TSTP Solution File: SWW567_5 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWW567_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:23:43 EDT 2024
% Result : Theorem 69.18s 52.84s
% Output : Refutation 69.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 103
% Syntax : Number of formulae : 208 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 11983 ( 111 equ; 0 cnn)
% Maximal formula atoms : 340 ( 57 avg)
% Number of connectives : 27552 ( 78 ~; 0 |; 38 &;27182 @)
% ( 12 <=>; 242 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 16 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 21 con; 0-5 aty)
% Number of variables : 1182 ( 0 ^1166 !; 16 ?;1182 :)
% Comments :
%------------------------------------------------------------------------------
thf(bop1_type,type,
bop1: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(char_type,type,
char: $tType ).
thf(ty_type,type,
ty: $tType ).
thf(val1_type,type,
val1: $tType ).
thf(eval_type,type,
eval: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( exp @ ( list @ char ) ) > ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) > ( exp @ ( list @ char ) ) > ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) > $o ).
thf(hconf_type,type,
hconf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) > $o ) ).
thf(lconf_type,type,
lconf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ val1 ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > $o ) ).
thf(binOp_type,type,
binOp:
!>[TA: $tType] : ( ( exp @ TA ) > bop1 > ( exp @ TA ) > ( exp @ TA ) ) ).
thf(fAss_type,type,
fAss:
!>[TA: $tType] : ( ( exp @ TA ) > ( list @ char ) > ( list @ char ) > ( exp @ TA ) > ( exp @ TA ) ) ).
thf(val_type,type,
val:
!>[TA: $tType] : ( val1 > ( exp @ TA ) ) ).
thf(throw_type,type,
throw:
!>[TA: $tType] : ( ( exp @ TA ) > ( exp @ TA ) ) ).
thf(in_rel_type,type,
in_rel:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TA ) @ bool ) > TB > TA > $o ) ).
thf(wf_J_mdecl_type,type,
wf_J_mdecl: fun @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) ).
thf(map_add_type,type,
map_add:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( option @ TA ) ) > ( fun @ TB @ ( option @ TA ) ) > ( fun @ TB @ ( option @ TA ) ) ) ).
thf(refl_type,type,
refl:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(hext_type,type,
hext: ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) > $o ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_prod_rec_type,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(red_type,type,
red: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ bool ) ).
thf(hp_type,type,
hp: ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) ).
thf(transitive_rtrancl_type,type,
transitive_rtrancl:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).
thf(widen_type,type,
widen:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ty > ty > $o ) ).
thf(typeSa976492716_sconf_type,type,
typeSa976492716_sconf: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) > $o ).
thf(is_refT_type,type,
is_refT: ty > $o ).
thf(wwf_J_mdecl_type,type,
wwf_J_mdecl: fun @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) ).
thf(wf_prog_type,type,
wf_prog:
!>[TA: $tType] : ( ( fun @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) @ bool ) ) ) > ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > $o ) ).
thf(wTrt_type,type,
wTrt: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > ( exp @ ( list @ char ) ) > ty > $o ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(e_type,type,
e: fun @ ( list @ char ) @ ( option @ ty ) ).
thf(p_type,type,
p: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ).
thf(t_type,type,
t: ty ).
thf(bop_type,type,
bop: bop1 ).
thf(e_2_type,type,
e_2: exp @ ( list @ char ) ).
thf(e_21_type,type,
e_21: exp @ ( list @ char ) ).
thf(h_a_type,type,
h_a: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ).
thf(ha_type,type,
ha: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ).
thf(l_a_type,type,
l_a: fun @ ( list @ char ) @ ( option @ val1 ) ).
thf(la_type,type,
la: fun @ ( list @ char ) @ ( option @ val1 ) ).
thf(v_1_type,type,
v_1: val1 ).
thf(97,axiom,
! [A: product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ),B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( pp @ ( aa @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool @ ( aa @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) @ ( aa @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) @ wf_J_mdecl @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool @ ( aa @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) @ ( aa @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) @ wwf_J_mdecl @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_wf__mdecl__wwf__mdecl) ).
thf(385,plain,
! [A: product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ),B: list @ char,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( pp @ ( aa @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool @ ( aa @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) @ ( aa @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) @ wf_J_mdecl @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool @ ( aa @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) @ ( aa @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) @ wwf_J_mdecl @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(21,axiom,
! [TA: $tType,A: exp @ TA,B: bop1,C: exp @ TA,D: exp @ TA] :
( ( throw @ TA @ D )
!= ( binOp @ TA @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_exp_Osimps_I113_J) ).
thf(173,plain,
! [TA: $tType,A: exp @ TA,B: bop1,C: exp @ TA,D: exp @ TA] :
( ( throw @ TA @ D )
!= ( binOp @ TA @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(91,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: fun @ ( list @ char ) @ ( option @ val1 ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),F: exp @ ( list @ char ),G: fun @ ( list @ char ) @ ( option @ val1 ),H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ I @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ H @ G ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ E @ D ) ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ H @ B @ I @ A )
=> ( ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ H @ G @ B )
=> ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ E @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_red__preserves__lconf) ).
