ D )
= ( fAcc @ TA @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_exp_Osimps_I7_J) ).
thf(324,plain,
! [TA: $tType,A: list @ char,B: list @ char,C: exp @ TA,D: list @ char,E: list @ char,F: exp @ TA] :
( ( ( ( fAcc @ TA @ F @ E @ D )
= ( fAcc @ TA @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( fAcc @ TA @ F @ E @ D )
= ( fAcc @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(31,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: exp @ TA] :
( ( while @ TA @ C @ B )
!= ( throw @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_exp_Osimps_I220_J) ).
thf(224,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: exp @ TA] :
( ( while @ TA @ C @ B )
!= ( throw @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(15,axiom,
! [TA: $tType,A: exp @ TA,B: TA,C: list @ char,D: exp @ TA,E: exp @ TA] :
( ( throw @ TA @ E )
!= ( tryCatch @ TA @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_exp_Osimps_I224_J) ).
thf(156,plain,
! [TA: $tType,A: exp @ TA,B: TA,C: list @ char,D: exp @ TA,E: exp @ TA] :
( ( throw @ TA @ E )
!= ( tryCatch @ TA @ D @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,axiom,
! [A: ty] :
( ( is_refT @ A )
<=> ( ( A = nt )
| ? [B: list @ char] :
( A
= ( class @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_is__refT__def) ).
thf(188,plain,
! [A: ty] :
( ( ( is_refT @ A )
=> ( ( A = nt )
| ? [B: list @ char] :
( A
= ( class @ B ) ) ) )
& ( ( ( A = nt )
| ? [B: list @ char] :
( A
= ( class @ B ) ) )
=> ( is_refT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_prod_Orecs) ).
thf(124,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(73,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ ( throw @ ( list @ char ) @ C ) ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_red__reds_OThrowThrow) ).
thf(339,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ ( throw @ ( list @ char ) @ C ) ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(27,axiom,
! [A: list @ char] :
( nt
!= ( class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Type_Oty_Osimps_I20_J) ).
thf(212,plain,
! [A: list @ char] :
( nt
!= ( class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(75,axiom,
! [TA: $tType,A: list @ char,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ nt @ ( class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_widen__null) ).
thf(343,plain,
! [TA: $tType,A: list @ char,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ nt @ ( class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1,conjecture,
? [A: ty] :
( ( wTrt @ p @ h_a @ e @ ( fAcc @ ( list @ char ) @ e_a @ f @ d ) @ A )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: ty] :
( ( wTrt @ p @ h_a @ e @ ( fAcc @ ( list @ char ) @ e_a @ f @ d ) @ A )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(105,plain,
~ ? [A: ty] :
( ( wTrt @ p @ h_a @ e @ ( fAcc @ ( list @ char ) @ e_a @ f @ d ) @ A )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(65,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: list @ char,D: list @ char,E: exp @ TA] :
( ( fAcc @ TA @ E @ D @ C )
!= ( while @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_exp_Osimps_I164_J) ).
thf(311,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: list @ char,D: list @ char,E: exp @ TA] :
( ( fAcc @ TA @ E @ D @ C )
!= ( while @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(98,axiom,
! [A: list @ char,B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ E @ B @ A ) @ D ) ) @ ( red @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_red__reds_OFAccRed) ).
thf(412,plain,
! [A: list @ char,B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ E @ B @ A ) @ D ) ) @ ( red @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(103,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ A ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_ThrowRedsThrow) ).
thf(425,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ A ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(45,axiom,
wTrt @ p @ ha @ e @ ea @ nt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096) ).
thf(264,plain,
wTrt @ p @ ha @ e @ ea @ nt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(51,axiom,
! [A: list @ char,B: ty,C: list @ char,D: list @ char,E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ ty ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),H: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ H @ G @ F @ E @ ( class @ D ) )
=> ( ( has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ H @ D @ C @ B @ A )
=> ( wTrt @ H @ G @ F @ ( fAcc @ ( list @ char ) @ E @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_WTrtFAcc) ).
thf(279,plain,
! [A: list @ char,B: ty,C: list @ char,D: list @ char,E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ ty ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),H: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ H @ G @ F @ E @ ( class @ D ) )
=> ( ( has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ H @ D @ C @ B @ A )
=> ( wTrt @ H @ G @ F @ ( fAcc @ ( list @ char ) @ E @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(102,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ ( transitive_rtrancl @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rtrancl_Ortrancl__refl) ).
thf(423,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ ( transitive_rtrancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(57,axiom,
! [A: list @ char,B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_FAccRedsThrow) ).
thf(291,plain,
! [A: list @ char,B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_curryD) ).
