%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW572_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 : n007.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 09:10:51 AM UTC 2026
% Result : Theorem 93.05s 76.19s
% Output : Refutation 93.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 101
% Syntax : Number of formulae : 204 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 6161 ( 155 equ; 0 cnn)
% Maximal formula atoms : 340 ( 30 avg)
% Number of connectives : 15680 ( 80 ~; 9 |; 56 &;15303 @)
% ( 12 <=>; 220 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 13 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 26 con; 0-7 aty)
% Number of variables : 1009 ( 0 ^; 975 !; 34 ?;1009 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(char_type,type,
char: $tType ).
thf(ty_type,type,
ty: $tType ).
thf(val_type,type,
val: $tType ).
thf(hconf_decl,type,
hconf:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > $o ) ).
thf(lconf_decl,type,
lconf:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( val @ option @ ( char @ list @ fun ) ) > ( ty @ option @ ( char @ list @ fun ) ) > $o ) ).
thf(fAss_decl,type,
fAss:
!>[TA: $tType] : ( ( TA @ exp ) > ( char @ list ) > ( char @ list ) > ( TA @ exp ) > ( TA @ exp ) ) ).
thf(tryCatch_decl,type,
tryCatch:
!>[TA: $tType] : ( ( TA @ exp ) > ( char @ list ) > TA > ( TA @ exp ) > ( TA @ exp ) ) ).
thf(val1_decl,type,
val1:
!>[TA: $tType] : ( val > ( TA @ exp ) ) ).
thf(throw_decl,type,
throw:
!>[TA: $tType] : ( ( TA @ exp ) > ( TA @ exp ) ) ).
thf(wf_J_mdecl_decl,type,
wf_J_mdecl: bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) ).
thf(map_add_decl,type,
map_add:
!>[TA: $tType,TB: $tType] : ( ( TA @ option @ ( TB @ fun ) ) > ( TA @ option @ ( TB @ fun ) ) > ( TA @ option @ ( TB @ fun ) ) ) ).
thf(hext_decl,type,
hext: ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > $o ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( TA @ ( TB @ product_prod ) ) ) ).
thf(product_prod_rec_decl,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(red_decl,type,
red: ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) ) ).
thf(hp_decl,type,
hp: ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) ).
thf(transitive_rtrancl_decl,type,
transitive_rtrancl:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) ) ).
thf(has_field_decl,type,
has_field:
!>[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 ) > ( char @ list ) > ( char @ list ) > ty > ( char @ list ) > $o ) ).
thf(subcls1_decl,type,
subcls1:
!>[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 ) > ( bool @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) ) ) ).
thf(widen_decl,type,
widen:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ty > ty > $o ) ).
thf(typeSa976492716_sconf_decl,type,
typeSa976492716_sconf: ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( ty @ option @ ( char @ list @ fun ) ) > ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) ) > $o ).
thf(class_decl,type,
class: ( char @ list ) > ty ).
thf(nt_decl,type,
nt: ty ).
thf(void_decl,type,
void: ty ).
thf(ty_rec_decl,type,
ty_rec:
!>[TA: $tType] : ( TA > TA > TA > TA > ( TA @ ( char @ list @ fun ) ) > ty > TA ) ).
thf(wf_prog_decl,type,
wf_prog:
!>[TA: $tType] : ( ( bool @ ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) ) > ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > $o ) ).
thf(wTrt_decl,type,
wTrt: ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( ty @ option @ ( char @ list @ fun ) ) > ( char @ list @ exp ) > ty > $o ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(c_decl,type,
c: char @ list ).
thf(c1_decl,type,
c1: char @ list ).
thf(d_decl,type,
d: char @ list ).
thf(e_decl,type,
e: ty @ option @ ( char @ list @ fun ) ).
thf(f_decl,type,
f: char @ list ).
thf(p_decl,type,
p: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ).
thf(tf_decl,type,
tf: ty ).
thf(t_2_decl,type,
t_2: ty ).
thf(t_decl,type,
t: ty ).
thf(u_decl,type,
u: ty ).
thf(e_2_decl,type,
e_2: char @ list @ exp ).
thf(e_a_decl,type,
e_a: char @ list @ exp ).
thf(ea_decl,type,
ea: char @ list @ exp ).
thf(h_a_decl,type,
h_a: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ).
thf(ha_decl,type,
ha: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ).
thf(l_a_decl,type,
l_a: val @ option @ ( char @ list @ fun ) ).
thf(la_decl,type,
la: val @ option @ ( char @ list @ fun ) ).
thf(63,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_34_Pair__eq) ).
thf(317,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)],[63]) ).
thf(31,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_40_Pair__inject) ).
thf(205,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)],[31]) ).
thf(19,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_53_prod__cases4) ).
thf(176,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)],[19]) ).
thf(77,axiom,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e @ ( p @ typeSa976492716_sconf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_conf) ).
