TSTP Solution File: SCT205_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT205_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:51:15 EDT 2023
% Result : Theorem 92.41s 46.64s
% Output : Refutation 93.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 161
% Syntax : Number of formulae : 280 ( 77 unt; 44 typ; 0 def)
% Number of atoms : 4840 ( 209 equ; 0 cnn)
% Maximal formula atoms : 298 ( 20 avg)
% Number of connectives : 17985 ( 127 ~; 22 |; 67 &;17487 @)
% ( 26 <=>; 256 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 14 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 16 con; 0-6 aty)
% Number of variables : 1056 ( 0 ^;1004 !; 13 ?;1056 :)
% ( 39 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(arrow_159774573e_indi_type,type,
arrow_159774573e_indi: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(arrow_1958449194le_IIA_type,type,
arrow_1958449194le_IIA: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(arrow_1985332922le_Lin_type,type,
arrow_1985332922le_Lin: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ).
thf(arrow_610318064e_Prof_type,type,
arrow_610318064e_Prof: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ).
thf(arrow_1158827142_above_type,type,
arrow_1158827142_above: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_319942042_below_type,type,
arrow_319942042_below: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_987702531ctator_type,type,
arrow_987702531ctator: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > arrow_159774573e_indi > $o ).
thf(arrow_276188178_mkbot_type,type,
arrow_276188178_mkbot: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_424895264_mktop_type,type,
arrow_424895264_mktop: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_2069624013nimity_type,type,
arrow_2069624013nimity: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combi_type,type,
combi:
!>[TA: $tType] : ( fun @ TA @ TA ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(in_rel_type,type,
in_rel:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TA ) @ bool ) > TB > TA > $o ) ).
thf(pi_type,type,
pi:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ bool ) > ( fun @ TB @ ( fun @ TA @ bool ) ) > ( fun @ ( fun @ TB @ TA ) @ bool ) ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(prod_type,type,
prod:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ bool ) > ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TB @ TA ) @ bool ) ) ).
thf(refl_type,type,
refl:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(inv_imagep_type,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ bool ) ) > ( fun @ TA @ TB ) > TA > TA > $o ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( fun @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) ) ).
thf(product_curry_type,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ ( product_prod @ TC @ TB ) @ TA ) > ( fun @ TC @ ( fun @ TB @ TA ) ) ) ).
thf(produc1605651328_split_type,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TA ) ) ).
thf(product_prod_case_type,type,
product_prod_case:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TA ) ) ).
thf(product_prod_rec_type,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
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(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( TA > TA > bool ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(f_type,type,
f: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(p_type,type,
p: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(p1_type,type,
p1: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(q_type,type,
q: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(a1_type,type,
a1: arrow_411405190le_alt ).
thf(a_type,type,
a: arrow_411405190le_alt ).
thf(b1_type,type,
b1: arrow_411405190le_alt ).
thf(b_type,type,
b: arrow_411405190le_alt ).
thf(10,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
!= ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_prod__cases4) ).
thf(141,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
!= ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(61,axiom,
pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ q ) ) @ arrow_1985332922le_Lin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__096F_AQ_A_058_ALin_096) ).
thf(347,plain,
pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ q ) ) @ arrow_1985332922le_Lin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_splitD) ).
thf(234,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_in__inv__imagep) ).
thf(352,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) )
=> ( inv_imagep @ TB @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ),B: TC,C: product_prod @ TA @ TB] :
( ! [D: TA,E: TB] :
( ( C
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ D ) @ E ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ B ) @ ( aa @ TB @ ( fun @ TC @ bool ) @ ( aa @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) @ A @ D ) @ E ) ) ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ B ) @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TA @ TB @ ( fun @ TC @ bool ) ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mem__splitI2) ).
thf(365,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ),B: TC,C: product_prod @ TA @ TB] :
( ! [D: TA,E: TB] :
( ( C
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ D ) @ E ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ B ) @ ( aa @ TB @ ( fun @ TC @ bool ) @ ( aa @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) @ A @ D ) @ E ) ) ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ B ) @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TA @ TB @ ( fun @ TC @ bool ) ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(9,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(138,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ B ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_prod__cases3) ).
thf(170,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ B ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(120,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(85,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_319942042_below @ C @ E @ D ) ) )
<=> ( ( B != A )
& ( ( A = E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_in__below) ).
thf(440,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_319942042_below @ C @ E @ D ) ) )
=> ( ( B != A )
& ( ( A = E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( A = E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_319942042_below @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_curryI) ).
thf(202,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(75,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) )
<=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_in__mkbot) ).
thf(384,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) )
=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) ) )
& ( ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(106,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_424895264_mktop @ B @ A ) ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_mktop__Lin) ).
thf(538,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_424895264_mktop @ B @ A ) ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Pair__eq) ).
thf(417,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(54,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_1958449194le_IIA @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_IIA__def) ).