thf(281,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(44,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ D ) )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( ( pp @ ( aa @ TA @ bool @ A @ E ) )
=> ( pp @ ( aa @ TA @ bool @ A @ F ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rtrancl__induct) ).
thf(259,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ D ) )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( ( pp @ ( aa @ TA @ bool @ A @ E ) )
=> ( pp @ ( aa @ TA @ bool @ A @ F ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_split__paired__Ex) ).
thf(419,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ bool,B: TB,C: TA,D: TB,E: TA] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ D ) @ ( product_Pair @ TA @ TB @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ A ) )
=> ( ( ( product_Pair @ TA @ TB @ E @ D )
!= ( product_Pair @ TA @ TB @ C @ B ) )
=> ~ ! [F: TA,G: TB] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ D ) @ ( product_Pair @ TA @ TB @ F @ G ) ) @ A )
=> ~ ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ F @ G ) @ ( product_Pair @ TA @ TB @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_converse__rtranclE2) ).
thf(245,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ bool,B: TB,C: TA,D: TB,E: TA] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ D ) @ ( product_Pair @ TA @ TB @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ A ) )
=> ( ( ( product_Pair @ TA @ TB @ E @ D )
!= ( product_Pair @ TA @ TB @ C @ B ) )
=> ~ ! [F: TA,G: TB] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ D ) @ ( product_Pair @ TA @ TB @ F @ G ) ) @ A )
=> ~ ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ F @ G ) @ ( product_Pair @ TA @ TB @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(93,axiom,
! [A: fun @ ( list @ char ) @ ( option @ val ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: fun @ ( list @ char ) @ ( option @ val ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ val ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ G @ F ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ D @ C ) ) ) @ ( red @ B ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ G @ ( map_add @ ( list @ char ) @ val @ A @ F ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ D @ ( map_add @ ( list @ char ) @ val @ A @ C ) ) ) ) @ ( red @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_red__lcl__add) ).
thf(387,plain,
! [A: fun @ ( list @ char ) @ ( option @ val ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: fun @ ( list @ char ) @ ( option @ val ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ val ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ G @ F ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ D @ C ) ) ) @ ( red @ B ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ G @ ( map_add @ ( list @ char ) @ val @ A @ F ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ D @ ( map_add @ ( list @ char ) @ val @ A @ C ) ) ) ) @ ( red @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(37,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty )] :
( ( typeSa976492716_sconf @ p @ B @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ B @ ea @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_a @ C )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_FAccRed_I2_J) ).
thf(240,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty )] :
( ( typeSa976492716_sconf @ p @ B @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ B @ ea @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_a @ C )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(14,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(155,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(198,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(76,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( hext @ E @ A )
=> ( wTrt @ F @ A @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_WTrt__hext__mono) ).
thf(345,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( hext @ E @ A )
=> ( wTrt @ F @ A @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(85,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ C @ B ) ) @ ( red @ A ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_red__reds_OThrowRed) ).
thf(367,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ C @ B ) ) @ ( red @ A ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(63,axiom,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ E ) ) @ ( red @ D ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( tryCatch @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( tryCatch @ ( list @ char ) @ F @ C @ B @ A ) @ E ) ) @ ( red @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_red__reds_OTryRed) ).
thf(306,plain,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ E ) ) @ ( red @ D ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( tryCatch @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( tryCatch @ ( list @ char ) @ F @ C @ B @ A ) @ E ) ) @ ( red @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(17,axiom,
! [A: list @ char,B: list @ char] :
( ( ( class @ B )
= ( class @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Type_Oty_Oinject) ).
thf(167,plain,
! [A: list @ char,B: list @ char] :
( ( ( ( class @ B )
= ( class @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( class @ B )
= ( class @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(88,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ A ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_ThrowReds) ).
thf(374,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ A ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(42,axiom,
! [TA: $tType,A: ty,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_widen__refl) ).
thf(255,plain,
! [TA: $tType,A: ty,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( option @ TB ),B: fun @ TA @ ( option @ TB ),C: fun @ TA @ ( option @ TB )] :
( ( map_add @ TA @ TB @ C @ ( map_add @ TA @ TB @ B @ A ) )
= ( map_add @ TA @ TB @ ( map_add @ TA @ TB @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_map__add__assoc) ).
thf(209,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( option @ TB ),B: fun @ TA @ ( option @ TB ),C: fun @ TA @ ( option @ TB )] :
( ( map_add @ TA @ TB @ C @ ( map_add @ TA @ TB @ B @ A ) )
= ( map_add @ TA @ TB @ ( map_add @ TA @ TB @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( produc1605651328_split @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_internal__split__conv) ).