thf(391,plain,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e @ ( p @ typeSa976492716_sconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(54,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_52_prod__induct4) ).
thf(282,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)],[54]) ).
thf(10,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_91_exp_Osimps_I14_J) ).
thf(139,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)],[10]) ).
thf(79,axiom,
t_2 @ ( e_2 @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_wt_092_060_094isub_0622) ).
thf(395,plain,
t_2 @ ( e_2 @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(45,axiom,
! [A: char @ list,B: char @ list,C: val,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_FAssReds2) ).
thf(249,plain,
! [A: char @ list,B: char @ list,C: val,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(96,axiom,
! [TA: $tType,A: char @ list,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 @ class @ ( nt @ ( B @ ( TA @ widen ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_widen__null) ).
thf(468,plain,
! [TA: $tType,A: char @ list,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 @ class @ ( nt @ ( B @ ( TA @ widen ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(17,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_47_prod__cases5) ).
thf(170,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)],[17]) ).
thf(52,axiom,
void != nt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Type_Oty_Osimps_I6_J) ).
thf(276,plain,
void != nt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(49,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ lconf ) ) ) ) )
=> ( ( A @ ( D @ hext ) )
=> ( B @ ( C @ ( A @ ( E @ ( TA @ lconf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_lconf__hext) ).
thf(269,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ lconf ) ) ) ) )
=> ( ( A @ ( D @ hext ) )
=> ( B @ ( C @ ( A @ ( E @ ( TA @ lconf ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(7,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_81_map__add__assoc) ).
thf(120,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)],[7]) ).
thf(44,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_22_r__into__rtrancl) ).
thf(247,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)],[44]) ).
thf(74,axiom,
! [A: char @ list,B: char @ list,C: ty,D: char @ list @ exp,E: char @ list @ exp,F: ty @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( nt @ ( E @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( ( C @ ( D @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( void @ ( D @ ( A @ ( B @ ( E @ ( char @ list @ fAss ) ) ) ) @ ( F @ ( G @ ( H @ wTrt ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_WTrtFAssNT) ).
thf(384,plain,
! [A: char @ list,B: char @ list,C: ty,D: char @ list @ exp,E: char @ list @ exp,F: ty @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( nt @ ( E @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( ( C @ ( D @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( void @ ( D @ ( A @ ( B @ ( E @ ( char @ list @ fAss ) ) ) ) @ ( F @ ( G @ ( H @ wTrt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(66,axiom,
! [TA: $tType,A: char @ list,B: char @ list,C: 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 @ class @ ( B @ class @ ( C @ ( TA @ widen ) ) ) )
<=> ( C @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( A @ ( B @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Class__widen__Class) ).
thf(340,plain,
! [TA: $tType,A: char @ list,B: char @ list,C: 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] :
( ( ( C @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( A @ ( B @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
=> ( A @ class @ ( B @ class @ ( C @ ( TA @ widen ) ) ) ) )
& ( ( A @ class @ ( B @ class @ ( C @ ( TA @ widen ) ) ) )
=> ( C @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( A @ ( B @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(82,axiom,
! [TA: $tType,A: ty,B: ty,C: 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 @ ( B @ ( C @ ( TA @ widen ) ) ) )
<=> ( ? [D: char @ list] :
( ( A
= ( D @ class ) )
& ( B = nt ) )
| ? [D: char @ list,E: char @ list] :
( ( C @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( E @ ( D @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
& ( A
= ( E @ class ) )
& ( B
= ( D @ class ) ) )
| ? [D: ty] :
( ( A = D )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_widen_Osimps) ).
thf(404,plain,
! [TA: $tType,A: ty,B: ty,C: 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] :
( ( ( ? [D: char @ list] :
( ( A
= ( D @ class ) )
& ( B = nt ) )
| ? [D: char @ list,E: char @ list] :
( ( C @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( E @ ( D @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
& ( A
= ( E @ class ) )
& ( B
= ( D @ class ) ) )
| ? [D: ty] :
( ( A = D )
& ( B = D ) ) )
=> ( A @ ( B @ ( C @ ( TA @ widen ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( TA @ widen ) ) ) )
=> ( ? [D: char @ list] :
( ( A
= ( D @ class ) )
& ( B = nt ) )
| ? [D: char @ list,E: char @ list] :
( ( C @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( E @ ( D @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
& ( A
= ( E @ class ) )
& ( B
= ( D @ class ) ) )
| ? [D: ty] :
( ( A = D )
& ( B = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(22,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_18_widen__refl) ).
thf(185,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)],[22]) ).
thf(87,axiom,
! [A: char @ list,B: char @ list] :
( ( ( B @ class )
= ( A @ class ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Type_Oty_Oinject) ).
thf(436,plain,
! [A: char @ list,B: char @ list] :
( ( ( B = A )
=> ( ( B @ class )
= ( A @ class ) ) )
& ( ( ( B @ class )
= ( A @ class ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(76,axiom,
( u
= ( c @ class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_UClass) ).
