%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW571_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:50 AM UTC 2026
% Result : Theorem 115.95s 97.72s
% Output : Refutation 116.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 103
% Syntax : Number of formulae : 208 ( 83 unt; 0 typ; 0 def)
% Number of atoms : 8935 ( 134 equ; 0 cnn)
% Maximal formula atoms : 340 ( 42 avg)
% Number of connectives : 20662 ( 94 ~; 0 |; 40 &;20319 @)
% ( 11 <=>; 198 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 14 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 24 con; 0-5 aty)
% Number of variables : 1075 ( 0 ^;1059 !; 16 ?;1075 :)
% Comments :
%------------------------------------------------------------------------------
thf(bop_type,type,
bop: $tType ).
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_decl,type,
hconf:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > $o ) ).
thf(lconf_decl,type,
lconf:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( val @ option @ ( char @ list @ fun ) ) > ( ty @ option @ ( char @ list @ fun ) ) > $o ) ).
thf(binOp_decl,type,
binOp:
!>[TA: $tType] : ( ( TA @ exp ) > bop > ( TA @ exp ) > ( TA @ exp ) ) ).
thf(fAss_decl,type,
fAss:
!>[TA: $tType] : ( ( TA @ exp ) > ( char @ list ) > ( char @ list ) > ( TA @ exp ) > ( TA @ exp ) ) ).
thf(val1_decl,type,
val1:
!>[TA: $tType] : ( val > ( TA @ exp ) ) ).
thf(while_decl,type,
while:
!>[TA: $tType] : ( ( TA @ exp ) > ( TA @ exp ) > ( TA @ exp ) ) ).
thf(throw_decl,type,
throw:
!>[TA: $tType] : ( ( TA @ exp ) > ( TA @ exp ) ) ).
thf(wf_J_mdecl_decl,type,
wf_J_mdecl: bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) ).
thf(map_add_decl,type,
map_add:
!>[TA: $tType,TB: $tType] : ( ( TA @ option @ ( TB @ fun ) ) > ( TA @ option @ ( TB @ fun ) ) > ( TA @ option @ ( TB @ fun ) ) ) ).
thf(hext_decl,type,
hext: ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > $o ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( TA @ ( TB @ product_prod ) ) ) ).
thf(produc1605651328_split_decl,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(product_prod_rec_decl,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(red_decl,type,
red: ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) ) ).
thf(hp_decl,type,
hp: ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) ).
thf(transitive_rtrancl_decl,type,
transitive_rtrancl:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) ) ).
thf(widen_decl,type,
widen:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ty > ty > $o ) ).
thf(typeSa976492716_sconf_decl,type,
typeSa976492716_sconf: ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( ty @ option @ ( char @ list @ fun ) ) > ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) ) > $o ).
thf(is_refT_decl,type,
is_refT: ty > $o ).
thf(nt_decl,type,
nt: ty ).
thf(void_decl,type,
void: ty ).
thf(wf_prog_decl,type,
wf_prog:
!>[TA: $tType] : ( ( bool @ ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) ) > ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > $o ) ).
thf(wTrt_decl,type,
wTrt: ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( ty @ option @ ( char @ list @ fun ) ) > ( char @ list @ exp ) > ty > $o ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(d_decl,type,
d: char @ list ).
thf(e_decl,type,
e: ty @ option @ ( char @ list @ fun ) ).
thf(f_decl,type,
f: char @ list ).
thf(p_decl,type,
p: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ).
thf(t_2_decl,type,
t_2: ty ).
thf(t_decl,type,
t: ty ).
thf(e_2_decl,type,
e_2: char @ list @ exp ).
thf(e_a_decl,type,
e_a: char @ list @ exp ).
thf(ea_decl,type,
ea: char @ list @ exp ).
thf(h_a_decl,type,
h_a: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ).
thf(ha_decl,type,
ha: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ).
thf(l_a_decl,type,
l_a: val @ option @ ( char @ list @ fun ) ).
thf(la_decl,type,
la: val @ option @ ( char @ list @ fun ) ).
thf(86,axiom,
! [A: val @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( C @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( C @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_red__lcl__add) ).
thf(385,plain,
! [A: val @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( C @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( C @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_prod__cases6) ).
thf(289,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(35,axiom,
! [A: ty,B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( F @ wTrt ) ) ) ) )
=> ( ( B @ is_refT )
=> ( A @ ( C @ ( char @ list @ throw ) @ ( D @ ( E @ ( F @ wTrt ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_WTrtThrow) ).