thf(347,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: fun @ ( list @ char ) @ ( option @ val1 ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),F: exp @ ( list @ char ),G: fun @ ( list @ char ) @ ( option @ val1 ),H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ I @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ H @ G ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ E @ D ) ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ H @ B @ I @ A )
=> ( ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ H @ G @ B )
=> ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ E @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(93,axiom,
! [TA: $tType,A: exp @ TA,B: bop1,C: exp @ TA,D: exp @ TA,E: bop1,F: exp @ TA] :
( ( ( binOp @ TA @ F @ E @ D )
= ( binOp @ TA @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_exp_Osimps_I4_J) ).
thf(352,plain,
! [TA: $tType,A: exp @ TA,B: bop1,C: exp @ TA,D: exp @ TA,E: bop1,F: exp @ TA] :
( ( ( ( binOp @ TA @ F @ E @ D )
= ( binOp @ TA @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( binOp @ TA @ F @ E @ D )
= ( binOp @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(6,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: list @ char,D: list @ char,E: exp @ TA] :
( ( fAss @ TA @ E @ D @ C @ B )
!= ( throw @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_exp_Osimps_I180_J) ).
thf(115,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: list @ char,D: list @ char,E: exp @ TA] :
( ( fAss @ TA @ E @ D @ C @ B )
!= ( throw @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(61,axiom,
typeSa976492716_sconf @ p @ e @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_conf) ).
thf(276,plain,
typeSa976492716_sconf @ p @ e @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(96,axiom,
! [TA: $tType,A: val1,B: val1] :
( ( ( val @ TA @ B )
= ( val @ TA @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_exp_Osimps_I3_J) ).
thf(379,plain,
! [TA: $tType,A: val1,B: val1] :
( ( ( ( val @ TA @ B )
= ( val @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( val @ TA @ B )
= ( val @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(33,axiom,
! [A: ty,B: exp @ ( list @ char ),C: fun @ ( list @ char ) @ ( option @ ty ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ E @ D @ C @ ( throw @ ( list @ char ) @ B ) @ A )
=> ~ ! [F: ty] :
( ( wTrt @ E @ D @ C @ B @ F )
=> ~ ( is_refT @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_WTrt__elim__cases_I4_J) ).
thf(202,plain,
! [A: ty,B: exp @ ( list @ char ),C: fun @ ( list @ char ) @ ( option @ ty ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ E @ D @ C @ ( throw @ ( list @ char ) @ B ) @ A )
=> ~ ! [F: ty] :
( ( wTrt @ E @ D @ C @ B @ F )
=> ~ ( is_refT @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [TA: $tType,A: val1,B: exp @ TA,C: bop1,D: exp @ TA] :
( ( binOp @ TA @ D @ C @ B )
!= ( val @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_exp_Osimps_I71_J) ).
thf(185,plain,
! [TA: $tType,A: val1,B: exp @ TA,C: bop1,D: exp @ TA] :
( ( binOp @ TA @ D @ C @ B )
!= ( val @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prod__induct6) ).
thf(288,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(72,axiom,
wTrt @ p @ ha @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_21 ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_BinOpRed2_I4_J) ).
thf(301,plain,
wTrt @ p @ ha @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_21 ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(99,axiom,
! [A: list @ char,B: list @ char,C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: exp @ ( list @ char ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: val1,I: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),J: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ J @ I ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( val @ ( list @ char ) @ H ) @ G ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ F ) ) )
=> ( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ D ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ F ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ J @ B @ A @ E ) @ I ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ D ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_FAssRedsThrow2) ).
thf(389,plain,
! [A: list @ char,B: list @ char,C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: exp @ ( list @ char ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: val1,I: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),J: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ J @ I ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( val @ ( list @ char ) @ H ) @ G ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ F ) ) )
=> ( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ D ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ F ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ J @ B @ A @ E ) @ I ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ D ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(4,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(110,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(66,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: list @ char,E: list @ char,F: val1] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ F ) @ E @ D @ ( throw @ ( list @ char ) @ C ) ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_red__reds_OFAssThrow2) ).
thf(284,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: list @ char,E: list @ char,F: val1] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ F ) @ E @ D @ ( throw @ ( list @ char ) @ C ) ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_prod__cases6) ).
thf(228,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(78,axiom,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: val1] :
( ( val @ TA @ E )
!= ( fAss @ TA @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_exp_Osimps_I78_J) ).
thf(316,plain,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: val1] :
( ( val @ TA @ E )
!= ( fAss @ TA @ D @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_split__paired__Ex) ).
thf(261,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(38,axiom,
! [A: bop1,B: val1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ B ) @ A @ G ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ B ) @ A @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_BinOp2Reds) ).
thf(216,plain,
! [A: bop1,B: val1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ B ) @ A @ G ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ B ) @ A @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( option @ TB ),B: fun @ TA @ ( option @ TB ),C: fun @ TA @ ( option @ TB )] :
( ( map_add @ TA @ TB @ C @ ( map_add @ TA @ TB @ B @ A ) )
= ( map_add @ TA @ TB @ ( map_add @ TA @ TB @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_map__add__assoc) ).
thf(164,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( option @ TB ),B: fun @ TA @ ( option @ TB ),C: fun @ TA @ ( option @ TB )] :
( ( map_add @ TA @ TB @ C @ ( map_add @ TA @ TB @ B @ A ) )
= ( map_add @ TA @ TB @ ( map_add @ TA @ TB @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(37,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ ( transitive_rtrancl @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_converse__rtranclE) ).