thf(389,plain,
( u
= ( c @ class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(70,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_IH) ).
thf(372,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(5,axiom,
! [TA: $tType,A: TA @ exp,B: TA,C: char @ list,D: TA @ exp,E: val] :
( ( E @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ tryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_exp_Osimps_I92_J) ).
thf(110,plain,
! [TA: $tType,A: TA @ exp,B: TA,C: char @ list,D: TA @ exp,E: val] :
( ( E @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ tryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(67,axiom,
! [A: ty,B: char @ list @ exp,C: char @ list,D: char @ list,E: char @ list @ exp,F: ty @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( char @ list @ fAss ) ) ) ) @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( ( ( A = void )
=> ! [I: char @ list] :
( ( I @ class @ ( E @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ! [J: ty] :
( ( C @ ( J @ ( D @ ( I @ ( H @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ) )
=> ! [K: ty] :
( ( K @ ( B @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ~ ( J @ ( K @ ( H @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) ) ) ) ) )
=> ~ ( ( A = void )
=> ( ( nt @ ( E @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ! [I: ty] :
~ ( I @ ( B @ ( F @ ( G @ ( H @ wTrt ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_WTrt__elim__cases_I8_J) ).
thf(344,plain,
! [A: ty,B: char @ list @ exp,C: char @ list,D: char @ list,E: char @ list @ exp,F: ty @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( char @ list @ fAss ) ) ) ) @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ( ( ( A = void )
=> ! [I: char @ list] :
( ( I @ class @ ( E @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ! [J: ty] :
( ( C @ ( J @ ( D @ ( I @ ( H @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ) )
=> ! [K: ty] :
( ( K @ ( B @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ~ ( J @ ( K @ ( H @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) ) ) ) ) )
=> ~ ( ( A = void )
=> ( ( nt @ ( E @ ( F @ ( G @ ( H @ wTrt ) ) ) ) )
=> ! [I: ty] :
~ ( I @ ( B @ ( F @ ( G @ ( H @ wTrt ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(27,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_98_exp_Osimps_I180_J) ).
thf(196,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)],[27]) ).
thf(92,axiom,
t @ ( e_2 @ ( d @ ( f @ ( ea @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_FAssRed1_I4_J) ).
thf(460,plain,
t @ ( e_2 @ ( d @ ( f @ ( ea @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(55,axiom,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: char @ list @ exp,E: val @ option @ ( char @ list @ fun ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: char @ list @ exp] :
( ( A @ red @ ( B @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( C @ ( F @ hext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_red__hext__incr) ).
thf(284,plain,
! [A: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: val @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: char @ list @ exp,E: val @ option @ ( char @ list @ fun ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: char @ list @ exp] :
( ( A @ red @ ( B @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( C @ ( F @ hext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(12,axiom,
! [TA: $tType,A: val,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_exp_Osimps_I79_J) ).
thf(152,plain,
! [TA: $tType,A: val,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,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_97_exp_Osimps_I181_J) ).
thf(216,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)],[34]) ).
thf(100,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( G @ ( B @ ( F @ hp @ ( C @ wTrt ) ) ) ) )
=> ( ( F @ ( B @ ( C @ typeSa976492716_sconf ) ) )
=> ( D @ ( B @ ( C @ typeSa976492716_sconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_red__preserves__sconf) ).
thf(475,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),G: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( G @ ( B @ ( F @ hp @ ( C @ wTrt ) ) ) ) )
=> ( ( F @ ( B @ ( C @ typeSa976492716_sconf ) ) )
=> ( D @ ( B @ ( C @ typeSa976492716_sconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(20,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_72_prod__cases3) ).
thf(179,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)],[20]) ).
thf(71,axiom,
t @ ( e_2 @ ( d @ ( f @ ( ea @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_wt) ).
thf(376,plain,
t @ ( e_2 @ ( d @ ( f @ ( ea @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(32,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_71_prod__induct3) ).
thf(211,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)],[32]) ).
thf(36,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_25_rtrancl__trans) ).
thf(221,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)],[36]) ).
thf(57,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_35_split__paired__All) ).
thf(293,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)],[57]) ).
thf(80,axiom,
( ( nt @ ( ea @ ( e @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [A: ty] :
( ( t @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( A @ ( e_2 @ ( d @ ( f @ ( e_a @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_061_061_062_AEX_AT_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062F_123D_125_A_058_061_Ae_092_060_094isub_0622_A_058_AT_H_A_G_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_096) ).
thf(396,plain,
( ( nt @ ( ea @ ( e @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [A: ty] :
( ( t @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( A @ ( e_2 @ ( d @ ( f @ ( e_a @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(83,axiom,
p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( c1 @ ( c @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__Csubclass_C) ).