thf(301,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_1958449194le_IIA @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) ) )
=> ( arrow_1958449194le_IIA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(47,axiom,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(257,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(71,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(372,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(97,axiom,
arrow_1958449194le_IIA @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).
thf(504,plain,
arrow_1958449194le_IIA @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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_36_prod_Orecs) ).
thf(344,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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)],[60]) ).
thf(55,axiom,
! [A: arrow_159774573e_indi] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ q @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096) ).
thf(325,plain,
! [A: arrow_159774573e_indi] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ q @ A ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ q @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(14,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
!= ( aa @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( aa @ TF @ ( fun @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) ) @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ E ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_prod__cases6) ).
thf(152,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
!= ( aa @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( aa @ TF @ ( fun @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) ) @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ E ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(39,axiom,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) ) )
=> ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C ) ) ) ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_dictatorI) ).
thf(228,plain,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) ) )
=> ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C ) ) ) ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(37,axiom,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_987702531ctator @ B @ A )
<=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_dictator__def) ).
thf(216,plain,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_987702531ctator @ B @ A )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) )
& ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_splitI) ).
thf(475,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(93,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(492,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)],[93]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( in_rel @ TA @ TB @ C @ B @ A )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_in__rel__def) ).
thf(485,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ( in_rel @ TA @ TB @ C @ B @ A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) ) @ C ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( 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)],[90]) ).
thf(62,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ E ) @ ( aa @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) ) @ F ) @ ( aa @ TF @ ( product_prod @ TE @ TF ) @ ( aa @ TE @ ( fun @ TF @ ( product_prod @ TE @ TF ) ) @ ( 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_44_prod__induct6) ).
thf(348,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ E ) @ ( aa @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) ) @ F ) @ ( aa @ TF @ ( product_prod @ TE @ TF ) @ ( aa @ TE @ ( fun @ TF @ ( product_prod @ TE @ TF ) ) @ ( 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)],[62]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(602,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(12,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) ) @ arrow_610318064e_Prof ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_const__Lin__Prof) ).
thf(147,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) ) @ arrow_610318064e_Prof ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ TB ),C: fun @ TB @ bool] :
( ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TB @ bool @ C @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_splitE2) ).
thf(293,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ TB ),C: fun @ TB @ bool] :
( ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TB @ bool @ C @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(132,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(243,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_prod__caseI) ).
thf(428,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC,B: fun @ TA @ ( fun @ TB @ TC )] :
( ! [C: TA,D: TB] :
( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ C ) @ D )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ A @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) )
=> ( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_cond__split__eta) ).
thf(512,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC,B: fun @ TA @ ( fun @ TB @ TC )] :
( ! [C: TA,D: TB] :
( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ C ) @ D )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ A @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) )
=> ( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(104,axiom,
pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) ).
thf(534,plain,
pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(48,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_424895264_mktop @ B @ A ) ) )
<=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_in__mktop) ).
thf(260,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_424895264_mktop @ B @ A ) ) )
=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) ) )
& ( ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_424895264_mktop @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(114,axiom,
( arrow_610318064e_Prof
= ( pi @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ arrow_159774573e_indi @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Prof__def) ).
thf(598,plain,
( arrow_610318064e_Prof
= ( pi @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ arrow_159774573e_indi @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(52,axiom,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ p1 ) @ arrow_610318064e_Prof ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__096P_A_058_AProf_096) ).
thf(297,plain,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ p1 ) @ arrow_610318064e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ B @ D ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Pi__I) ).
thf(165,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ B @ D ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(45,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(252,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(111,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_1158827142_above @ C @ E @ D ) ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_in__above) ).
thf(551,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_1158827142_above @ C @ E @ D ) ) )
=> ( ( B != A )
& ( ( B = D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( B = D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_1158827142_above @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
( ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ D ) @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TB @ TA @ ( fun @ TC @ bool ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_mem__splitI) ).
thf(488,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
( ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ D ) @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TB @ TA @ ( fun @ TC @ bool ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
( ! [D: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TB @ TA @ B @ D ) ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TB @ TA ) ) @ B ) @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_funcsetI) ).
thf(225,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
( ! [D: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TB @ TA @ B @ D ) ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TB @ TA ) ) @ B ) @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(26,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 @ ( aa @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) ) @ C ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( 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_52_prod__induct3) ).
thf(193,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 @ ( aa @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) ) @ C ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( 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)],[26]) ).
thf(35,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_mkbot__Lin) ).
thf(212,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ! [C: TA,D: TB] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_pred__equals__eq2) ).
thf(515,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ! [C: TA,D: TB] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(20,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 @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_split__paired__All) ).
thf(173,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 @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( 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)],[20]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc1605651328_split @ TA @ TB @ TC )
= ( product_prod_case @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_internal__split__def) ).
thf(129,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc1605651328_split @ TA @ TB @ TC )
= ( product_prod_case @ TA @ TB @ TC ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ B ) @ A ) )
=> ~ ! [C: TB,D: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_splitE) ).