thf(229,plain,
! [A: ty,B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( F @ wTrt ) ) ) ) )
=> ( ( B @ is_refT )
=> ( A @ ( C @ ( char @ list @ throw ) @ ( D @ ( E @ ( F @ wTrt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ exp,B: val] :
( ( B @ ( TA @ val1 ) )
!= ( A @ ( TA @ throw ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_exp_Osimps_I90_J) ).
thf(129,plain,
! [TA: $tType,A: TA @ exp,B: val] :
( ( B @ ( TA @ val1 ) )
!= ( A @ ( TA @ throw ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_prod__induct3) ).
thf(336,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(36,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: val] :
( ( E @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_exp_Osimps_I78_J) ).
thf(231,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: val] :
( ( E @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(21,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(178,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: TA @ exp,D: bop,E: TA @ exp] :
( ( C @ ( D @ ( E @ ( TA @ binOp ) ) ) )
!= ( A @ ( B @ ( TA @ while ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_exp_Osimps_I110_J) ).
thf(138,plain,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: TA @ exp,D: bop,E: TA @ exp] :
( ( C @ ( D @ ( E @ ( TA @ binOp ) ) ) )
!= ( A @ ( B @ ( TA @ while ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(70,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: bop,G: TA @ exp] :
( ( E @ ( F @ ( G @ ( TA @ binOp ) ) ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_exp_Osimps_I100_J) ).
thf(347,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: bop,G: TA @ exp] :
( ( E @ ( F @ ( G @ ( TA @ binOp ) ) ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(37,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_FAssRed1_I2_J) ).
thf(234,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prod__induct4) ).
thf(352,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(94,axiom,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: char @ list,E: char @ list,F: char @ list @ exp] : ( A @ red @ ( B @ ( F @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( F @ ( char @ list @ throw ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_red__reds_OFAssThrow1) ).
thf(408,plain,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: char @ list,E: char @ list,F: char @ list @ exp] : ( A @ red @ ( B @ ( F @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( F @ ( char @ list @ throw ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(31,axiom,
! [TA: $tType,A: TA @ exp,B: bop,C: TA @ exp,D: TA @ exp] :
( ( D @ ( TA @ throw ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_exp_Osimps_I113_J) ).
thf(217,plain,
! [TA: $tType,A: TA @ exp,B: bop,C: TA @ exp,D: TA @ exp] :
( ( D @ ( TA @ throw ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: TA @ exp] :
( ( C @ ( TA @ throw ) )
!= ( A @ ( B @ ( TA @ while ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_exp_Osimps_I221_J) ).
thf(120,plain,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: TA @ exp] :
( ( C @ ( TA @ throw ) )
!= ( A @ ( B @ ( TA @ while ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(83,axiom,
! [A: char @ list,B: char @ list,C: val,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( E @ ( F @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_red__reds_OFAssRed2) ).
thf(379,plain,
! [A: char @ list,B: char @ list,C: val,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( E @ ( F @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(49,axiom,
p @ red @ ( l_a @ ( h_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( ea @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_red) ).
thf(269,plain,
p @ red @ ( l_a @ ( h_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( ea @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(24,axiom,
! [TA: $tType,A: TA @ exp,B: TA @ exp] :
( ( ( B @ ( TA @ throw ) )
= ( A @ ( TA @ throw ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_exp_Osimps_I14_J) ).
thf(185,plain,
! [TA: $tType,A: TA @ exp,B: TA @ exp] :
( ( ( B = A )
=> ( ( B @ ( TA @ throw ) )
= ( A @ ( TA @ throw ) ) ) )
& ( ( ( B @ ( TA @ throw ) )
= ( A @ ( TA @ throw ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_prod__cases3) ).
thf(417,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ) @ ( TB @ fun ),B: bool @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ fun ),C: TA,D: TB,E: TA,F: TB] :
( ( B @ ( TA @ ( TB @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( E @ ( F @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( B @ ( TA @ ( TB @ product_prod ) @ transitive_rtrancl ) @ ( H @ ( G @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( B @ ( J @ ( I @ ( TA @ ( TB @ product_Pair ) ) ) @ ( H @ ( G @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( H @ ( G @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( J @ ( I @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( C @ ( D @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rtrancl__induct2) ).