thf(428,plain,
p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( c1 @ ( c @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(40,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( B @ ( C @ hext ) )
=> ( ( A @ ( B @ hext ) )
=> ( A @ ( C @ hext ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_hext__trans) ).
thf(233,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( B @ ( C @ hext ) )
=> ( ( A @ ( B @ hext ) )
=> ( A @ ( C @ hext ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(29,axiom,
t = void,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_void) ).
thf(201,plain,
t = void,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(14,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_67_converse__rtranclE) ).
thf(160,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)],[14]) ).
thf(78,axiom,
! [TA: $tType,A: char @ list,B: TA @ ( char @ list @ fun ),C: TA,D: TA,E: TA,F: TA] :
( ( A @ class @ ( B @ ( C @ ( D @ ( E @ ( F @ ( TA @ ty_rec ) ) ) ) ) ) )
= ( A @ ( B @ ( TA @ ( char @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Type_Oty_Orecs_I5_J) ).
thf(392,plain,
! [TA: $tType,A: char @ list,B: TA @ ( char @ list @ fun ),C: TA,D: TA,E: TA,F: TA] :
( ( A @ class @ ( B @ ( C @ ( D @ ( E @ ( F @ ( TA @ ty_rec ) ) ) ) ) ) )
= ( A @ ( B @ ( TA @ ( char @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(25,axiom,
! [A: val @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Red__lcl__add) ).
thf(192,plain,
! [A: val @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(84,axiom,
p @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_assms) ).
thf(429,plain,
p @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(95,axiom,
d @ ( tf @ ( f @ ( c1 @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_has) ).
thf(467,plain,
d @ ( tf @ ( f @ ( c1 @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(38,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] : ( A @ ( A @ hext ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_hext__refl) ).
thf(229,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] : ( A @ ( A @ hext ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(93,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( F @ wTrt ) ) ) ) )
=> ( ( A @ ( E @ hext ) )
=> ( B @ ( C @ ( D @ ( A @ ( F @ wTrt ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_WTrt__hext__mono) ).
thf(461,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( F @ wTrt ) ) ) ) )
=> ( ( A @ ( E @ hext ) )
=> ( B @ ( C @ ( D @ ( A @ ( F @ wTrt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(91,axiom,
! [A: char @ list] :
( ( A @ class )
!= nt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Type_Oty_Osimps_I21_J) ).
thf(456,plain,
! [A: char @ list] :
( ( A @ class )
!= nt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(65,axiom,
! [TA: $tType,A: char @ list,B: ty,C: 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 @ class @ ( B @ ( C @ ( TA @ widen ) ) ) )
<=> ( ? [D: char @ list] :
( ( C @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( A @ ( D @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
& ( B
= ( D @ class ) ) )
| ( B = nt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_widen__Class) ).
thf(328,plain,
! [TA: $tType,A: char @ list,B: ty,C: 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] :
( ( ( ? [D: char @ list] :
( ( C @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( A @ ( D @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
& ( B
= ( D @ class ) ) )
| ( B = nt ) )
=> ( A @ class @ ( B @ ( C @ ( TA @ widen ) ) ) ) )
& ( ( A @ class @ ( B @ ( C @ ( TA @ widen ) ) ) )
=> ( ? [D: char @ list] :
( ( C @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( A @ ( D @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
& ( B
= ( D @ class ) ) )
| ( B = nt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(98,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ),H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( I @ ( B @ ( H @ ( C @ wTrt ) ) ) ) )
=> ( ( B @ ( G @ ( H @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ) ) ) )
=> ( B @ ( D @ ( E @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_red__preserves__lconf) ).
thf(471,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ),H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( I @ ( B @ ( H @ ( C @ wTrt ) ) ) ) )
=> ( ( B @ ( G @ ( H @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ) ) ) )
=> ( B @ ( D @ ( E @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(48,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_56_exp_Osimps_I8_J) ).
thf(256,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)],[48]) ).
thf(18,axiom,
! [TA: $tType,A: TA @ ( char @ list @ fun ),B: TA,C: TA,D: TA,E: TA] :
( ( nt @ ( A @ ( B @ ( C @ ( D @ ( E @ ( TA @ ty_rec ) ) ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Type_Oty_Orecs_I4_J) ).
thf(173,plain,
! [TA: $tType,A: TA @ ( char @ list @ fun ),B: TA,C: TA,D: TA,E: TA] :
( ( nt @ ( A @ ( B @ ( C @ ( D @ ( E @ ( TA @ ty_rec ) ) ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(69,axiom,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e @ ( p @ typeSa976492716_sconf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_FAssRed1_I3_J) ).
thf(371,plain,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e @ ( p @ typeSa976492716_sconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(58,axiom,
! [A: char @ list,B: char @ list,C: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: char @ list @ exp,F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: val,I: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),J: char @ list @ exp] :
( ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( G @ ( H @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( J @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( E @ ( A @ ( B @ ( J @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_FAssRedsThrow2) ).