thf(211,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ ( transitive_rtrancl @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(47,axiom,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ F ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ F ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_FAssRedsThrow1) ).
thf(238,plain,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ F ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ F ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(40,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: fun @ ( list @ char ) @ ( option @ val1 ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),F: exp @ ( list @ char ),G: fun @ ( list @ char ) @ ( option @ val1 ),H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ I @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ H @ G ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ E @ D ) ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ H @ B @ I @ A )
=> ( ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ H )
=> ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_red__preserves__hconf) ).
thf(221,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: fun @ ( list @ char ) @ ( option @ val1 ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),F: exp @ ( list @ char ),G: fun @ ( list @ char ) @ ( option @ val1 ),H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ I @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ H @ G ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ E @ D ) ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ H @ B @ I @ A )
=> ( ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ H )
=> ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ D ) @ C ) )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ B )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ I @ J ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ I ) @ J ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ G ) @ H ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_converse__rtrancl__induct2) ).
thf(293,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ D ) @ C ) )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ B )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ I @ J ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ I ) @ J ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ G ) @ H ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(11,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA] :
( ( ( throw @ TA @ B )
= ( throw @ TA @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_exp_Osimps_I14_J) ).
thf(133,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA] :
( ( ( ( throw @ TA @ B )
= ( throw @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( throw @ TA @ B )
= ( throw @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(56,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: fun @ ( list @ char ) @ ( option @ val1 ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),D: exp @ ( list @ char ),E: fun @ ( list @ char ) @ ( option @ val1 ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ F @ E ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ C @ B ) ) ) @ ( red @ A ) )
=> ( hext @ F @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_red__hext__incr) ).
thf(265,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: fun @ ( list @ char ) @ ( option @ val1 ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),D: exp @ ( list @ char ),E: fun @ ( list @ char ) @ ( option @ val1 ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ F @ E ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ C @ B ) ) ) @ ( red @ A ) )
=> ( hext @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(76,axiom,
! [A: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),B: exp @ ( list @ char ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wwf_J_mdecl @ G )
=> ( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ C ) ) @ ( red @ G ) )
=> ( ( eval @ G @ D @ C @ B @ A )
=> ( eval @ G @ F @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_extend__1__eval) ).
thf(312,plain,
! [A: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),B: exp @ ( list @ char ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wwf_J_mdecl @ G )
=> ( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ C ) ) @ ( red @ G ) )
=> ( ( eval @ G @ D @ C @ B @ A )
=> ( eval @ G @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(74,axiom,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: exp @ TA,F: bop1,G: exp @ TA] :
( ( binOp @ TA @ G @ F @ E )
!= ( fAss @ TA @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_exp_Osimps_I100_J) ).
thf(307,plain,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: exp @ TA,F: bop1,G: exp @ TA] :
( ( binOp @ TA @ G @ F @ E )
!= ( fAss @ TA @ D @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ F ) @ E ) )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ G @ H ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ B )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ G ) @ H ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ I ) @ J ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rtrancl__induct2) ).
thf(233,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ F ) @ E ) )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ F @ E ) @ ( product_Pair @ TB @ TA @ G @ H ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ B ) )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ B )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ G ) @ H ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ I ) @ J ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(50,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ ( transitive_rtrancl @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_rtrancl_Ortrancl__refl) ).
thf(248,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ ( transitive_rtrancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(58,axiom,
wTrt @ p @ ha @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_21 ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_wt) ).
thf(270,plain,
wTrt @ p @ ha @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_21 ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(85,axiom,
! [A: exp @ ( list @ char ),B: bop1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_BinOpRedsThrow1) ).
thf(334,plain,
! [A: exp @ ( list @ char ),B: bop1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(73,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ ( transitive_rtrancl @ TA @ A ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rtranclE) ).
thf(302,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( C != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ ( transitive_rtrancl @ TA @ A ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(92,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty )] :
( ( typeSa976492716_sconf @ p @ B @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ B @ e_21 @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_2 @ C )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_BinOpRed2_I2_J) ).
thf(349,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty )] :
( ( typeSa976492716_sconf @ p @ B @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ B @ e_21 @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_2 @ C )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(52,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ A ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_ThrowRedsThrow) ).
thf(252,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ A ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(31,axiom,
! [A: bop1,B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: exp @ ( list @ char ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: val1,G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char ),I: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( eval @ I @ H @ G @ ( val @ ( list @ char ) @ F ) @ E )
=> ( ( eval @ I @ D @ E @ ( throw @ ( list @ char ) @ C ) @ B )
=> ( eval @ I @ ( binOp @ ( list @ char ) @ H @ A @ D ) @ G @ ( throw @ ( list @ char ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_eval__evals_OBinOpThrow2) ).
thf(197,plain,
! [A: bop1,B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: exp @ ( list @ char ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: val1,G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char ),I: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( eval @ I @ H @ G @ ( val @ ( list @ char ) @ F ) @ E )
=> ( ( eval @ I @ D @ E @ ( throw @ ( list @ char ) @ C ) @ B )
=> ( eval @ I @ ( binOp @ ( list @ char ) @ H @ A @ D ) @ G @ ( throw @ ( list @ char ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(82,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: bop1,E: val1] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ E ) @ D @ ( throw @ ( list @ char ) @ C ) ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_red__reds_OBinOpThrow2) ).