thf(150,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( produc1605651328_split @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(99,axiom,
! [A: ty,B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( is_refT @ B )
=> ( wTrt @ F @ E @ D @ ( throw @ ( list @ char ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_WTrtThrow) ).
thf(414,plain,
! [A: ty,B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( is_refT @ B )
=> ( wTrt @ F @ E @ D @ ( throw @ ( list @ char ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(20,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( transitive_rtrancl @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( transitive_rtrancl @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rtrancl__idemp) ).
thf(182,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( transitive_rtrancl @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( transitive_rtrancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [A: list @ char] :
( ( class @ A )
!= nt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Type_Oty_Osimps_I21_J) ).
thf(127,plain,
! [A: list @ char] :
( ( class @ A )
!= nt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(82,axiom,
! [A: ty,B: list @ char,C: list @ char,D: exp @ ( list @ char ),E: fun @ ( list @ char ) @ ( option @ ty ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ G @ F @ E @ D @ nt )
=> ( wTrt @ G @ F @ E @ ( fAcc @ ( list @ char ) @ D @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_WTrtFAccNT) ).
thf(359,plain,
! [A: ty,B: list @ char,C: list @ char,D: exp @ ( list @ char ),E: fun @ ( list @ char ) @ ( option @ ty ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ G @ F @ E @ D @ nt )
=> ( wTrt @ G @ F @ E @ ( fAcc @ ( list @ char ) @ D @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(66,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ F ) )
=> ( pp @ ( aa @ TA @ bool @ A @ E ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_converse__rtrancl__induct) ).
thf(314,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ F ) )
=> ( pp @ ( aa @ TA @ bool @ A @ E ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(18,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: exp @ TA,D: TA,E: list @ char,F: exp @ TA] :
( ( tryCatch @ TA @ F @ E @ D @ C )
!= ( while @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_exp_Osimps_I223_J) ).
thf(175,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: exp @ TA,D: TA,E: list @ char,F: exp @ TA] :
( ( tryCatch @ TA @ F @ E @ D @ C )
!= ( while @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,axiom,
typeSa976492716_sconf @ p @ e @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_conf) ).
thf(386,plain,
typeSa976492716_sconf @ p @ e @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_PairE) ).
thf(218,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_prod__cases4) ).
thf(250,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_rtrancl_Ortrancl__into__rtrancl) ).
thf(231,plain,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(67,axiom,
wTrt @ p @ h_a @ e @ e_a @ nt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_ANT_096) ).
thf(319,plain,
wTrt @ p @ h_a @ e @ e_a @ nt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(62,axiom,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ D ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( tryCatch @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( tryCatch @ ( list @ char ) @ F @ C @ B @ A ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_TryReds) ).
thf(304,plain,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ F @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ D ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( tryCatch @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( tryCatch @ ( list @ char ) @ F @ C @ B @ A ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(79,axiom,
! [TA: $tType,A: list @ char,B: list @ char,C: exp @ TA,D: exp @ TA] :
( ( throw @ TA @ D )
!= ( fAcc @ TA @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_exp_Osimps_I167_J) ).
thf(351,plain,
! [TA: $tType,A: list @ char,B: list @ char,C: exp @ TA,D: exp @ TA] :
( ( throw @ TA @ D )
!= ( fAcc @ TA @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(10,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(139,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] : ( hext @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_hext__refl) ).
thf(119,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] : ( hext @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(91,axiom,
! [TA: $tType,A: list @ char,B: list @ char,C: exp @ TA,D: exp @ TA,E: TA,F: list @ char,G: exp @ TA] :
( ( tryCatch @ TA @ G @ F @ E @ D )
!= ( fAcc @ TA @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_exp_Osimps_I169_J) ).
thf(383,plain,
! [TA: $tType,A: list @ char,B: list @ char,C: exp @ TA,D: exp @ TA,E: TA,F: list @ char,G: exp @ TA] :
( ( tryCatch @ TA @ G @ F @ E @ D )
!= ( fAcc @ TA @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(55,axiom,
! [A: list @ char,B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ E @ B @ A ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_FAccReds) ).
thf(287,plain,
! [A: list @ char,B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ E @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fAcc @ ( list @ char ) @ E @ B @ A ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( red @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(3,axiom,
! [TA: $tType,A: exp @ TA,B: TA,C: list @ char,D: exp @ TA,E: exp @ TA,F: TA,G: list @ char,H: exp @ TA] :
( ( ( tryCatch @ TA @ H @ G @ F @ E )
= ( tryCatch @ TA @ D @ C @ B @ A ) )
<=> ( ( H = D )
& ( G = C )
& ( F = B )
& ( E = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_exp_Osimps_I15_J) ).
