%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW567_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 : n014.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 09:10:49 AM UTC 2026
% Result : Theorem 115.89s 98.42s
% Output : Refutation 116.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 103
% Syntax : Number of formulae : 208 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 11983 ( 111 equ; 0 cnn)
% Maximal formula atoms : 340 ( 57 avg)
% Number of connectives : 27552 ( 78 ~; 0 |; 38 &;27182 @)
% ( 12 <=>; 242 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 16 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 21 con; 0-5 aty)
% Number of variables : 1182 ( 0 ^;1166 !; 16 ?;1182 :)
% Comments :
%------------------------------------------------------------------------------
thf(bop1_type,type,
bop1: $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(val1_type,type,
val1: $tType ).
thf(eval_decl,type,
eval: ( 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 ) > ( char @ list @ exp ) > ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) ) > ( char @ list @ exp ) > ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) ) > $o ).
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 ) > ( val1 @ 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 ) > ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( val1 @ option @ ( char @ list @ fun ) ) > ( ty @ option @ ( char @ list @ fun ) ) > $o ) ).
thf(binOp_decl,type,
binOp:
!>[TA: $tType] : ( ( TA @ exp ) > bop1 > ( TA @ exp ) > ( TA @ exp ) ) ).
thf(fAss_decl,type,
fAss:
!>[TA: $tType] : ( ( TA @ exp ) > ( char @ list ) > ( char @ list ) > ( TA @ exp ) > ( TA @ exp ) ) ).
thf(val_decl,type,
val:
!>[TA: $tType] : ( val1 > ( TA @ exp ) ) ).
thf(throw_decl,type,
throw:
!>[TA: $tType] : ( ( TA @ exp ) > ( TA @ exp ) ) ).
thf(in_rel_decl,type,
in_rel:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) ) > TB > TA > $o ) ).
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(refl_decl,type,
refl:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(hext_decl,type,
hext: ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( val1 @ 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(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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) ) > ( val1 @ 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 ) ) > ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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(wwf_J_mdecl_decl,type,
wwf_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(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 ) > ( val1 @ 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(e_decl,type,
e: ty @ option @ ( char @ list @ fun ) ).
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_decl,type,
t: ty ).
thf(bop_decl,type,
bop: bop1 ).
thf(e_2_decl,type,
e_2: char @ list @ exp ).
thf(e_21_decl,type,
e_21: char @ list @ exp ).
thf(h_a_decl,type,
h_a: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ).
thf(ha_decl,type,
ha: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ).
thf(l_a_decl,type,
l_a: val1 @ option @ ( char @ list @ fun ) ).
thf(la_decl,type,
la: val1 @ option @ ( char @ list @ fun ) ).
thf(v_1_decl,type,
v_1: val1 ).
thf(42,axiom,
p @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_assms) ).
thf(234,plain,
p @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(49,axiom,
! [A: bop1,B: val1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( D @ ( E @ ( A @ ( B @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( A @ ( B @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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__reds_OBinOpRed2) ).
thf(257,plain,
! [A: bop1,B: val1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( D @ ( E @ ( A @ ( B @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( A @ ( B @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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(38,axiom,
! [A: bop1,B: val1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( A @ ( B @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( A @ ( B @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_58_BinOp2Reds) ).
thf(224,plain,
! [A: bop1,B: val1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( A @ ( B @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( A @ ( B @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[38]) ).
thf(9,axiom,
! [TA: $tType,A: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ option @ ( char @ list @ fun ),C: val1 @ option @ ( char @ list @ fun ),D: val1 @ 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_52_lconf__hext) ).
thf(129,plain,
! [TA: $tType,A: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ option @ ( char @ list @ fun ),C: val1 @ option @ ( char @ list @ fun ),D: val1 @ 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)],[9]) ).
thf(98,axiom,
! [A: char @ list,B: char @ list,C: val1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_92_FAssReds2) ).
thf(408,plain,
! [A: char @ list,B: char @ list,C: val1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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(6,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_83_exp_Osimps_I180_J) ).
thf(115,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)],[6]) ).