thf(257,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ) @ ( TB @ fun ),B: bool @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ fun ),C: TA,D: TB,E: TA,F: TB] :
( ( B @ ( TA @ ( TB @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( E @ ( F @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( B @ ( TA @ ( TB @ product_prod ) @ transitive_rtrancl ) @ ( H @ ( G @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( B @ ( J @ ( I @ ( TA @ ( TB @ product_Pair ) ) ) @ ( H @ ( G @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( H @ ( G @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( J @ ( I @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( C @ ( D @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(88,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( F @ wTrt ) ) ) ) )
=> ( ( A @ ( E @ hext ) )
=> ( B @ ( C @ ( D @ ( A @ ( F @ wTrt ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_WTrt__hext__mono) ).
thf(389,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( F @ wTrt ) ) ) ) )
=> ( ( A @ ( E @ hext ) )
=> ( B @ ( C @ ( D @ ( A @ ( F @ wTrt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(79,axiom,
h_a @ ( ha @ hext ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__096h_A_092_060unlhd_062_Ah_H_096) ).
thf(372,plain,
h_a @ ( ha @ hext ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(68,axiom,
t_2 @ ( e_2 @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096P_ME_Mh_H_A_092_060turnstile_062_Ae_092_060_094isub_0622_A_058_AT_092_060_094isub_0622_096) ).
thf(344,plain,
t_2 @ ( e_2 @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(22,axiom,
! [TA: $tType,A: val,B: TA @ exp] :
( ( B @ ( TA @ throw ) )
!= ( A @ ( TA @ val1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_exp_Osimps_I91_J) ).
thf(179,plain,
! [TA: $tType,A: val,B: TA @ exp] :
( ( B @ ( TA @ throw ) )
!= ( A @ ( TA @ val1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(29,axiom,
! [TA: $tType,A: TA @ exp,B: bop,C: TA @ exp,D: val] :
( ( D @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_exp_Osimps_I70_J) ).
thf(211,plain,
! [TA: $tType,A: TA @ exp,B: bop,C: TA @ exp,D: val] :
( ( D @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(38,axiom,
nt @ ( ea @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096) ).
thf(238,plain,
nt @ ( ea @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_prod_Orecs) ).
thf(132,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(102,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA] : ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_rtrancl_Ortrancl__refl) ).
thf(428,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA] : ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(5,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( B @ ( C @ hext ) )
=> ( ( A @ ( B @ hext ) )
=> ( A @ ( C @ hext ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_hext__trans) ).
thf(116,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( B @ ( C @ hext ) )
=> ( ( A @ ( B @ hext ) )
=> ( A @ ( C @ hext ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rtrancl_Ortrancl__into__rtrancl) ).
thf(243,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(59,axiom,
! [A: val @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Red__lcl__add) ).
thf(307,plain,
! [A: val @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(53,axiom,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: char @ list @ exp,E: val @ option @ ( char @ list @ fun ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: char @ list @ exp] :
( ( A @ red @ ( B @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( C @ ( F @ hext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_red__hext__incr) ).
thf(292,plain,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: char @ list @ exp,E: val @ option @ ( char @ list @ fun ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: char @ list @ exp] :
( ( A @ red @ ( B @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( C @ ( F @ hext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB] :
( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
<=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_pred__equals__eq2) ).
thf(270,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
& ( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) ) )
& ( ! [C: TA,D: TB] :
( ( ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
& ( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(84,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ),H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( I @ ( B @ ( H @ ( C @ wTrt ) ) ) ) )
=> ( ( B @ ( G @ ( H @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ) ) ) )
=> ( B @ ( D @ ( E @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_red__preserves__lconf) ).
thf(381,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ),H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( I @ ( B @ ( H @ ( C @ wTrt ) ) ) ) )
=> ( ( B @ ( G @ ( H @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ) ) ) )
=> ( B @ ( D @ ( E @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(32,axiom,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: bop,D: TA @ exp] :
( ( B @ ( C @ ( D @ ( TA @ binOp ) ) ) )
!= ( A @ ( TA @ throw ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_exp_Osimps_I112_J) ).
thf(220,plain,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: bop,D: TA @ exp] :
( ( B @ ( C @ ( D @ ( TA @ binOp ) ) ) )
!= ( A @ ( TA @ throw ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(78,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_converse__rtranclE) ).
thf(366,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(55,axiom,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e @ ( p @ typeSa976492716_sconf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_conf) ).
thf(297,plain,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e @ ( p @ typeSa976492716_sconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(25,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ transitive_rtrancl ) @ ( TA @ transitive_rtrancl ) )
= ( A @ ( TA @ transitive_rtrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rtrancl__idemp) ).
thf(192,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ transitive_rtrancl ) @ ( TA @ transitive_rtrancl ) )
= ( A @ ( TA @ transitive_rtrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_split__paired__All) ).