thf(329,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: bop1,E: val1] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ E ) @ D @ ( throw @ ( list @ char ) @ C ) ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(103,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: bop1,E: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( throw @ ( list @ char ) @ E ) @ D @ C ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ B ) ) @ ( red @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_red__reds_OBinOpThrow1) ).
thf(403,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: bop1,E: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( throw @ ( list @ char ) @ E ) @ D @ C ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ B ) ) @ ( red @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_converse__rtrancl__into__rtrancl) ).
thf(188,plain,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ bool,B: TB,C: TA,D: TB,E: TA] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ D ) @ ( product_Pair @ TA @ TB @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ A ) )
=> ( ( ( product_Pair @ TA @ TB @ E @ D )
!= ( product_Pair @ TA @ TB @ C @ B ) )
=> ~ ! [F: TA,G: TB] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ D ) @ ( product_Pair @ TA @ TB @ F @ G ) ) @ A )
=> ~ ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ F @ G ) @ ( product_Pair @ TA @ TB @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_converse__rtranclE2) ).
thf(256,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ bool,B: TB,C: TA,D: TB,E: TA] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ D ) @ ( product_Pair @ TA @ TB @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ A ) )
=> ( ( ( product_Pair @ TA @ TB @ E @ D )
!= ( product_Pair @ TA @ TB @ C @ B ) )
=> ~ ! [F: TA,G: TB] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ D ) @ ( product_Pair @ TA @ TB @ F @ G ) ) @ A )
=> ~ ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ F @ G ) @ ( product_Pair @ TA @ TB @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(42,axiom,
wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wf_J_mdecl @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_assms) ).
thf(225,plain,
wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wf_J_mdecl @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(87,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: list @ char,E: list @ char,F: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( throw @ ( list @ char ) @ F ) @ E @ D @ C ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ F ) @ B ) ) @ ( red @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_red__reds_OFAssThrow1) ).
thf(339,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: list @ char,E: list @ char,F: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( throw @ ( list @ char ) @ F ) @ E @ D @ C ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ F ) @ B ) ) @ ( red @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(29,axiom,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) ) @ ( red @ D ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ F @ C @ B @ A ) @ E ) ) @ ( red @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_red__reds_OFAssRed1) ).
thf(193,plain,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) ) @ ( red @ D ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ F @ C @ B @ A ) @ E ) ) @ ( red @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1,conjecture,
? [A: ty] :
( ( wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ A )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: ty] :
( ( wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ A )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(105,plain,
~ ? [A: ty] :
( ( wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ A )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,axiom,
! [TA: $tType,A: val1,B: exp @ TA] :
( ( throw @ TA @ B )
!= ( val @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_exp_Osimps_I91_J) ).
thf(205,plain,
! [TA: $tType,A: val1,B: exp @ TA] :
( ( throw @ TA @ B )
!= ( val @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,axiom,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),B: fun @ ( list @ char ) @ ( option @ ty ),C: fun @ ( list @ char ) @ ( option @ val1 ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ E @ D @ C @ B )
=> ( ( hext @ D @ A )
=> ( lconf @ TA @ E @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_lconf__hext) ).
thf(128,plain,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),B: fun @ ( list @ char ) @ ( option @ ty ),C: fun @ ( list @ char ) @ ( option @ val1 ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ E @ D @ C @ B )
=> ( ( hext @ D @ A )
=> ( lconf @ TA @ E @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(89,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ C @ B ) ) @ ( red @ A ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_red__reds_OThrowRed) ).
thf(343,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ C @ B ) ) @ ( red @ A ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(71,axiom,
! [TA: $tType,A: exp @ TA,B: bop1,C: exp @ TA,D: exp @ TA,E: list @ char,F: list @ char,G: exp @ TA] :
( ( fAss @ TA @ G @ F @ E @ D )
!= ( binOp @ TA @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_exp_Osimps_I101_J) ).
thf(298,plain,
! [TA: $tType,A: exp @ TA,B: bop1,C: exp @ TA,D: exp @ TA,E: list @ char,F: list @ char,G: exp @ TA] :
( ( fAss @ TA @ G @ F @ E @ D )
!= ( binOp @ TA @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_prod_Orecs) ).
thf(161,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(63,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( hext @ E @ A )
=> ( wTrt @ F @ A @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_WTrt__hext__mono) ).
thf(279,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( hext @ E @ A )
=> ( wTrt @ F @ A @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_rtrancl_Ortrancl__into__rtrancl) ).
thf(176,plain,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_prod__induct5) ).
thf(286,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Pair__eq) ).
thf(118,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(64,axiom,
! [A: fun @ ( list @ char ) @ ( option @ val1 ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: fun @ ( list @ char ) @ ( option @ val1 ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ val1 ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ G @ F ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ D @ C ) ) ) @ ( red @ B ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ G @ ( map_add @ ( list @ char ) @ val1 @ A @ F ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ D @ ( map_add @ ( list @ char ) @ val1 @ A @ C ) ) ) ) @ ( red @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_red__lcl__add) ).