thf(31,axiom,
! [A: bop1,B: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: val1,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp,I: 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 @ ( F @ ( char @ list @ val ) @ ( G @ ( H @ ( I @ eval ) ) ) ) )
=> ( ( B @ ( C @ ( char @ list @ throw ) @ ( E @ ( D @ ( I @ eval ) ) ) ) )
=> ( B @ ( C @ ( char @ list @ throw ) @ ( G @ ( D @ ( A @ ( H @ ( char @ list @ binOp ) ) ) @ ( I @ eval ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_eval__evals_OBinOpThrow2) ).
thf(202,plain,
! [A: bop1,B: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: val1,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp,I: 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 @ ( F @ ( char @ list @ val ) @ ( G @ ( H @ ( I @ eval ) ) ) ) )
=> ( ( B @ ( C @ ( char @ list @ throw ) @ ( E @ ( D @ ( I @ eval ) ) ) ) )
=> ( B @ ( C @ ( char @ list @ throw ) @ ( G @ ( D @ ( A @ ( H @ ( char @ list @ binOp ) ) ) @ ( I @ eval ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(110,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(81,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_60_ThrowReds) ).
thf(344,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[81]) ).
thf(102,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_14_split__paired__All) ).
thf(421,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)],[102]) ).
thf(59,axiom,
! [A: ty,B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val1 @ 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_77_WTrtThrow) ).
thf(284,plain,
! [A: ty,B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val1 @ 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)],[59]) ).
thf(72,axiom,
t @ ( e_21 @ ( bop @ ( v_1 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_BinOpRed2_I4_J) ).
thf(316,plain,
t @ ( e_21 @ ( bop @ ( v_1 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(51,axiom,
! [A: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),B: char @ list @ exp,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: 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 @ ( wwf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) )
=> ( ( G @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( B @ ( C @ ( D @ ( G @ eval ) ) ) ) )
=> ( A @ ( B @ ( E @ ( F @ ( G @ eval ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_extend__eval) ).
thf(261,plain,
! [A: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),B: char @ list @ exp,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: 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 @ ( wwf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) )
=> ( ( G @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( B @ ( C @ ( D @ ( G @ eval ) ) ) ) )
=> ( A @ ( B @ ( E @ ( F @ ( G @ eval ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(36,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_4_widen__refl) ).
thf(216,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)],[36]) ).
thf(83,axiom,
la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_12_BinOpRed2_I3_J) ).
thf(348,plain,
la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[83]) ).
thf(86,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_35_prod__cases3) ).
thf(353,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)],[86]) ).
thf(13,axiom,
! [A: val1 @ 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_50_hext__refl) ).
thf(147,plain,
! [A: val1 @ 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)],[13]) ).
thf(95,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_48_red__reds_OThrowThrow) ).
thf(397,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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(63,axiom,
! [A: val1 @ 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: val1 @ 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_53_WTrt__hext__mono) ).
thf(293,plain,
! [A: val1 @ 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: val1 @ 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)],[63]) ).
thf(104,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_28_prod__cases5) ).
thf(428,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)],[104]) ).
thf(53,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_34_prod__induct3) ).
thf(265,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)],[53]) ).
thf(70,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_69_converse__rtrancl__induct2) ).
thf(307,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)],[70]) ).
thf(47,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_93_FAssRedsThrow1) ).
thf(248,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[47]) ).
thf(94,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_17_pred__equals__eq2) ).
thf(381,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)],[94]) ).
thf(92,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( e_21 @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_2 @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_BinOpRed2_I2_J) ).
thf(366,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( e_21 @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_2 @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(68,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_31_prod__induct6) ).
thf(302,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)],[68]) ).
thf(84,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_27_prod__induct4) ).
thf(349,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)],[84]) ).
thf(65,axiom,
p @ red @ ( l_a @ ( h_a @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e_2 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e_21 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_16_red) ).
thf(297,plain,
p @ red @ ( l_a @ ( h_a @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e_2 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e_21 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[65]) ).
thf(16,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_37_prod_Orecs) ).
thf(165,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)],[16]) ).
thf(73,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_71_rtranclE) ).
thf(317,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)],[73]) ).
thf(25,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_9_widen__trans) ).