thf(403,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(74,axiom,
~ ! [A: ty] :
~ ( A @ ( e_2 @ ( e @ ( ha @ ( p @ wTrt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096_B_Bthesis_O_A_I_B_BT_092_060_094isub_0622_O_AP_ME_Mh_A_092_060turnstile_062_Ae_092_060_094isub_0622_A_058_AT_092_060_094isub_0622_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(356,plain,
~ ! [A: ty] :
~ ( A @ ( e_2 @ ( e @ ( ha @ ( p @ wTrt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_prod_Oexhaust) ).
thf(141,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_split__paired__Ex) ).
thf(420,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(62,axiom,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( E @ ( A @ ( B @ ( C @ ( F @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_red__reds_OFAssRed1) ).
thf(328,plain,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( E @ ( A @ ( B @ ( C @ ( F @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(66,axiom,
! [TA: $tType,A: val,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_exp_Osimps_I79_J) ).
thf(339,plain,
! [TA: $tType,A: val,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1,conjecture,
? [A: ty] :
( ( t @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( A @ ( e_2 @ ( d @ ( f @ ( e_a @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: ty] :
( ( t @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( A @ ( e_2 @ ( d @ ( f @ ( e_a @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(105,plain,
~ ? [A: ty] :
( ( t @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( A @ ( e_2 @ ( d @ ( f @ ( e_a @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(75,axiom,
! [A: char @ list,B: char @ list,C: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: char @ list @ exp,F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: val,I: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),J: char @ list @ exp] :
( ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( G @ ( H @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( J @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( E @ ( A @ ( B @ ( J @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_FAssRedsThrow2) ).
thf(360,plain,
! [A: char @ list,B: char @ list,C: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: char @ list @ exp,F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: val,I: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),J: char @ list @ exp] :
( ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( G @ ( H @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( J @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( E @ ( A @ ( B @ ( J @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(56,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( A @ ( TA @ transitive_rtrancl ) @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( A @ ( B @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_rtranclE) ).
thf(298,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( A @ ( TA @ transitive_rtrancl ) @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( A @ ( B @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_prod__induct6) ).
thf(412,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(101,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: TA @ exp] :
( ( E @ ( F @ ( TA @ while ) ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_exp_Osimps_I179_J) ).
thf(425,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: TA @ exp] :
( ( E @ ( F @ ( TA @ while ) ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(103,axiom,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( A @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ThrowRedsThrow) ).
thf(430,plain,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( A @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_PairE) ).
thf(148,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(47,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp] :
( ( E @ ( TA @ throw ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_exp_Osimps_I181_J) ).
thf(264,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp] :
( ( E @ ( TA @ throw ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(81,axiom,
! [TA: $tType,A: ty,B: ty,C: ty,D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( TA @ widen ) ) ) )
=> ( ( A @ ( B @ ( D @ ( TA @ widen ) ) ) )
=> ( A @ ( C @ ( D @ ( TA @ widen ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_widen__trans) ).
thf(375,plain,
! [TA: $tType,A: ty,B: ty,C: ty,D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( TA @ widen ) ) ) )
=> ( ( A @ ( B @ ( D @ ( TA @ widen ) ) ) )
=> ( A @ ( C @ ( D @ ( TA @ widen ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(92,axiom,
t_2 @ ( e_2 @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096P_ME_Mh_A_092_060turnstile_062_Ae_092_060_094isub_0622_A_058_AT_092_060_094isub_0622_096) ).
thf(402,plain,
t_2 @ ( e_2 @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(51,axiom,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ throw ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_exp_Osimps_I180_J) ).
thf(286,plain,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ throw ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] : ( A @ ( A @ hext ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_hext__refl) ).
thf(118,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] : ( A @ ( A @ hext ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(204,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_prod__cases5) ).
thf(391,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(15,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ lconf ) ) ) ) )
=> ( ( A @ ( D @ hext ) )
=> ( B @ ( C @ ( A @ ( E @ ( TA @ lconf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_lconf__hext) ).
thf(144,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ lconf ) ) ) ) )
=> ( ( A @ ( D @ hext ) )
=> ( B @ ( C @ ( A @ ( E @ ( TA @ lconf ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(71,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rtrancl__trans) ).
thf(350,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(4,axiom,
! [TA: $tType,A: val,B: TA @ exp,C: TA @ exp] :
( ( B @ ( C @ ( TA @ while ) ) )
!= ( A @ ( TA @ val1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_exp_Osimps_I89_J) ).