thf(281,plain,
! [A: fun @ ( list @ char ) @ ( option @ val1 ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: fun @ ( list @ char ) @ ( option @ val1 ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ val1 ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ G @ F ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ D @ C ) ) ) @ ( red @ B ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ G @ ( map_add @ ( list @ char ) @ val1 @ A @ F ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ D @ ( map_add @ ( list @ char ) @ val1 @ A @ C ) ) ) ) @ ( red @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(100,axiom,
! [TA: $tType,A: exp @ TA,B: bop1,C: exp @ TA,D: val1] :
( ( val @ TA @ D )
!= ( binOp @ TA @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_exp_Osimps_I70_J) ).
thf(391,plain,
! [TA: $tType,A: exp @ TA,B: bop1,C: exp @ TA,D: val1] :
( ( val @ TA @ D )
!= ( binOp @ TA @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(13,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) )] : ( hext @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_hext__refl) ).
thf(144,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) )] : ( hext @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [A: exp @ ( list @ char ),B: bop1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ E @ B @ A ) @ D ) ) @ ( red @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_red__reds_OBinOpRed1) ).
thf(181,plain,
! [A: exp @ ( list @ char ),B: bop1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ E @ B @ A ) @ D ) ) @ ( red @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(95,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ ( throw @ ( list @ char ) @ C ) ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_red__reds_OThrowThrow) ).
thf(377,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char )] : ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ ( throw @ ( list @ char ) @ C ) ) @ B ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( red @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
<=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_pred__equals__eq2) ).
thf(362,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ! [C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(59,axiom,
! [A: ty,B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( is_refT @ B )
=> ( wTrt @ F @ E @ D @ ( throw @ ( list @ char ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_WTrtThrow) ).
thf(271,plain,
! [A: ty,B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( is_refT @ B )
=> ( wTrt @ F @ E @ D @ ( throw @ ( list @ char ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(35,axiom,
wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096P_ME_Mh_H_A_092_060turnstile_062_AVal_Av_092_060_094isub_0621_A_092_060guillemotleft_062bop_092_060guillemotright_062_Ae_092_060_094isub_0622_H_A_058_AT_096) ).
thf(208,plain,
wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(98,axiom,
! [A: list @ char,B: list @ char,C: val1,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ C ) @ B @ A @ H ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ C ) @ B @ A @ F ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_FAssReds2) ).
thf(387,plain,
! [A: list @ char,B: list @ char,C: val1,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ C ) @ B @ A @ H ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ C ) @ B @ A @ F ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(90,axiom,
! [A: fun @ ( list @ char ) @ ( option @ val1 ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: fun @ ( list @ char ) @ ( option @ val1 ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ val1 ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ G @ F ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ D @ C ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ B ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ G @ ( map_add @ ( list @ char ) @ val1 @ A @ F ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ D @ ( map_add @ ( list @ char ) @ val1 @ A @ C ) ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Red__lcl__add) ).
thf(345,plain,
! [A: fun @ ( list @ char ) @ ( option @ val1 ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: fun @ ( list @ char ) @ ( option @ val1 ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),E: exp @ ( list @ char ),F: fun @ ( list @ char ) @ ( option @ val1 ),G: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ G @ F ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ D @ C ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ B ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ G @ ( map_add @ ( list @ char ) @ val1 @ A @ F ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ D @ ( map_add @ ( list @ char ) @ val1 @ A @ C ) ) ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(48,axiom,
! [A: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),B: exp @ ( list @ char ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: val1,E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( eval @ E @ ( val @ ( list @ char ) @ D ) @ C @ B @ A )
=> ~ ( ( B
= ( val @ ( list @ char ) @ D ) )
=> ( A != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_eval__cases_I2_J) ).
thf(240,plain,
! [A: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),B: exp @ ( list @ char ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: val1,E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( eval @ E @ ( val @ ( list @ char ) @ D ) @ C @ B @ A )
=> ~ ( ( B
= ( val @ ( list @ char ) @ D ) )
=> ( A != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_prod_Oexhaust) ).
thf(130,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_split__paired__All) ).
thf(399,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(41,axiom,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ F @ C @ B @ A ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_FAssReds1) ).
thf(223,plain,
! [A: exp @ ( list @ char ),B: list @ char,C: list @ char,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ H @ C @ B @ A ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ F @ C @ B @ A ) @ E ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(101,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ D ) )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( ( pp @ ( aa @ TA @ bool @ A @ E ) )
=> ( pp @ ( aa @ TA @ bool @ A @ F ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_rtrancl__induct) ).
thf(394,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ D ) )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( ( pp @ ( aa @ TA @ bool @ A @ E ) )
=> ( pp @ ( aa @ TA @ bool @ A @ F ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(43,axiom,
! [A: exp @ ( list @ char ),B: bop1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ E @ B @ A ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_BinOp1Reds) ).
thf(226,plain,
! [A: exp @ ( list @ char ),B: bop1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ G @ B @ A ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ E @ B @ A ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(18,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(167,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(36,axiom,
! [TA: $tType,A: ty,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_widen__refl) ).
thf(209,plain,
! [TA: $tType,A: ty,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(5,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( transitive_rtrancl @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( transitive_rtrancl @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_rtrancl__idemp) ).