thf(188,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)],[25]) ).
thf(87,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_89_red__reds_OFAssThrow1) ).
thf(356,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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(12,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_18_Pair__inject) ).
thf(141,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)],[12]) ).
thf(76,axiom,
! [A: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),B: char @ list @ exp,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: 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 @ ( wwf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) )
=> ( ( G @ red @ ( C @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( B @ ( C @ ( D @ ( G @ eval ) ) ) ) )
=> ( A @ ( B @ ( E @ ( F @ ( G @ eval ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_extend__1__eval) ).
thf(328,plain,
! [A: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),B: char @ list @ exp,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: 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 @ ( wwf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) )
=> ( ( G @ red @ ( C @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( B @ ( C @ ( D @ ( G @ eval ) ) ) ) )
=> ( A @ ( B @ ( E @ ( F @ ( G @ eval ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(27,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_65_converse__rtrancl__into__rtrancl) ).
thf(193,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)],[27]) ).
thf(34,axiom,
! [TA: $tType,A: val1,B: TA @ exp] :
( ( B @ ( TA @ throw ) )
!= ( A @ ( TA @ val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_exp_Osimps_I91_J) ).
thf(212,plain,
! [TA: $tType,A: val1,B: TA @ exp] :
( ( B @ ( TA @ throw ) )
!= ( A @ ( TA @ val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(11,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_42_exp_Osimps_I14_J) ).
thf(134,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)],[11]) ).
thf(44,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_30_prod__cases6) ).
thf(237,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)],[44]) ).
thf(1,conjecture,
? [A: ty] :
( ( t @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( A @ ( e_2 @ ( bop @ ( v_1 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( 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 @ ( bop @ ( v_1 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( 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 @ ( bop @ ( v_1 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(89,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_47_red__reds_OThrowRed) ).
thf(360,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[89]) ).
thf(66,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1] : ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_91_red__reds_OFAssThrow2) ).
thf(298,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1] : ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[66]) ).
thf(100,axiom,
! [TA: $tType,A: TA @ exp,B: bop1,C: TA @ exp,D: val1] :
( ( D @ ( TA @ val ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_exp_Osimps_I70_J) ).
thf(412,plain,
! [TA: $tType,A: TA @ exp,B: bop1,C: TA @ exp,D: val1] :
( ( D @ ( TA @ val ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(14,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_80_exp_Osimps_I8_J) ).
thf(149,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)],[14]) ).
thf(20,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_36_red__preserves__sconf) ).
thf(176,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[20]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ in_rel ) ) ) ) )
<=> ( C @ ( A @ ( B @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_in__rel__def) ).
thf(286,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( C @ ( A @ ( B @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( B @ ( C @ ( TB @ ( TA @ in_rel ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( TB @ ( TA @ in_rel ) ) ) ) )
=> ( C @ ( A @ ( B @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(62,axiom,
! [A: bop1,B: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: val1,H: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),I: char @ list @ exp] :
( ( E @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( H @ ( I @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_56_BinOpRedsThrow2) ).
thf(291,plain,
! [A: bop1,B: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: val1,H: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),I: char @ list @ exp] :
( ( E @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( H @ ( I @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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(7,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_15_Pair__eq) ).
thf(118,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)],[7]) ).
thf(50,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_62_rtrancl_Ortrancl__refl) ).
thf(259,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)],[50]) ).
thf(57,axiom,
! [A: char @ list,B: char @ list,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: val1,H: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),I: char @ list @ exp,J: 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 @ ( G @ ( char @ list @ val ) @ ( H @ ( I @ ( J @ eval ) ) ) ) )
=> ( ( C @ ( D @ ( char @ list @ throw ) @ ( F @ ( E @ ( J @ eval ) ) ) ) )
=> ( C @ ( D @ ( char @ list @ throw ) @ ( H @ ( E @ ( A @ ( B @ ( I @ ( char @ list @ fAss ) ) ) ) @ ( J @ eval ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_eval__evals_OFAssThrow2) ).