thf(107,plain,
! [TA: $tType,A: exp @ TA,B: TA,C: list @ char,D: exp @ TA,E: exp @ TA,F: TA,G: list @ char,H: exp @ TA] :
( ( ( ( tryCatch @ TA @ H @ G @ F @ E )
= ( tryCatch @ TA @ D @ C @ B @ A ) )
=> ( ( H = D )
& ( G = C )
& ( F = B )
& ( E = A ) ) )
& ( ( ( H = D )
& ( G = C )
& ( F = B )
& ( E = A ) )
=> ( ( tryCatch @ TA @ H @ G @ F @ E )
= ( tryCatch @ TA @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( product_curry @ TB @ TA @ TC @ C @ B @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_curry__conv) ).
thf(294,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( product_curry @ TB @ TA @ TC @ C @ B @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_curryE) ).
thf(341,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ F ) @ E ) )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ G @ H ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ B )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ G ) @ H ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ I ) @ J ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rtrancl__induct2) ).
thf(268,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ F ) @ E ) )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ G @ H ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ B )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ G ) @ H ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ I ) @ J ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(53,axiom,
typeSa976492716_sconf @ p @ e @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_FAccRed_I3_J) ).
thf(283,plain,
typeSa976492716_sconf @ p @ e @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) )
=> ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_curryI) ).
thf(395,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) )
=> ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(104,axiom,
! [TA: $tType,A: exp @ TA,B: TA,C: list @ char,D: exp @ TA,E: list @ char,F: list @ char,G: exp @ TA] :
( ( fAcc @ TA @ G @ F @ E )
!= ( tryCatch @ TA @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_exp_Osimps_I168_J) ).
thf(427,plain,
! [TA: $tType,A: exp @ TA,B: TA,C: list @ char,D: exp @ TA,E: list @ char,F: list @ char,G: exp @ TA] :
( ( fAcc @ TA @ G @ F @ E )
!= ( tryCatch @ TA @ D @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(8,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(131,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: ty] :
( ( is_refT @ A )
=> ( ( A != nt )
=> ~ ! [B: list @ char] :
( A
!= ( class @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_refTE) ).
thf(178,plain,
! [A: ty] :
( ( is_refT @ A )
=> ( ( A != nt )
=> ~ ! [B: list @ char] :
( A
!= ( class @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(86,axiom,
! [TA: $tType,A: ty,B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( widen @ TA @ C @ ( class @ B ) @ A )
=> ? [D: list @ char] :
( A
= ( class @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Class__widen) ).
thf(369,plain,
! [TA: $tType,A: ty,B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( widen @ TA @ C @ ( class @ B ) @ A )
=> ? [D: list @ char] :
( A
= ( class @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(32,axiom,
member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ea @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ e_a @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ h_a @ l_a ) ) ) @ ( red @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_FAccRed_I1_J) ).
thf(227,plain,
member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ea @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ e_a @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ h_a @ l_a ) ) ) @ ( red @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(69,axiom,
! [TA: $tType,A: ty,B: ty,C: ty,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( widen @ TA @ D @ C @ B )
=> ( ( widen @ TA @ D @ B @ A )
=> ( widen @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_widen__trans) ).
thf(322,plain,
! [TA: $tType,A: ty,B: ty,C: ty,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( widen @ TA @ D @ C @ B )
=> ( ( widen @ TA @ D @ B @ A )
=> ( widen @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(72,axiom,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_rtrancl__trans) ).
thf(337,plain,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(80,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty )] :
( ( typeSa976492716_sconf @ p @ B @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ B @ ea @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_a @ C )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_IH) ).
thf(354,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty )] :
( ( typeSa976492716_sconf @ p @ B @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ B @ ea @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_a @ C )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(430,plain,
$false,
inference(e,[status(thm)],[347,159,273,276,308,142,153,185,320,257,389,372,357,284,416,228,289,216,376,253,238,121,397,221,293,133,243,265,206,233,380,201,366,334,302,349,392,297,275,361,324,224,156,188,124,339,212,343,105,311,412,425,264,279,423,291,281,259,419,245,387,240,155,198,345,367,306,167,374,255,209,150,414,182,127,359,314,175,386,218,250,231,319,304,351,139,119,383,287,107,294,341,268,283,395,427,131,178,369,227,322,337,354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW569_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n029.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 22:36:29 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.80/1.08 % [INFO] Parsing done (231ms).
% 1.80/1.09 % [INFO] Running in sequential loop mode.
% 2.31/1.28 % [INFO] eprover registered as external prover.