thf(113,plain,
! [TA: $tType,A: val,B: TA @ exp,C: TA @ exp] :
( ( B @ ( C @ ( TA @ while ) ) )
!= ( A @ ( TA @ val1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(82,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( G @ ( B @ ( F @ hp @ ( C @ wTrt ) ) ) ) )
=> ( ( F @ ( B @ ( C @ typeSa976492716_sconf ) ) )
=> ( D @ ( B @ ( C @ typeSa976492716_sconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_red__preserves__sconf) ).
thf(377,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( G @ ( B @ ( F @ hp @ ( C @ wTrt ) ) ) ) )
=> ( ( F @ ( B @ ( C @ typeSa976492716_sconf ) ) )
=> ( D @ ( B @ ( C @ typeSa976492716_sconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_prod__induct5) ).
thf(362,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(41,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA,F: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( E @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( F @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_rtrancl__induct) ).
thf(245,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA,F: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( E @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( F @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_internal__split__conv) ).
thf(208,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(87,axiom,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_FAssRedsThrow1) ).
thf(387,plain,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(69,axiom,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( B @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_red__reds_OThrowRed) ).
thf(345,plain,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( B @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_prod__cases4) ).
thf(251,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_prod ) @ fun ),B: TB,C: TA,D: TB,E: TA] :
( ( A @ ( TB @ ( TA @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( ( D @ ( E @ ( TB @ ( TA @ product_Pair ) ) ) )
!= ( B @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) ) )
=> ~ ! [F: TA,G: TB] :
( ( A @ ( G @ ( F @ ( TB @ ( TA @ product_Pair ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_prod ) @ member ) ) )
=> ~ ( A @ ( TB @ ( TA @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( G @ ( F @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_converse__rtranclE2) ).
thf(330,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_prod ) @ fun ),B: TB,C: TA,D: TB,E: TA] :
( ( A @ ( TB @ ( TA @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( ( D @ ( E @ ( TB @ ( TA @ product_Pair ) ) ) )
!= ( B @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) ) )
=> ~ ! [F: TA,G: TB] :
( ( A @ ( G @ ( F @ ( TB @ ( TA @ product_Pair ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_prod ) @ member ) ) )
=> ~ ( A @ ( TB @ ( TA @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( G @ ( F @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(33,axiom,
! [TA: $tType,A: val,B: TA @ exp,C: bop,D: TA @ exp] :
( ( B @ ( C @ ( D @ ( TA @ binOp ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_exp_Osimps_I71_J) ).
thf(223,plain,
! [TA: $tType,A: val,B: TA @ exp,C: bop,D: TA @ exp] :
( ( B @ ( C @ ( D @ ( TA @ binOp ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ) @ ( TB @ fun ),B: bool @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ fun ),C: TA,D: TB,E: TA,F: TB] :
( ( B @ ( TA @ ( TB @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( C @ ( D @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( B @ ( J @ ( I @ ( TA @ ( TB @ product_Pair ) ) ) @ ( H @ ( G @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ ( TB @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( J @ ( I @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( J @ ( I @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( H @ ( G @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( E @ ( F @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_converse__rtrancl__induct2) ).
thf(394,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ) @ ( TB @ fun ),B: bool @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ fun ),C: TA,D: TB,E: TA,F: TB] :
( ( B @ ( TA @ ( TB @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( C @ ( D @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( B @ ( J @ ( I @ ( TA @ ( TB @ product_Pair ) ) ) @ ( H @ ( G @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ ( TB @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( J @ ( I @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( J @ ( I @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( H @ ( G @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( E @ ( F @ ( A @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(12,axiom,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: val] :
( ( C @ ( TA @ val1 ) )
!= ( A @ ( B @ ( TA @ while ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_exp_Osimps_I88_J) ).
thf(135,plain,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: val] :
( ( C @ ( TA @ val1 ) )
!= ( A @ ( B @ ( TA @ while ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,axiom,
nt != void,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Type_Oty_Osimps_I7_J) ).
thf(226,plain,
nt != void,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_converse__rtrancl__into__rtrancl) ).
thf(267,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_rtrancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(20,axiom,
! [TA: $tType,A: TA @ exp,B: bop,C: TA @ exp,D: TA @ exp,E: bop,F: TA @ exp] :
( ( ( D @ ( E @ ( F @ ( TA @ binOp ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_exp_Osimps_I4_J) ).
thf(167,plain,
! [TA: $tType,A: TA @ exp,B: bop,C: TA @ exp,D: TA @ exp,E: bop,F: TA @ exp] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( TA @ binOp ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( TA @ binOp ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(44,axiom,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( A @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ThrowReds) ).
thf(255,plain,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( A @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(67,axiom,
t = void,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_void) ).