thf(281,plain,
! [A: char @ list,B: char @ list,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: val1,H: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),I: char @ list @ exp,J: 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 @ ( G @ ( char @ list @ val ) @ ( H @ ( I @ ( J @ eval ) ) ) ) )
=> ( ( C @ ( D @ ( char @ list @ throw ) @ ( F @ ( E @ ( J @ eval ) ) ) ) )
=> ( C @ ( D @ ( char @ list @ throw ) @ ( H @ ( E @ ( A @ ( B @ ( I @ ( char @ list @ fAss ) ) ) ) @ ( J @ eval ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(32,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( e_21 @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_2 @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_IH) ).
thf(204,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( e_21 @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_2 @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(71,axiom,
! [TA: $tType,A: TA @ exp,B: bop1,C: TA @ exp,D: TA @ exp,E: char @ list,F: char @ list,G: TA @ exp] :
( ( D @ ( E @ ( F @ ( G @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_exp_Osimps_I101_J) ).
thf(313,plain,
! [TA: $tType,A: TA @ exp,B: bop1,C: TA @ exp,D: TA @ exp,E: char @ list,F: char @ list,G: TA @ exp] :
( ( D @ ( E @ ( F @ ( G @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(79,axiom,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: bop1,D: TA @ exp] :
( ( B @ ( C @ ( D @ ( TA @ binOp ) ) ) )
!= ( A @ ( TA @ throw ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_exp_Osimps_I112_J) ).
thf(335,plain,
! [TA: $tType,A: TA @ exp,B: TA @ exp,C: bop1,D: TA @ exp] :
( ( B @ ( C @ ( D @ ( TA @ binOp ) ) ) )
!= ( A @ ( TA @ throw ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(22,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_66_rtrancl_Ortrancl__into__rtrancl) ).
thf(181,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)],[22]) ).
thf(97,axiom,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ),B: char @ list,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] :
( ( A @ ( B @ ( C @ ( 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 @ aa ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ aa ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( wwf_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 @ aa ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ aa ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_wf__mdecl__wwf__mdecl) ).
thf(406,plain,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ),B: char @ list,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] :
( ( A @ ( B @ ( C @ ( 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 @ aa ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ aa ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( wwf_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 @ aa ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ aa ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(19,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_76_mem__def) ).
thf(172,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)],[19]) ).
thf(40,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: val1 @ option @ ( char @ list @ fun ),E: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ),H: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_32_red__preserves__hconf) ).
thf(230,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: val1 @ option @ ( char @ list @ fun ),E: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ),H: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[40]) ).
thf(90,axiom,
! [A: val1 @ 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: val1 @ option @ ( char @ list @ fun ),D: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ),G: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ ( char @ list @ map_add ) ) ) @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val1 @ ( char @ list @ map_add ) ) ) @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_54_Red__lcl__add) ).
thf(362,plain,
! [A: val1 @ 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: val1 @ option @ ( char @ list @ fun ),D: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ),G: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ ( char @ list @ map_add ) ) ) @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val1 @ ( char @ list @ map_add ) ) ) @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[90]) ).
thf(33,axiom,
! [A: ty,B: char @ list @ exp,C: ty @ option @ ( char @ list @ fun ),D: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),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] :
( ( A @ ( B @ ( char @ list @ throw ) @ ( C @ ( D @ ( E @ wTrt ) ) ) ) )
=> ~ ! [F: ty] :
( ( F @ ( B @ ( C @ ( D @ ( E @ wTrt ) ) ) ) )
=> ~ ( F @ is_refT ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_WTrt__elim__cases_I4_J) ).
thf(208,plain,
! [A: ty,B: char @ list @ exp,C: ty @ option @ ( char @ list @ fun ),D: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),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] :
( ( A @ ( B @ ( char @ list @ throw ) @ ( C @ ( D @ ( E @ wTrt ) ) ) ) )
=> ~ ! [F: ty] :
( ( F @ ( B @ ( C @ ( D @ ( E @ wTrt ) ) ) ) )
=> ~ ( F @ is_refT ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(74,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: bop1,G: TA @ exp] :
( ( E @ ( F @ ( G @ ( TA @ binOp ) ) ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_exp_Osimps_I100_J) ).
thf(323,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: bop1,G: TA @ exp] :
( ( E @ ( F @ ( G @ ( TA @ binOp ) ) ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(45,axiom,
! [A: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),B: char @ list @ exp,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( 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 @ ( wwf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ eval ) ) ) ) )
=> ( E @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( A @ ( B @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( C @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_95_big__by__small) ).
thf(240,plain,
! [A: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),B: char @ list @ exp,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( 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 @ ( wwf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ eval ) ) ) ) )
=> ( E @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( A @ ( B @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( C @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[45]) ).
thf(29,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_87_red__reds_OFAssRed1) ).
thf(198,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[29]) ).