thf(298,plain,
! [A: char @ list,B: char @ list,C: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),D: char @ list @ exp,E: char @ list @ exp,F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: val,I: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),J: char @ list @ exp] :
( ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( G @ ( H @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( J @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( F @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( C @ ( D @ ( char @ list @ throw ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( I @ ( E @ ( A @ ( B @ ( J @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(85,axiom,
! [A: char @ list] :
( nt
!= ( A @ class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Type_Oty_Osimps_I20_J) ).
thf(430,plain,
! [A: char @ list] :
( nt
!= ( A @ class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(15,axiom,
! [A: val @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( C @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( C @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_red__lcl__add) ).
thf(166,plain,
! [A: val @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: char @ list @ exp,F: val @ option @ ( char @ list @ fun ),G: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),H: char @ list @ exp] :
( ( B @ red @ ( C @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( B @ red @ ( C @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( F @ ( A @ ( val @ ( char @ list @ map_add ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(53,axiom,
nt != void,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Type_Oty_Osimps_I7_J) ).
thf(279,plain,
nt != void,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(23,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: val] :
( ( E @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_exp_Osimps_I78_J) ).
thf(187,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: val] :
( ( E @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(6,axiom,
! [TA: $tType,A: val,B: val] :
( ( ( B @ ( TA @ val1 ) )
= ( A @ ( TA @ val1 ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_exp_Osimps_I3_J) ).
thf(113,plain,
! [TA: $tType,A: val,B: val] :
( ( ( B = A )
=> ( ( B @ ( TA @ val1 ) )
= ( A @ ( TA @ val1 ) ) ) )
& ( ( ( B @ ( TA @ val1 ) )
= ( A @ ( TA @ val1 ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,axiom,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( A @ ( B @ ( C @ ( F @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_FAssReds1) ).
thf(219,plain,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( A @ ( B @ ( C @ ( F @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(51,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_16_rtrancl_Ortrancl__refl) ).
thf(274,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)],[51]) ).
thf(72,axiom,
( ( u = nt )
=> ? [A: ty] :
( ( t @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( A @ ( e_2 @ ( d @ ( f @ ( e_a @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_calculation) ).
thf(377,plain,
( ( u = nt )
=> ? [A: ty] :
( ( t @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( A @ ( e_2 @ ( d @ ( f @ ( e_a @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(90,axiom,
~ ! [A: ty] :
( ( A @ ( e_a @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) )
=> ~ ( c1 @ class @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096_B_Bthesis_O_A_I_B_BU_O_A_091_124_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_059_AP_A_092_060turnstile_062_AU_A_092_060le_062_AClass_AC_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(451,plain,
~ ! [A: ty] :
( ( A @ ( e_a @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) )
=> ~ ( c1 @ class @ ( A @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(43,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_26_rtrancl_Ortrancl__into__rtrancl) ).
thf(245,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)],[43]) ).
thf(86,axiom,
! [A: ty,B: char @ list @ exp,C: char @ list,D: ty,E: char @ list,F: char @ list,G: char @ list @ exp,H: ty @ option @ ( char @ list @ fun ),I: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),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 @ class @ ( G @ ( H @ ( I @ ( J @ wTrt ) ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ ( J @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ) )
=> ( ( A @ ( B @ ( H @ ( I @ ( J @ wTrt ) ) ) ) )
=> ( ( D @ ( A @ ( J @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
=> ( void @ ( B @ ( C @ ( E @ ( G @ ( char @ list @ fAss ) ) ) ) @ ( H @ ( I @ ( J @ wTrt ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_WTrtFAss) ).
thf(434,plain,
! [A: ty,B: char @ list @ exp,C: char @ list,D: ty,E: char @ list,F: char @ list,G: char @ list @ exp,H: ty @ option @ ( char @ list @ fun ),I: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),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 @ class @ ( G @ ( H @ ( I @ ( J @ wTrt ) ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ ( J @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ) )
=> ( ( A @ ( B @ ( H @ ( I @ ( J @ wTrt ) ) ) ) )
=> ( ( D @ ( A @ ( J @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
=> ( void @ ( B @ ( C @ ( E @ ( G @ ( char @ list @ fAss ) ) ) ) @ ( H @ ( I @ ( J @ wTrt ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(50,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_74_prod_Orecs) ).
thf(271,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)],[50]) ).
thf(101,axiom,
c1 @ class @ ( u @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_UsubC) ).
thf(477,plain,
c1 @ class @ ( u @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1,conjecture,
c @ class @ ( e_a @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( c @ class @ ( e_a @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(103,plain,
~ ( c @ class @ ( e_a @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,axiom,
! [TA: $tType,A: TA @ exp,B: TA,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 @ tryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_exp_Osimps_I182_J) ).