thf(112,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( transitive_rtrancl @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( transitive_rtrancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(81,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ A ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_ThrowReds) ).
thf(327,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ C @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ A ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ E ) @ D ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(75,axiom,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_rtrancl__trans) ).
thf(310,plain,
! [TA: $tType,A: TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ A ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(32,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty )] :
( ( typeSa976492716_sconf @ p @ B @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ B @ e_21 @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_2 @ C )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_IH) ).
thf(199,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty )] :
( ( typeSa976492716_sconf @ p @ B @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ) )
=> ( ( wTrt @ p @ ha @ B @ e_21 @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_2 @ C )
& ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(83,axiom,
typeSa976492716_sconf @ p @ e @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_BinOpRed2_I3_J) ).
thf(331,plain,
typeSa976492716_sconf @ p @ e @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_prod__cases3) ).
thf(336,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(77,axiom,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wf_J_mdecl @ A )
=> ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wwf_J_mdecl @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_wf__prog__wwf__prog) ).
thf(314,plain,
! [A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wf_J_mdecl @ A )
=> ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wwf_J_mdecl @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(39,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( refl @ TA @ A )
<=> ! [B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Nitpick_Orefl_H__def) ).
thf(218,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( ( refl @ TA @ A )
=> ! [B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A ) )
& ( ! [B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A )
=> ( refl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(51,axiom,
! [A: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),B: exp @ ( list @ char ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wwf_J_mdecl @ G )
=> ( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ G ) ) )
=> ( ( eval @ G @ D @ C @ B @ A )
=> ( eval @ G @ F @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_extend__eval) ).
thf(250,plain,
! [A: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),B: exp @ ( list @ char ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wwf_J_mdecl @ G )
=> ( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ G ) ) )
=> ( ( eval @ G @ D @ C @ B @ A )
=> ( eval @ G @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(45,axiom,
! [A: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),B: exp @ ( list @ char ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wwf_J_mdecl @ E )
=> ( ( eval @ E @ D @ C @ B @ A )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ C ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ B @ A ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_big__by__small) ).
thf(231,plain,
! [A: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),B: exp @ ( list @ char ),C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ wwf_J_mdecl @ E )
=> ( ( eval @ E @ D @ C @ B @ A )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ C ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ B @ A ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(79,axiom,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: bop1,D: exp @ TA] :
( ( binOp @ TA @ D @ C @ B )
!= ( throw @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_exp_Osimps_I112_J) ).
thf(319,plain,
! [TA: $tType,A: exp @ TA,B: exp @ TA,C: bop1,D: exp @ TA] :
( ( binOp @ TA @ D @ C @ B )
!= ( throw @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(158,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ ( hp @ F ) @ B @ G @ A )
=> ( ( typeSa976492716_sconf @ C @ B @ F )
=> ( typeSa976492716_sconf @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_red__preserves__sconf) ).
thf(171,plain,
! [A: ty,B: fun @ ( list @ char ) @ ( option @ ty ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( ( wTrt @ C @ ( hp @ F ) @ B @ G @ A )
=> ( ( typeSa976492716_sconf @ C @ B @ F )
=> ( typeSa976492716_sconf @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Pair__inject) ).
thf(139,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(69,axiom,
! [TA: $tType,A: val1,B: exp @ TA,C: list @ char,D: list @ char,E: exp @ TA] :
( ( fAss @ TA @ E @ D @ C @ B )
!= ( val @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_exp_Osimps_I79_J) ).
thf(290,plain,
! [TA: $tType,A: val1,B: exp @ TA,C: list @ char,D: list @ char,E: exp @ TA] :
( ( fAss @ TA @ E @ D @ C @ B )
!= ( val @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(49,axiom,
! [A: bop1,B: val1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ B ) @ A @ G ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ B ) @ A @ E ) @ D ) ) @ ( red @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_red__reds_OBinOpRed2) ).
thf(246,plain,
! [A: bop1,B: val1,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),D: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ G @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ E @ D ) ) @ ( red @ C ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ B ) @ A @ G ) @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ B ) @ A @ E ) @ D ) ) @ ( red @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(19,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(168,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: exp @ TA,F: list @ char,G: list @ char,H: exp @ TA] :
( ( ( fAss @ TA @ H @ G @ F @ E )
= ( fAss @ TA @ D @ C @ B @ A ) )
<=> ( ( H = D )
& ( G = C )
& ( F = B )
& ( E = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_exp_Osimps_I8_J) ).
thf(146,plain,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: exp @ TA,F: list @ char,G: list @ char,H: exp @ TA] :
( ( ( ( fAss @ TA @ H @ G @ F @ E )
= ( fAss @ TA @ D @ C @ B @ A ) )
=> ( ( H = D )
& ( G = C )
& ( F = B )
& ( E = A ) ) )
& ( ( ( H = D )
& ( G = C )
& ( F = B )
& ( E = A ) )
=> ( ( fAss @ TA @ H @ G @ F @ E )
= ( fAss @ TA @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_prod__cases5) ).
thf(405,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(28,axiom,
! [TA: $tType,A: exp @ TA,B: val1] :
( ( val @ TA @ B )
!= ( throw @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_exp_Osimps_I90_J) ).