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] :
( ( A @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) )
=> ( A @ ( wwf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_wf__prog__wwf__prog) ).
thf(330,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] :
( ( A @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) )
=> ( A @ ( wwf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(96,axiom,
! [TA: $tType,A: val1,B: val1] :
( ( ( B @ ( TA @ val ) )
= ( A @ ( TA @ val ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_exp_Osimps_I3_J) ).
thf(399,plain,
! [TA: $tType,A: val1,B: val1] :
( ( ( B = A )
=> ( ( B @ ( TA @ val ) )
= ( A @ ( TA @ val ) ) ) )
& ( ( ( B @ ( TA @ val ) )
= ( A @ ( TA @ val ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(56,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: val1 @ option @ ( char @ list @ fun ),C: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: char @ list @ exp,E: val1 @ option @ ( char @ list @ fun ),F: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: char @ list @ exp] :
( ( A @ red @ ( B @ ( C @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_38_red__hext__incr) ).
thf(278,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: val1 @ option @ ( char @ list @ fun ),C: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: char @ list @ exp,E: val1 @ option @ ( char @ list @ fun ),F: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: char @ list @ exp] :
( ( A @ red @ ( B @ ( C @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[56]) ).
thf(39,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ refl ) )
<=> ! [B: TA] : ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Nitpick_Orefl_H__def) ).
thf(226,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ! [B: TA] : ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ refl ) ) )
& ( ( A @ ( TA @ refl ) )
=> ! [B: TA] : ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(54,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_68_converse__rtranclE2) ).
thf(267,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)],[54]) ).
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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: bop1,E: char @ list @ exp] : ( A @ red @ ( B @ ( E @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( char @ list @ throw ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_red__reds_OBinOpThrow1) ).
thf(426,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: bop1,E: char @ list @ exp] : ( A @ red @ ( B @ ( E @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( char @ list @ throw ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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(15,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(162,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,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_63_rtrancl__idemp) ).
thf(112,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)],[5]) ).
thf(64,axiom,
! [A: val1 @ 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: val1 @ option @ ( char @ list @ fun ),D: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ),G: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( C @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ ( char @ list @ map_add ) ) ) @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val1 @ ( char @ list @ map_add ) ) ) @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_40_red__lcl__add) ).
thf(295,plain,
! [A: val1 @ 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: val1 @ option @ ( char @ list @ fun ),D: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ),G: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( C @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ ( char @ list @ map_add ) ) ) @ ( D @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val1 @ ( char @ list @ map_add ) ) ) @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[64]) ).
thf(52,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_61_ThrowRedsThrow) ).
thf(263,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp] :
( ( A @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[52]) ).
thf(93,axiom,
! [TA: $tType,A: TA @ exp,B: bop1,C: TA @ exp,D: TA @ exp,E: bop1,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_3_exp_Osimps_I4_J) ).
thf(370,plain,
! [TA: $tType,A: TA @ exp,B: bop1,C: TA @ exp,D: TA @ exp,E: bop1,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)],[93]) ).
thf(8,axiom,
! [A: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: val1 @ 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_55_hext__trans) ).
thf(127,plain,
! [A: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: val1 @ 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)],[8]) ).
thf(80,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_73_converse__rtrancl__induct) ).
thf(338,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)],[80]) ).
thf(48,axiom,
! [A: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),B: char @ list @ exp,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: val1,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] :
( ( A @ ( B @ ( C @ ( D @ ( char @ list @ val ) @ ( E @ eval ) ) ) ) )
=> ~ ( ( B
= ( D @ ( char @ list @ val ) ) )
=> ( A != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_eval__cases_I2_J) ).