% 2.31/1.28 % [INFO] cvc4 registered as external prover.
% 2.31/1.29 % [INFO] Scanning for conjecture ...
% 2.81/1.42 % [INFO] Found a conjecture and 102 axioms. Running axiom selection ...
% 3.34/1.51 % [INFO] Axiom selection finished. Selected 102 axioms (removed 0 axioms).
% 3.86/1.71 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.86/1.73 % [INFO] Type checking passed.
% 3.86/1.73 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 64.52/51.20 % External prover 'e' found a proof!
% 64.52/51.20 % [INFO] Killing All external provers ...
% 64.52/51.20 % Time passed: 50674ms (effective reasoning time: 50109ms)
% 64.52/51.20 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 64.52/51.20 % Axioms used in derivation (102): fact_58_FAccReds, fact_60_rtrancl__idemp, fact_77_exp_Osimps_I15_J, fact_64_rtrancl__trans, fact_41_red__lcl__add, fact_1_FAccRed_I4_J, fact_36_prod__induct3, fact_23_FAccRed_I1_J, fact_12_FAccRed_I3_J, fact_31_prod__cases6, fact_29_prod__cases5, fact_96_exp_Osimps_I220_J, fact_3_exp_Osimps_I7_J, fact_24_pred__equals__eq2, fact_15_WTrtFAcc, fact_28_prod__induct4, fact_55_curryD, fact_4_widen__refl, fact_40_red__hext__incr, fact_94_exp_Osimps_I223_J, fact_42_is__refT__def, fact_73_TryReds, fact_38_red__preserves__sconf, fact_69_converse__rtranclE, fact_27_prod__cases4, fact_43_prod_Oexhaust, fact_59_rtrancl_Ortrancl__refl, fact_34_red__preserves__hconf, fact_65_converse__rtranclE2, fact_26_red__reds_OFAccRed, fact_84_exp_Osimps_I166_J, fact_80_exp_Osimps_I224_J, fact_10_FAccRed_I2_J, fact_88_ThrowReds, fact_48_lconf__hext, fact_25_Pair__inject, fact_5__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096, fact_39_prod_Orecs, fact_99_exp_Osimps_I165_J, fact_6_assms, fact_83_exp_Osimps_I167_J, fact_44_WTrt__hext__mono, fact_11_IH, fact_35_red__preserves__lconf, fact_13_conf, fact_71_rtrancl__induct, fact_85_red__reds_OThrowRed, fact_22_Type_Oty_Osimps_I21_J, fact_47_map__add__assoc, fact_70_converse__rtrancl__induct, fact_37_prod__cases3, fact_7_calculation, fact_54_curryI, fact_53_curry__conv, fact_68_rtranclE, fact_67_rtrancl__induct2, fact_18_Class__widen, fact_45_refTE, fact_20_Pair__eq, fact_16_WTrt__elim__cases_I7_J, fact_81_exp_Osimps_I168_J, fact_90_red__reds_OFAccThrow, fact_19_split__paired__All, fact_56_curryE, fact_49_hext__trans, fact_14_widen__null, fact_95_exp_Osimps_I222_J, fact_86_red__reds_OThrowThrow, fact_62_converse__rtrancl__into__rtrancl, fact_82_exp_Osimps_I169_J, fact_66_converse__rtrancl__induct2, fact_76_mem__def, fact_87_red__reds_OTryRed, fact_46_hext__refl, fact_21_Type_Oty_Osimps_I20_J, fact_2_wt, fact_9_widen__trans, fact_92_WhileRedsThrow, fact_78_WTrtThrow, fact_8_WTrtFAccNT, fact_93_exp_Osimps_I13_J, fact_33_split__paired__Ex, fact_30_prod__induct5, fact_74_exp_Osimps_I14_J, fact_89_ThrowRedsThrow, fact_57_curry__def, fact_97_exp_Osimps_I221_J, fact_61_r__into__rtrancl, help_pp_1_1_U, fact_63_rtrancl_Ortrancl__into__rtrancl, fact_32_prod__induct6, fact_50_Red__lcl__add, fact_17_Type_Oty_Oinject, fact_51_PairE, fact_75_ext, fact_0__096P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_ANT_096, fact_98_exp_Osimps_I164_J, fact_72_FAccRedsThrow, fact_52_internal__split__conv, help_pp_2_1_U, fact_79_exp_Osimps_I225_J, fact_91_WTrt__elim__cases_I4_J
% 64.52/51.20 % No. of inferences in proof: 208
% 64.52/51.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 50674 ms resp. 50109 ms w/o parsing
% 65.27/51.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 65.27/51.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------