thf(342,plain,
t = void,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TB @ option @ ( TA @ fun ),B: TB @ option @ ( TA @ fun ),C: TB @ option @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map_add ) ) ) @ ( C @ ( TB @ ( TA @ map_add ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ map_add ) ) ) @ ( TB @ ( TA @ map_add ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_map__add__assoc) ).
thf(123,plain,
! [TA: $tType,TB: $tType,A: TB @ option @ ( TA @ fun ),B: TB @ option @ ( TA @ fun ),C: TB @ option @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map_add ) ) ) @ ( C @ ( TB @ ( TA @ map_add ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ map_add ) ) ) @ ( TB @ ( TA @ map_add ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,axiom,
! [A: char @ list,B: char @ list,C: ty,D: char @ list @ exp,E: char @ list @ exp,F: ty @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( nt @ ( E @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( ( C @ ( D @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( void @ ( D @ ( A @ ( B @ ( E @ ( char @ list @ fAss ) ) ) ) @ ( F @ ( G @ ( H @ wTrt ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_WTrtFAssNT) ).
thf(295,plain,
! [A: char @ list,B: char @ list,C: ty,D: char @ list @ exp,E: char @ list @ exp,F: ty @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( nt @ ( E @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( ( C @ ( D @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( void @ ( D @ ( A @ ( B @ ( E @ ( char @ list @ fAss ) ) ) ) @ ( F @ ( G @ ( H @ wTrt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(97,axiom,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e @ ( p @ typeSa976492716_sconf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_FAssRed1_I3_J) ).
thf(414,plain,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e @ ( p @ typeSa976492716_sconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(46,axiom,
nt @ ( e_a @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_ANT_096) ).
thf(263,plain,
nt @ ( e_a @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(23,axiom,
! [TA: $tType,A: TA @ exp,B: bop,C: TA @ exp,D: TA @ exp,E: TA @ exp] :
( ( D @ ( E @ ( TA @ while ) ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_exp_Osimps_I111_J) ).
thf(182,plain,
! [TA: $tType,A: TA @ exp,B: bop,C: TA @ exp,D: TA @ exp,E: TA @ exp] :
( ( D @ ( E @ ( TA @ while ) ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(65,axiom,
t @ ( e_2 @ ( d @ ( f @ ( ea @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_wt) ).
thf(338,plain,
t @ ( e_2 @ ( d @ ( f @ ( ea @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(57,axiom,
t @ ( e_2 @ ( d @ ( f @ ( ea @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_FAssRed1_I4_J) ).
thf(304,plain,
t @ ( e_2 @ ( d @ ( f @ ( ea @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Pair__eq) ).
thf(158,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(85,axiom,
! [A: char @ list,B: char @ list,C: val,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_FAssReds2) ).
thf(383,plain,
! [A: char @ list,B: char @ list,C: val,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(30,axiom,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: TA @ exp] :
( ( B @ ( C @ ( TA @ while ) ) )
!= ( A @ ( TA @ throw ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_exp_Osimps_I220_J) ).
thf(214,plain,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: TA @ exp] :
( ( B @ ( C @ ( TA @ while ) ) )
!= ( A @ ( TA @ throw ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(18,axiom,
! [TA: $tType,A: val,B: val] :
( ( ( B @ ( TA @ val1 ) )
= ( A @ ( TA @ val1 ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_exp_Osimps_I3_J) ).
thf(151,plain,
! [TA: $tType,A: val,B: val] :
( ( ( B = A )
=> ( ( B @ ( TA @ val1 ) )
= ( A @ ( TA @ val1 ) ) ) )
& ( ( ( B @ ( TA @ val1 ) )
= ( A @ ( TA @ val1 ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(61,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: char @ list,G: char @ list,H: TA @ exp] :
( ( ( E @ ( F @ ( G @ ( H @ ( TA @ fAss ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) )
<=> ( ( E = A )
& ( F = B )
& ( G = C )
& ( H = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_exp_Osimps_I8_J) ).
thf(315,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: char @ list,G: char @ list,H: TA @ exp] :
( ( ( ( E = A )
& ( F = B )
& ( G = C )
& ( H = D ) )
=> ( ( E @ ( F @ ( G @ ( H @ ( TA @ fAss ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ) )
& ( ( ( E @ ( F @ ( G @ ( H @ ( TA @ fAss ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) )
=> ( ( E = A )
& ( F = B )
& ( G = C )
& ( H = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(104,axiom,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( A @ ( B @ ( C @ ( F @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_FAssReds1) ).