thf(213,plain,
! [TA: $tType,A: TA @ exp,B: TA,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 @ tryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(46,axiom,
! [TA: $tType,A: TA @ ( char @ list @ fun ),B: TA,C: TA,D: TA,E: TA] :
( ( void @ ( A @ ( B @ ( C @ ( D @ ( E @ ( TA @ ty_rec ) ) ) ) ) ) )
= E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Type_Oty_Orecs_I1_J) ).
thf(251,plain,
! [TA: $tType,A: TA @ ( char @ list @ fun ),B: TA,C: TA,D: TA,E: TA] :
( ( void @ ( A @ ( B @ ( C @ ( D @ ( E @ ( TA @ ty_rec ) ) ) ) ) ) )
= E ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(13,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_54_split__paired__Ex) ).
thf(155,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)],[13]) ).
thf(37,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_50_converse__rtrancl__induct2) ).
thf(223,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)],[37]) ).
thf(60,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_46_prod__cases6) ).
thf(306,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)],[60]) ).
thf(99,axiom,
! [TA: $tType,A: 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: char @ list,C: char @ list] :
( ( A @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
=> ( B @ class @ ( C @ class @ ( A @ ( TA @ widen ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_widen__subcls) ).
thf(473,plain,
! [TA: $tType,A: 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: char @ list,C: char @ list] :
( ( A @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( B @ ( C @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
=> ( B @ class @ ( C @ class @ ( A @ ( TA @ widen ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(8,axiom,
! [TA: $tType,A: TA @ exp,B: TA,C: char @ list,D: TA @ exp,E: TA @ exp,F: TA,G: char @ list,H: TA @ exp] :
( ( ( E @ ( F @ ( G @ ( H @ ( TA @ tryCatch ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ tryCatch ) ) ) ) ) )
<=> ( ( E = A )
& ( F = B )
& ( G = C )
& ( H = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_exp_Osimps_I15_J) ).
thf(123,plain,
! [TA: $tType,A: TA @ exp,B: TA,C: char @ list,D: TA @ exp,E: TA @ exp,F: TA,G: char @ list,H: TA @ exp] :
( ( ( ( E = A )
& ( F = B )
& ( G = C )
& ( H = D ) )
=> ( ( E @ ( F @ ( G @ ( H @ ( TA @ tryCatch ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ tryCatch ) ) ) ) ) ) )
& ( ( ( E @ ( F @ ( G @ ( H @ ( TA @ tryCatch ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ tryCatch ) ) ) ) ) )
=> ( ( E = A )
& ( F = B )
& ( G = C )
& ( H = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,axiom,
! [TA: $tType,A: char @ list,B: char @ list,C: ty,D: char @ list,E: char @ list,F: 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 @ ( F @ ( TA @ has_field ) ) ) ) ) )
=> ( ( F @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( E @ ( A @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
=> ( B @ ( C @ ( D @ ( A @ ( F @ ( TA @ has_field ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_has__field__mono) ).
thf(194,plain,
! [TA: $tType,A: char @ list,B: char @ list,C: ty,D: char @ list,E: char @ list,F: 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 @ ( F @ ( TA @ has_field ) ) ) ) ) )
=> ( ( F @ ( TA @ subcls1 ) @ ( char @ list @ transitive_rtrancl ) @ ( E @ ( A @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( char @ list @ ( char @ list @ product_prod ) @ member ) ) )
=> ( B @ ( C @ ( D @ ( A @ ( F @ ( TA @ has_field ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(28,axiom,
! [A: char @ list,B: char @ list,C: val,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( E @ ( F @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_red__reds_OFAssRed2) ).
thf(199,plain,
! [A: char @ list,B: char @ list,C: val,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( E @ ( F @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( A @ ( B @ ( C @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,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_21_rtrancl__idemp) ).
thf(182,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)],[21]) ).
thf(68,axiom,
c1 @ class @ ( ea @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_wt_092_060_094isub_0621) ).
thf(370,plain,
c1 @ class @ ( ea @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(94,axiom,
! [A: char @ list] :
( ( A @ class )
!= void ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Type_Oty_Osimps_I9_J) ).
thf(463,plain,
! [A: char @ list] :
( ( A @ class )
!= void ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(97,axiom,
t_2 @ ( e_2 @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_wt_092_060_094isub_0622_H) ).
thf(470,plain,
t_2 @ ( e_2 @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(75,axiom,
! [TA: $tType,A: ty,B: char @ list,C: 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 @ ( B @ class @ ( C @ ( TA @ widen ) ) ) )
=> ? [D: char @ list] :
( A
= ( D @ class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Class__widen) ).
thf(386,plain,
! [TA: $tType,A: ty,B: char @ list,C: 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 @ ( B @ class @ ( C @ ( TA @ widen ) ) ) )
=> ? [D: char @ list] :
( A
= ( D @ class ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(88,axiom,
u @ ( e_a @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_wt_092_060_094isub_0621_H) ).
thf(446,plain,
u @ ( e_a @ ( e @ ( h_a @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(39,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_45_prod__induct6) ).