thf(250,plain,
! [A: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),B: char @ list @ exp,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: val1,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] :
( ( A @ ( B @ ( C @ ( D @ ( char @ list @ val ) @ ( E @ eval ) ) ) ) )
=> ~ ( ( B
= ( D @ ( char @ list @ val ) ) )
=> ( A != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(37,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_72_converse__rtranclE) ).
thf(218,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)],[37]) ).
thf(69,axiom,
! [TA: $tType,A: val1,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_exp_Osimps_I79_J) ).
thf(304,plain,
! [TA: $tType,A: val1,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(85,axiom,
! [A: char @ list @ exp,B: bop1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( B @ ( G @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_57_BinOpRedsThrow1) ).
thf(351,plain,
! [A: char @ list @ exp,B: bop1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( B @ ( G @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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(24,axiom,
! [A: char @ list @ exp,B: bop1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( D @ ( A @ ( B @ ( E @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( B @ ( G @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_25_red__reds_OBinOpRed1) ).
thf(186,plain,
! [A: char @ list @ exp,B: bop1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( D @ ( A @ ( B @ ( E @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( B @ ( G @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[24]) ).
thf(18,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(171,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(61,axiom,
la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_13_conf) ).
thf(290,plain,
la @ ( ha @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[61]) ).
thf(43,axiom,
! [A: char @ list @ exp,B: bop1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( A @ ( B @ ( E @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( B @ ( G @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_59_BinOp1Reds) ).
thf(235,plain,
! [A: char @ list @ exp,B: bop1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( D @ ( A @ ( B @ ( E @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( B @ ( G @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[43]) ).
thf(82,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: bop1,E: val1] : ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_39_red__reds_OBinOpThrow2) ).
thf(346,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),C: char @ list @ exp,D: bop1,E: val1] : ( A @ red @ ( B @ ( C @ ( char @ list @ throw ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[82]) ).
thf(67,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_29_prod__induct5) ).
thf(300,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)],[67]) ).
thf(99,axiom,
! [A: char @ list,B: char @ list,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: val1,I: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),J: char @ list @ exp] :
( ( F @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( J @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_FAssRedsThrow2) ).
thf(410,plain,
! [A: char @ list,B: char @ list,C: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: val1,I: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),J: char @ list @ exp] :
( ( F @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( J @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[99]) ).
thf(17,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_51_map__add__assoc) ).
thf(168,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)],[17]) ).
thf(26,axiom,
! [TA: $tType,A: val1,B: TA @ exp,C: bop1,D: TA @ exp] :
( ( B @ ( C @ ( D @ ( TA @ binOp ) ) ) )
!= ( A @ ( TA @ val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_exp_Osimps_I71_J) ).
thf(190,plain,
! [TA: $tType,A: val1,B: TA @ exp,C: bop1,D: TA @ exp] :
( ( B @ ( C @ ( D @ ( TA @ binOp ) ) ) )
!= ( A @ ( TA @ val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(23,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_26_prod__cases4) ).
thf(183,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)],[23]) ).
thf(55,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_21_split__paired__Ex) ).
thf(273,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)],[55]) ).
thf(46,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_70_rtrancl__induct2) ).
thf(242,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)],[46]) ).
thf(88,axiom,
! [A: char @ list,B: char @ list,C: val1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_88_red__reds_OFAssRed2) ).
thf(358,plain,
! [A: char @ list,B: char @ list,C: val1,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ val ) @ ( char @ list @ fAss ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[88]) ).
thf(28,axiom,
! [TA: $tType,A: TA @ exp,B: val1] :
( ( B @ ( TA @ val ) )
!= ( A @ ( TA @ throw ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_exp_Osimps_I90_J) ).
thf(195,plain,
! [TA: $tType,A: TA @ exp,B: val1] :
( ( B @ ( TA @ val ) )
!= ( A @ ( TA @ throw ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(58,axiom,
t @ ( e_21 @ ( bop @ ( v_1 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_wt) ).
thf(283,plain,
t @ ( e_21 @ ( bop @ ( v_1 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(101,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_74_rtrancl__induct) ).