thf(432,plain,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( A @ ( B @ ( C @ ( F @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(95,axiom,
! [A: char @ list @ exp,B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp] :
( ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( A @ ( F @ ( char @ list @ while ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_WhileRedsThrow) ).
thf(410,plain,
! [A: char @ list @ exp,B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp] :
( ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( A @ ( F @ ( char @ list @ while ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(16,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(146,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(80,axiom,
! [TA: $tType,A: ty,B: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( A @ ( B @ ( TA @ widen ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_widen__refl) ).
thf(373,plain,
! [TA: $tType,A: ty,B: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( A @ ( B @ ( TA @ widen ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(58,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ),H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( I @ ( B @ ( H @ ( C @ wTrt ) ) ) ) )
=> ( ( H @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ) )
=> ( E @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_red__preserves__hconf) ).
thf(305,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ),H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( I @ ( B @ ( H @ ( C @ wTrt ) ) ) ) )
=> ( ( H @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ) )
=> ( E @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Pair__inject) ).
thf(107,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(39,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_IH) ).
thf(239,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(9,axiom,
void != nt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_Type_Oty_Osimps_I6_J) ).
thf(126,plain,
void != nt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: TA @ exp,D: TA @ exp] :
( ( ( C @ ( D @ ( TA @ while ) ) )
= ( A @ ( B @ ( TA @ while ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_exp_Osimps_I13_J) ).
thf(195,plain,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: TA @ exp,D: TA @ exp] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ while ) ) )
= ( A @ ( B @ ( TA @ while ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ while ) ) )
= ( A @ ( B @ ( TA @ while ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(91,axiom,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: char @ list,E: char @ list,F: val] : ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( D @ ( E @ ( F @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_red__reds_OFAssThrow2) ).
thf(400,plain,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: char @ list,E: char @ list,F: val] : ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( D @ ( E @ ( F @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(98,axiom,
! [A: bop,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: char @ list @ exp,E: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,F: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: val,H: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),I: char @ list @ exp] :
( ( E @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( F @ ( G @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( H @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( E @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( E @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( H @ ( D @ ( A @ ( I @ ( char @ list @ binOp ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_BinOpRedsThrow2) ).
thf(415,plain,
! [A: bop,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: char @ list @ exp,E: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,F: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: val,H: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),I: char @ list @ exp] :
( ( E @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( F @ ( G @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( H @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( E @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( E @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( H @ ( D @ ( A @ ( I @ ( char @ list @ binOp ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(43,axiom,
p @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_assms) ).
thf(254,plain,
p @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(73,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ ( TA @ product_prod )] :
( ( A @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_r__into__rtrancl) ).
thf(354,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ ( TA @ product_prod )] :
( ( A @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_rtrancl ) @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(60,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA,F: TA] :
( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( F @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( F @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_converse__rtrancl__induct) ).
thf(309,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA,F: TA] :
( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_rtrancl ) @ ( C @ ( F @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( F @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(77,axiom,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp] : ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_red__reds_OThrowThrow) ).
thf(364,plain,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp] : ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( B @ ( C @ ( char @ list @ throw ) @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(434,plain,
$false,
inference(e,[status(thm)],[385,289,229,129,336,231,178,138,347,234,352,408,217,120,379,269,185,417,257,389,372,344,179,211,238,132,428,116,243,307,292,270,381,220,366,297,192,403,356,141,420,328,339,105,360,298,412,425,430,148,264,375,402,286,118,204,391,144,350,113,377,362,245,208,387,345,251,330,223,394,135,226,267,167,255,342,123,295,414,263,182,338,304,158,383,214,151,315,432,410,146,373,305,107,239,126,195,400,415,254,354,309,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW571_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.38 % Computer : n003.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 16:15:40 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.61/0.68 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/0.94 % [INFO] Parsing done (258ms).
% 1.54/0.94 % [INFO] Running in sequential loop mode.
% 2.58/1.15 % [INFO] eprover registered as external prover.
% 2.58/1.15 % [INFO] Scanning for conjecture ...
% 3.32/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 102 axioms. Running axiom selection ...
% 3.81/1.47 % [INFO] Axiom selection finished. Selected 102 axioms (removed 0 axioms).
% 5.54/1.88 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.95/1.93 % [INFO] Type checking passed.
% 5.95/1.94 % [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 ...
% 115.95/97.71 % External prover 'e' found a proof!
% 115.95/97.71 % [INFO] Killing All external provers ...