thf(231,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)],[39]) ).
thf(30,axiom,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( E @ ( A @ ( B @ ( C @ ( F @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_red__reds_OFAssRed1) ).
thf(203,plain,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( E @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( E @ ( A @ ( B @ ( C @ ( F @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ fAss ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3,axiom,
! [TA: $tType,A: TA @ exp,B: val] :
( ( B @ ( TA @ val1 ) )
!= ( A @ ( TA @ throw ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_exp_Osimps_I90_J) ).
thf(104,plain,
! [TA: $tType,A: TA @ exp,B: val] :
( ( B @ ( TA @ val1 ) )
!= ( A @ ( TA @ throw ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(41,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(235,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)],[41]) ).
thf(102,axiom,
tf @ ( t_2 @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_sub) ).
thf(478,plain,
tf @ ( t_2 @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(73,axiom,
p @ red @ ( l_a @ ( h_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( ea @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_red) ).
thf(383,plain,
p @ red @ ( l_a @ ( h_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( e_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( ea @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(56,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_49_rtrancl__induct2) ).
thf(287,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)],[56]) ).
thf(59,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_68_converse__rtrancl__induct) ).
thf(300,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)],[59]) ).
thf(89,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_FAssRed1_I2_J) ).
thf(447,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun )] :
( ( la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( B @ ( p @ typeSa976492716_sconf ) ) )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(62,axiom,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: val,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ tryCatch ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_TryRedsVal) ).
thf(315,plain,
! [A: char @ list @ exp,B: char @ list,C: char @ list,D: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),F: val,G: val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ),H: char @ list @ exp] :
( ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( D @ red @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ transitive_rtrancl ) @ ( E @ ( F @ ( char @ list @ val1 ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( A @ ( B @ ( C @ ( H @ ( char @ list @ tryCatch ) ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(16,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_48_prod__induct5) ).
thf(168,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)],[16]) ).
thf(11,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_51_converse__rtranclE2) ).
thf(146,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)],[11]) ).
thf(24,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_27_converse__rtrancl__into__rtrancl) ).
thf(190,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)],[24]) ).
thf(42,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_69_rtrancl__induct) ).
thf(239,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)],[42]) ).
thf(9,axiom,
! [TA: $tType,A: val,B: TA @ exp,C: TA,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ tryCatch ) ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_exp_Osimps_I93_J) ).
thf(136,plain,
! [TA: $tType,A: val,B: TA @ exp,C: TA,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ tryCatch ) ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(81,axiom,
! [A: char @ list] :
( void
!= ( A @ class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Type_Oty_Osimps_I8_J) ).
thf(400,plain,
! [A: char @ list] :
( void
!= ( A @ class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(64,axiom,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ),H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( I @ ( B @ ( H @ ( C @ wTrt ) ) ) ) )
=> ( ( H @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ) )
=> ( E @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_red__preserves__hconf) ).
thf(326,plain,
! [A: ty,B: ty @ option @ ( char @ list @ fun ),C: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp,G: val @ option @ ( char @ list @ fun ),H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),I: char @ list @ exp] :
( ( C @ red @ ( D @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( A @ ( I @ ( B @ ( H @ ( C @ wTrt ) ) ) ) )
=> ( ( H @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ) )
=> ( E @ ( C @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(4,axiom,
! [TA: $tType,A: val,B: TA @ exp] :
( ( B @ ( TA @ throw ) )
!= ( A @ ( TA @ val1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_exp_Osimps_I91_J) ).
thf(107,plain,
! [TA: $tType,A: val,B: TA @ exp] :
( ( B @ ( TA @ throw ) )
!= ( A @ ( TA @ val1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(47,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_24_widen__trans) ).
thf(254,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)],[47]) ).
thf(61,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_58_rtranclE) ).
thf(309,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)],[61]) ).
thf(479,plain,
$false,
inference(e,[status(thm)],[317,205,176,391,282,139,395,249,468,170,276,269,120,247,384,340,404,185,436,389,372,110,344,196,460,284,152,216,475,179,376,211,221,293,396,428,233,201,160,392,192,429,467,229,461,456,328,471,256,173,371,298,430,166,279,187,113,219,274,377,451,245,434,271,477,103,213,251,155,223,306,473,123,194,199,182,370,463,470,386,446,231,203,104,235,478,383,287,300,447,315,168,146,190,239,136,400,326,107,254,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW572_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n007.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 16:11:39 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.87/1.35 % [INFO] Parsing done (358ms).
% 1.87/1.37 % [INFO] Running in sequential loop mode.
% 3.14/1.77 % [INFO] eprover registered as external prover.
% 3.14/1.78 % [INFO] Scanning for conjecture ...
% 3.79/2.02 % [INFO] Found a conjecture (or negated_conjecture) and 102 axioms. Running axiom selection ...