thf(415,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)],[101]) ).
thf(75,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_67_rtrancl__trans) ).
thf(326,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)],[75]) ).
thf(3,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_84_exp_Osimps_I181_J) ).
thf(107,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)],[3]) ).
thf(78,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: val1] :
( ( E @ ( TA @ val ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_exp_Osimps_I78_J) ).
thf(332,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: val1] :
( ( E @ ( TA @ val ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(10,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_41_prod_Oexhaust) ).
thf(131,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)],[10]) ).
thf(30,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_64_r__into__rtrancl) ).
thf(200,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)],[30]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ exp,B: bop1,C: TA @ exp,D: TA @ exp] :
( ( D @ ( TA @ throw ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_exp_Osimps_I113_J) ).
thf(178,plain,
! [TA: $tType,A: TA @ exp,B: bop1,C: TA @ exp,D: TA @ exp] :
( ( D @ ( TA @ throw ) )
!= ( A @ ( B @ ( C @ ( TA @ binOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(35,axiom,
t @ ( e_2 @ ( bop @ ( v_1 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096P_ME_Mh_H_A_092_060turnstile_062_AVal_Av_092_060_094isub_0621_A_092_060guillemotleft_062bop_092_060guillemotright_062_Ae_092_060_094isub_0622_H_A_058_AT_096) ).
thf(215,plain,
t @ ( e_2 @ ( bop @ ( v_1 @ ( char @ list @ val ) @ ( char @ list @ binOp ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(91,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: val1 @ option @ ( char @ list @ fun ),E: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ),H: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_33_red__preserves__lconf) ).
thf(364,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: val1 @ option @ ( char @ list @ fun ),E: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ),H: val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[91]) ).
thf(41,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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_90_FAssReds1) ).
thf(232,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: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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 ) ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val1 @ option @ ( char @ list @ fun ) @ ( val1 @ 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)],[41]) ).
thf(434,plain,
$false,
inference(e,[status(thm)],[234,257,224,129,408,115,202,110,344,421,284,316,261,216,348,353,147,397,293,428,265,307,248,381,366,302,349,297,165,317,188,356,141,328,193,212,134,237,105,360,298,412,149,176,286,291,118,259,281,204,313,335,181,406,172,230,362,208,323,240,198,330,399,278,226,267,426,162,112,295,263,370,127,338,250,218,304,351,186,171,290,235,346,300,410,168,190,183,273,242,358,195,283,415,326,107,332,131,200,178,215,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW567_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.09 % 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
% 0.16/5.41 % Computer : n014.cluster.edu
% 0.16/5.41 % Model : x86_64 x86_64
% 0.16/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.41 % Memory : 8046.5625MB
% 0.16/5.41 % OS : Linux 6.8.0-71-generic
% 0.16/5.41 % CPULimit : 300
% 0.16/5.41 % WCLimit : 300
% 0.16/5.41 % DateTime : Sat Sep 26 16:13:23 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.42 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
% 0.18/6.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.81/6.42 % [INFO] Parsing done (420ms).
% 2.43/6.44 % [INFO] Running in sequential loop mode.
% 3.67/6.83 % [INFO] eprover registered as external prover.
% 3.67/6.84 % [INFO] Scanning for conjecture ...
% 4.83/7.15 % [INFO] Found a conjecture (or negated_conjecture) and 102 axioms. Running axiom selection ...
% 5.59/7.36 % [INFO] Axiom selection finished. Selected 102 axioms (removed 0 axioms).
% 7.08/7.78 % [INFO] Problem is typed first-order (TPTP TFF).
% 7.50/7.82 % [INFO] Type checking passed.
% 7.50/7.82 % [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 ...
% 115.89/98.41 % External prover 'e' found a proof!
% 115.89/98.41 % [INFO] Killing All external provers ...