thf(190,plain,
! [TA: $tType,A: exp @ TA,B: val1] :
( ( val @ TA @ B )
!= ( throw @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(25,axiom,
! [TA: $tType,A: ty,B: ty,C: ty,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( widen @ TA @ D @ C @ B )
=> ( ( widen @ TA @ D @ B @ A )
=> ( widen @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_widen__trans) ).
thf(183,plain,
! [TA: $tType,A: ty,B: ty,C: ty,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( widen @ TA @ D @ C @ B )
=> ( ( widen @ TA @ D @ B @ A )
=> ( widen @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( in_rel @ TA @ TB @ C @ B @ A )
<=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_in__rel__def) ).
thf(273,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ( in_rel @ TA @ TB @ C @ B @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C )
=> ( in_rel @ TA @ TB @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(3,axiom,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: exp @ TA] :
( ( throw @ TA @ E )
!= ( fAss @ TA @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_exp_Osimps_I181_J) ).
thf(107,plain,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: exp @ TA] :
( ( throw @ TA @ E )
!= ( fAss @ TA @ D @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) )] :
( ( hext @ C @ B )
=> ( ( hext @ B @ A )
=> ( hext @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_hext__trans) ).
thf(126,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) )] :
( ( hext @ C @ B )
=> ( ( hext @ B @ A )
=> ( hext @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(88,axiom,
! [A: list @ char,B: list @ char,C: val1,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) ) @ ( red @ D ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ C ) @ B @ A @ H ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ C ) @ B @ A @ F ) @ E ) ) @ ( red @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_red__reds_OFAssRed2) ).
thf(341,plain,
! [A: list @ char,B: list @ char,C: val1,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),E: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),F: exp @ ( list @ char ),G: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),H: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ H @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ F @ E ) ) @ ( red @ D ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ C ) @ B @ A @ H ) @ G ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( fAss @ ( list @ char ) @ ( val @ ( list @ char ) @ C ) @ B @ A @ F ) @ E ) ) @ ( red @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(57,axiom,
! [A: list @ char,B: list @ char,C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: val1,H: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),I: exp @ ( list @ char ),J: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( eval @ J @ I @ H @ ( val @ ( list @ char ) @ G ) @ F )
=> ( ( eval @ J @ E @ F @ ( throw @ ( list @ char ) @ D ) @ C )
=> ( eval @ J @ ( fAss @ ( list @ char ) @ I @ B @ A @ E ) @ H @ ( throw @ ( list @ char ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_eval__evals_OFAssThrow2) ).
thf(268,plain,
! [A: list @ char,B: list @ char,C: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),D: exp @ ( list @ char ),E: exp @ ( list @ char ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: val1,H: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),I: exp @ ( list @ char ),J: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( eval @ J @ I @ H @ ( val @ ( list @ char ) @ G ) @ F )
=> ( ( eval @ J @ E @ F @ ( throw @ ( list @ char ) @ D ) @ C )
=> ( eval @ J @ ( fAss @ ( list @ char ) @ I @ B @ A @ E ) @ H @ ( throw @ ( list @ char ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(30,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ B @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ B @ ( transitive_rtrancl @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_r__into__rtrancl) ).
thf(195,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ B @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ B @ ( transitive_rtrancl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(65,axiom,
member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ e_21 @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ e_2 @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ h_a @ l_a ) ) ) @ ( red @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_red) ).
thf(283,plain,
member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ e_21 @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ ha @ la ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ e_2 @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) @ h_a @ l_a ) ) ) @ ( red @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_prod__induct4) ).
thf(332,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_prod__cases4) ).
thf(178,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(62,axiom,
! [A: bop1,B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: exp @ ( list @ char ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: val1,H: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ I @ H ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( val @ ( list @ char ) @ G ) @ F ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ E ) ) )
=> ( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ E ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ I @ A @ D ) @ H ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_BinOpRedsThrow2) ).
thf(277,plain,
! [A: bop1,B: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),C: exp @ ( list @ char ),D: exp @ ( list @ char ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),F: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),G: val1,H: product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ),I: exp @ ( list @ char )] :
( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ I @ H ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( val @ ( list @ char ) @ G ) @ F ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ E ) ) )
=> ( ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ D @ F ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ E ) ) )
=> ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( binOp @ ( list @ char ) @ I @ A @ D ) @ H ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) @ ( throw @ ( list @ char ) @ C ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val1 ) ) ) ) @ ( red @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_prod__induct3) ).
thf(254,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(80,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ F ) )
=> ( pp @ ( aa @ TA @ bool @ A @ E ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_converse__rtrancl__induct) ).
thf(322,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ C ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ A @ F ) )
=> ( pp @ ( aa @ TA @ bool @ A @ E ) ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(410,plain,
$false,
inference(e,[status(thm)],[385,173,347,352,115,276,379,202,185,288,301,389,110,284,228,316,261,216,164,211,238,221,293,133,265,312,307,233,248,270,334,302,349,252,197,329,403,188,256,225,339,193,105,205,128,343,298,161,279,176,286,118,281,391,144,181,377,362,271,208,387,345,240,130,399,223,394,226,167,209,112,327,310,199,331,336,314,218,250,231,319,158,171,139,290,246,168,146,405,190,183,273,107,126,341,268,195,283,332,178,277,254,322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW567_5 : TPTP v8.2.0. Released v6.0.0.