% 115.95/97.71 % Time passed: 97246ms (effective reasoning time: 96766ms)
% 115.95/97.71 % 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)>
% 115.95/97.72 % Axioms used in derivation (102): fact_19_hext__refl, fact_25_pred__equals__eq2, fact_70_exp_Osimps_I90_J, fact_31_prod__induct4, fact_65_internal__split__conv, fact_36_split__paired__Ex, fact_17_conf, fact_95_exp_Osimps_I71_J, fact_60_rtranclE, fact_11_widen__trans, fact_40_lconf__hext, fact_77_red__reds_OThrowThrow, fact_44_red__lcl__add, fact_35_prod__cases6, fact_24_red, fact_23_Type_Oty_Osimps_I6_J, fact_4_FAssRed1_I4_J, fact_49_FAssReds1, fact_43_prod_Orecs, fact_61_converse__rtranclE, fact_37_red__preserves__hconf, fact_32_prod__cases5, fact_48_prod_Oexhaust, fact_10_assms, fact_41_prod__cases3, fact_96_exp_Osimps_I110_J, fact_29_red__reds_OFAssRed1, fact_3__096P_ME_Mh_A_092_060turnstile_062_Ae_092_060_094isub_0622_A_058_AT_092_060_094isub_0622_096, fact_89_exp_Osimps_I221_J, fact_71_exp_Osimps_I91_J, fact_79_ThrowRedsThrow, fact_90_exp_Osimps_I70_J, fact_75_mem__def, fact_97_exp_Osimps_I111_J, fact_98_exp_Osimps_I179_J, fact_47_PairE, fact_15__096h_A_092_060unlhd_062_Ah_H_096, fact_12_WTrtFAssNT, fact_53_converse__rtrancl__into__rtrancl, fact_39_prod__induct3, fact_2__096P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_ANT_096, fact_80_ThrowReds, fact_92_exp_Osimps_I220_J, fact_34_prod__induct6, fact_52_rtrancl__idemp, fact_84_BinOpRedsThrow2, fact_46_Red__lcl__add, fact_28_red__hext__incr, fact_57_converse__rtrancl__induct2, fact_87_exp_Osimps_I13_J, fact_73_exp_Osimps_I78_J, fact_30_prod__cases4, fact_62_converse__rtrancl__induct, fact_13_FAssRed1_I2_J, fact_45_map__add__assoc, fact_94_exp_Osimps_I112_J, fact_38_red__preserves__lconf, fact_86_exp_Osimps_I4_J, fact_93_exp_Osimps_I89_J, fact_59_rtrancl__induct, fact_8_widen__refl, fact_22_Type_Oty_Osimps_I7_J, fact_74_red__reds_OFAssThrow2, fact_91_exp_Osimps_I113_J, fact_50_rtrancl_Ortrancl__refl, fact_33_prod__induct5, fact_64_FAssRedsThrow1, fact_9__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096, fact_67_exp_Osimps_I14_J, fact_68_exp_Osimps_I180_J, fact_56_converse__rtranclE2, fact_63_FAssReds2, fact_7_exp_Osimps_I8_J, fact_78_red__reds_OThrowRed, fact_6__096_B_Bthesis_O_A_I_B_BT_092_060_094isub_0622_O_AP_ME_Mh_A_092_060turnstile_062_Ae_092_060_094isub_0622_A_058_AT_092_060_094isub_0622_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_18_WTrt__hext__mono, fact_99_exp_Osimps_I100_J, fact_81_red__reds_OFAssThrow1, fact_85_WhileRedsThrow, fact_83_WTrtThrow, fact_16_FAssRed1_I3_J, help_pp_1_1_U, fact_58_rtrancl__induct2, fact_20_split__paired__All, fact_27_Pair__inject, fact_69_exp_Osimps_I181_J, fact_51_r__into__rtrancl, fact_72_exp_Osimps_I79_J, fact_88_exp_Osimps_I88_J, fact_42_red__preserves__sconf, fact_1__096P_ME_Mh_H_A_092_060turnstile_062_Ae_092_060_094isub_0622_A_058_AT_092_060_094isub_0622_096, fact_21_Pair__eq, fact_0_void, fact_55_rtrancl__trans, help_pp_2_1_U, fact_66_exp_Osimps_I3_J, fact_82_red__reds_OFAssRed2, fact_5_wt, fact_14_IH, fact_26_hext__trans, fact_76_FAssRedsThrow2, fact_54_rtrancl_Ortrancl__into__rtrancl
% 115.95/97.72 % No. of inferences in proof: 208
% 115.95/97.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 97246 ms resp. 96766 ms w/o parsing
% 116.41/97.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 116.41/97.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------