% 115.89/98.41 % Time passed: 92851ms (effective reasoning time: 91960ms)
% 115.89/98.41 % 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)>
% 115.89/98.41 % Axioms used in derivation (102): fact_4_widen__refl, fact_79_FAssRedsThrow2, fact_37_prod_Orecs, fact_29_prod__induct5, fact_50_hext__refl, fact_61_ThrowRedsThrow, fact_62_rtrancl_Ortrancl__refl, fact_67_rtrancl__trans, fact_69_converse__rtrancl__induct2, fact_83_exp_Osimps_I180_J, fact_19_wf__prog__wwf__prog, fact_51_map__add__assoc, fact_57_BinOpRedsThrow1, fact_20_in__rel__def, fact_84_exp_Osimps_I181_J, fact_43_exp_Osimps_I91_J, fact_94_extend__eval, fact_34_prod__induct3, fact_25_red__reds_OBinOpRed1, fact_12_BinOpRed2_I3_J, fact_87_red__reds_OFAssRed1, fact_63_rtrancl__idemp, fact_78_WTrt__elim__cases_I4_J, fact_28_prod__cases5, fact_49_red__reds_OBinOpThrow1, fact_40_red__lcl__add, fact_3_exp_Osimps_I4_J, fact_45_exp_Osimps_I112_J, fact_18_Pair__inject, fact_98_eval__evals_OBinOpThrow2, fact_66_rtrancl_Ortrancl__into__rtrancl, fact_5_exp_Osimps_I3_J, fact_92_FAssReds2, fact_82_exp_Osimps_I100_J, fact_6_assms, fact_54_Red__lcl__add, fact_31_prod__induct6, fact_77_WTrtThrow, fact_96_extend__1__eval, fact_7_exp_Osimps_I70_J, fact_11_IH, fact_70_rtrancl__induct2, fact_13_conf, fact_71_rtranclE, fact_86_exp_Osimps_I78_J, fact_89_red__reds_OFAssThrow1, fact_74_rtrancl__induct, fact_59_BinOp1Reds, fact_42_exp_Osimps_I14_J, fact_47_red__reds_OThrowRed, fact_56_BinOpRedsThrow2, fact_44_exp_Osimps_I90_J, fact_41_prod_Oexhaust, fact_30_prod__cases6, fact_85_exp_Osimps_I79_J, fact_65_converse__rtrancl__into__rtrancl, fact_55_hext__trans, fact_15_Pair__eq, fact_21_split__paired__Ex, fact_76_mem__def, fact_58_BinOp2Reds, fact_48_red__reds_OThrowThrow, fact_23_wf__mdecl__wwf__mdecl, fact_33_red__preserves__lconf, fact_64_r__into__rtrancl, fact_2_wt, fact_9_widen__trans, fact_80_exp_Osimps_I8_J, fact_99_eval__cases_I2_J, fact_93_FAssRedsThrow1, fact_91_red__reds_OFAssThrow2, fact_14_split__paired__All, fact_97_eval__evals_OFAssThrow2, fact_72_converse__rtranclE, fact_32_red__preserves__hconf, fact_10_BinOpRed2_I2_J, fact_90_FAssReds1, fact_46_exp_Osimps_I113_J, fact_68_converse__rtranclE2, fact_73_converse__rtrancl__induct, fact_22_Nitpick_Orefl_H__def, help_pp_1_1_U, fact_26_prod__cases4, fact_52_lconf__hext, fact_0__096P_ME_Mh_H_A_092_060turnstile_062_AVal_Av_092_060_094isub_0621_A_092_060guillemotleft_062bop_092_060guillemotright_062_Ae_092_060_094isub_0622_H_A_058_AT_096, fact_36_red__preserves__sconf, fact_75_ext, fact_38_red__hext__incr, fact_16_red, fact_88_red__reds_OFAssRed2, fact_39_red__reds_OBinOpThrow2, help_pp_2_1_U, fact_24_red__reds_OBinOpRed2, fact_27_prod__induct4, fact_1_BinOpRed2_I4_J, fact_60_ThrowReds, fact_95_big__by__small, fact_53_WTrt__hext__mono, fact_8_exp_Osimps_I71_J, fact_17_pred__equals__eq2, fact_81_exp_Osimps_I101_J, fact_35_prod__cases3
% 115.89/98.42 % No. of inferences in proof: 208
% 115.89/98.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 92851 ms resp. 91960 ms w/o parsing
% 116.83/98.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 116.83/98.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------