% 4.87/2.21 % [INFO] Axiom selection finished. Selected 100 axioms (removed 2 axioms).
% 5.97/2.58 % [INFO] Problem is typed first-order (TPTP TFF).
% 6.31/2.61 % [INFO] Type checking passed.
% 6.31/2.62 % [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 ...
% 93.05/76.18 % External prover 'e' found a proof!
% 93.05/76.18 % [INFO] Killing All external provers ...
% 93.05/76.19 % Time passed: 75630ms (effective reasoning time: 74815ms)
% 93.05/76.19 % 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)>
% 93.05/76.19 % Axioms used in derivation (100): fact_73_red__preserves__sconf, fact_95_exp_Osimps_I92_J, fact_82_hext__trans, fact_35_split__paired__All, fact_66_WTrt__elim__cases_I8_J, fact_0_UClass, fact_54_split__paired__Ex, fact_48_prod__induct5, fact_34_Pair__eq, fact_9_sub, fact_45_prod__induct6, fact_17_FAssRed1_I3_J, fact_13_Type_Oty_Orecs_I5_J, fact_97_exp_Osimps_I181_J, fact_7_wt_092_060_094isub_0622, fact_30_wt, fact_77_red__hext__incr, fact_79_red__lcl__add, fact_29_FAssRed1_I4_J, fact_23_has__field__mono, fact_75_mem__def, fact_12_conf, fact_47_prod__cases5, fact_83_lconf__hext, fact_94_exp_Osimps_I91_J, fact_8_UsubC, fact_57_red__preserves__hconf, fact_22_r__into__rtrancl, fact_89_FAssRedsThrow2, fact_1_wt_092_060_094isub_0621_H, fact_76_Red__lcl__add, fact_86_exp_Osimps_I79_J, fact_19_has, fact_11_IH, fact_93_exp_Osimps_I90_J, fact_50_converse__rtrancl__induct2, fact_3_Type_Oty_Oinject, fact_58_rtranclE, fact_42_widen_Osimps, fact_41_widen__Class, fact_16_rtrancl_Ortrancl__refl, fact_38_Type_Oty_Osimps_I20_J, fact_32_calculation, fact_31__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_061_061_062_AEX_AT_H_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_092_060bullet_062F_123D_125_A_058_061_Ae_092_060_094isub_0622_A_058_AT_H_A_G_AP_A_092_060turnstile_062_AT_H_A_092_060le_062_AT_096, fact_59_Type_Oty_Osimps_I8_J, fact_67_converse__rtranclE, fact_18_widen__refl, fact_20_FAssRed1_I2_J, fact_46_prod__cases6, fact_5_assms, fact_26_rtrancl_Ortrancl__into__rtrancl, fact_91_exp_Osimps_I14_J, fact_27_converse__rtrancl__into__rtrancl, fact_85_exp_Osimps_I3_J, fact_98_exp_Osimps_I180_J, fact_39_Type_Oty_Orecs_I4_J, fact_80_hext__refl, fact_68_converse__rtrancl__induct, fact_90_TryRedsVal, fact_62_Type_Oty_Osimps_I7_J, fact_99_exp_Osimps_I182_J, fact_28_red, fact_36_widen__null, fact_63_Type_Oty_Orecs_I1_J, fact_21_rtrancl__idemp, fact_24_widen__trans, fact_81_map__add__assoc, fact_33_Class__widen, fact_64_WTrtFAss, fact_49_rtrancl__induct2, fact_43_red__reds_OFAssRed1, fact_71_prod__induct3, fact_40_Pair__inject, fact_4__096_B_Bthesis_O_A_I_B_BU_O_A_091_124_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_059_AP_A_092_060turnstile_062_AU_A_092_060le_062_AClass_AC_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_74_prod_Orecs, fact_6_wt_092_060_094isub_0621, fact_37_Type_Oty_Osimps_I21_J, fact_10__Csubclass_C, fact_96_exp_Osimps_I93_J, fact_52_prod__induct4, fact_92_exp_Osimps_I15_J, fact_84_FAssReds2, fact_53_prod__cases4, fact_55_void, fact_70_red__preserves__lconf, fact_14_Class__widen__Class, fact_61_Type_Oty_Osimps_I6_J, fact_69_rtrancl__induct, fact_72_prod__cases3, fact_2_wt_092_060_094isub_0622_H, fact_25_rtrancl__trans, fact_56_exp_Osimps_I8_J, fact_15_widen__subcls, fact_65_WTrtFAssNT, fact_60_Type_Oty_Osimps_I9_J, fact_88_red__reds_OFAssRed2, fact_87_exp_Osimps_I78_J, fact_78_WTrt__hext__mono, fact_44_FAssReds1, fact_51_converse__rtranclE2
% 93.05/76.19 % No. of inferences in proof: 204
% 93.05/76.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 75630 ms resp. 74815 ms w/o parsing
% 93.63/76.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 93.63/76.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------