% 0.03/0.13 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jun 19 09:42:40 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.03/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.11/1.17 % [INFO] Parsing done (272ms).
% 2.11/1.19 % [INFO] Running in sequential loop mode.
% 2.78/1.45 % [INFO] eprover registered as external prover.
% 2.78/1.45 % [INFO] Scanning for conjecture ...
% 3.51/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 102 axioms. Running axiom selection ...
% 3.87/1.79 % [INFO] Axiom selection finished. Selected 102 axioms (removed 0 axioms).
% 5.26/2.16 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.26/2.19 % [INFO] Type checking passed.
% 5.26/2.19 % [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 ...
% 69.18/52.84 % External prover 'e' found a proof!
% 69.18/52.84 % [INFO] Killing All external provers ...
% 69.18/52.84 % Time passed: 52280ms (effective reasoning time: 51646ms)
% 69.18/52.84 % 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)>
% 69.18/52.84 % Axioms used in derivation (102): fact_4_widen__refl, fact_79_FAssRedsThrow2, fact_37_prod_Orecs, fact_29_prod__induct5, fact_50_hext__refl, fact_61_ThrowRedsThrow, fact_62_rtrancl_Ortrancl__refl, fact_67_rtrancl__trans, fact_69_converse__rtrancl__induct2, fact_83_exp_Osimps_I180_J, fact_19_wf__prog__wwf__prog, fact_51_map__add__assoc, fact_57_BinOpRedsThrow1, fact_20_in__rel__def, fact_84_exp_Osimps_I181_J, fact_43_exp_Osimps_I91_J, fact_94_extend__eval, fact_34_prod__induct3, fact_25_red__reds_OBinOpRed1, fact_12_BinOpRed2_I3_J, fact_87_red__reds_OFAssRed1, fact_63_rtrancl__idemp, fact_78_WTrt__elim__cases_I4_J, fact_28_prod__cases5, fact_49_red__reds_OBinOpThrow1, fact_40_red__lcl__add, fact_3_exp_Osimps_I4_J, fact_45_exp_Osimps_I112_J, fact_18_Pair__inject, fact_98_eval__evals_OBinOpThrow2, fact_66_rtrancl_Ortrancl__into__rtrancl, fact_5_exp_Osimps_I3_J, fact_92_FAssReds2, fact_82_exp_Osimps_I100_J, fact_6_assms, fact_54_Red__lcl__add, fact_31_prod__induct6, fact_77_WTrtThrow, fact_96_extend__1__eval, fact_7_exp_Osimps_I70_J, fact_11_IH, fact_70_rtrancl__induct2, fact_13_conf, fact_71_rtranclE, fact_86_exp_Osimps_I78_J, fact_89_red__reds_OFAssThrow1, fact_74_rtrancl__induct, fact_59_BinOp1Reds, fact_42_exp_Osimps_I14_J, fact_47_red__reds_OThrowRed, fact_56_BinOpRedsThrow2, fact_44_exp_Osimps_I90_J, fact_41_prod_Oexhaust, fact_30_prod__cases6, fact_85_exp_Osimps_I79_J, fact_65_converse__rtrancl__into__rtrancl, fact_55_hext__trans, fact_15_Pair__eq, fact_21_split__paired__Ex, fact_76_mem__def, fact_58_BinOp2Reds, fact_48_red__reds_OThrowThrow, fact_23_wf__mdecl__wwf__mdecl, fact_33_red__preserves__lconf, fact_64_r__into__rtrancl, fact_2_wt, fact_9_widen__trans, fact_80_exp_Osimps_I8_J, fact_99_eval__cases_I2_J, fact_93_FAssRedsThrow1, fact_91_red__reds_OFAssThrow2, fact_14_split__paired__All, fact_97_eval__evals_OFAssThrow2, fact_72_converse__rtranclE, fact_32_red__preserves__hconf, fact_10_BinOpRed2_I2_J, fact_90_FAssReds1, fact_46_exp_Osimps_I113_J, fact_68_converse__rtranclE2, fact_73_converse__rtrancl__induct, fact_22_Nitpick_Orefl_H__def, help_pp_1_1_U, fact_26_prod__cases4, fact_52_lconf__hext, fact_0__096P_ME_Mh_H_A_092_060turnstile_062_AVal_Av_092_060_094isub_0621_A_092_060guillemotleft_062bop_092_060guillemotright_062_Ae_092_060_094isub_0622_H_A_058_AT_096, fact_36_red__preserves__sconf, fact_75_ext, fact_38_red__hext__incr, fact_16_red, fact_88_red__reds_OFAssRed2, fact_39_red__reds_OBinOpThrow2, help_pp_2_1_U, fact_24_red__reds_OBinOpRed2, fact_27_prod__induct4, fact_1_BinOpRed2_I4_J, fact_60_ThrowReds, fact_95_big__by__small, fact_53_WTrt__hext__mono, fact_8_exp_Osimps_I71_J, fact_17_pred__equals__eq2, fact_81_exp_Osimps_I101_J, fact_35_prod__cases3
% 69.18/52.84 % No. of inferences in proof: 208
% 69.18/52.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 52280 ms resp. 51646 ms w/o parsing
% 69.83/52.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 69.83/52.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------