thf(605,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ B ) @ A ) )
=> ~ ! [C: TB,D: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(67,axiom,
a != b1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_d2_I1_J) ).
thf(360,plain,
a != b1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(99,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_top1I) ).
thf(508,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ),C: product_prod @ TC @ TB] :
( ! [D: TC,E: TB] :
( ( ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ D ) @ E )
= C )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( aa @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ B @ D ) @ E ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TC @ TB @ ( fun @ TA @ bool ) ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_splitI2_H) ).
thf(530,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ),C: product_prod @ TC @ TB] :
( ! [D: TC,E: TB] :
( ( ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ D ) @ E )
= C )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( aa @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ B @ D ) @ E ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TC @ TB @ ( fun @ TA @ bool ) ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(112,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_2069624013nimity @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_unanimity__def) ).
thf(586,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_2069624013nimity @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) )
=> ( arrow_2069624013nimity @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(53,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_319942042_below @ A @ C @ B ) ) @ arrow_1985332922le_Lin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_below__Lin) ).
thf(298,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_319942042_below @ A @ C @ B ) ) @ arrow_1985332922le_Lin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(78,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( B != A )
=> ( ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_notin__Lin__iff) ).
thf(412,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( B != A )
=> ( ( ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) )
=> ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(80,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(425,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ A ) @ B ) @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_curry__def) ).
thf(430,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ A ) @ B ) @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TB @ ( fun @ TB @ bool ),C: TA,D: TA] :
( ( inv_imagep @ TB @ TA @ B @ A @ C @ D )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ B @ ( aa @ TA @ TB @ A @ C ) ) @ ( aa @ TA @ TB @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_inv__imagep__def) ).
thf(149,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TB @ ( fun @ TB @ bool ),C: TA,D: TA] :
( ( ( inv_imagep @ TB @ TA @ B @ A @ C @ D )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ B @ ( aa @ TA @ TB @ A @ C ) ) @ ( aa @ TA @ TB @ A @ D ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ B @ ( aa @ TA @ TB @ A @ C ) ) @ ( aa @ TA @ TB @ A @ D ) ) )
=> ( inv_imagep @ TB @ TA @ B @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( prod @ TB @ TA @ B @ A )
= ( collect @ ( product_prod @ TB @ TA ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ ( combc @ TB @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combb @ bool @ bool @ TA ) ) @ ( aa @ ( fun @ TB @ bool ) @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TB ) @ fconj ) @ ( combc @ TB @ ( fun @ TB @ bool ) @ bool @ ( member @ TB ) @ B ) ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Nitpick_Oprod__def) ).
thf(204,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ bool] :
( ( prod @ TB @ TA @ B @ A )
= ( collect @ ( product_prod @ TB @ TA ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ ( combc @ TB @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combb @ bool @ bool @ TA ) ) @ ( aa @ ( fun @ TB @ bool ) @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TB ) @ fconj ) @ ( combc @ TB @ ( fun @ TB @ bool ) @ bool @ ( member @ TB ) @ B ) ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(109,axiom,
! [A: arrow_159774573e_indi] :
( ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ q @ A )
= ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fequal @ arrow_411405190le_alt @ b @ b1 ) @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fequal @ arrow_411405190le_alt @ a @ a1 ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ ( arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ a1 @ a ) ) @ ( arrow_1158827142_above @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fequal @ arrow_411405190le_alt @ a @ a1 ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ ( arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ a1 @ a ) ) @ b @ b1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Q__def) ).
thf(545,plain,
! [A: arrow_159774573e_indi] :
( ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ q @ A )
= ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fequal @ arrow_411405190le_alt @ b @ b1 ) @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fequal @ arrow_411405190le_alt @ a @ a1 ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ ( arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ a1 @ a ) ) @ ( arrow_1158827142_above @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fequal @ arrow_411405190le_alt @ a @ a1 ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ ( arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ a1 @ a ) ) @ b @ b1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(74,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(382,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC )] :
( ( product_curry @ TA @ TB @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_curry__split) ).
thf(144,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC )] :
( ( product_curry @ TA @ TB @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_prod_Oexhaust) ).
thf(498,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(335,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ TB,D: fun @ TA @ bool] :
( ! [E: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ D ) )
=> ( ( aa @ TA @ TB @ C @ E )
= ( aa @ TA @ TB @ B @ E ) ) )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ C ) @ ( pi @ TA @ TB @ D @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Pi__cong) ).
thf(236,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ TB,D: fun @ TA @ bool] :
( ! [E: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ D ) )
=> ( ( aa @ TA @ TB @ C @ E )
= ( aa @ TA @ TB @ B @ E ) ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ C ) @ ( pi @ TA @ TB @ D @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ D @ A ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ D @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ C ) @ ( pi @ TA @ TB @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(63,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_iso__tuple__UNIV__I) ).
thf(350,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(107,axiom,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_UNIV__def) ).
thf(540,plain,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( product_curry @ TA @ TB @ TC @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_split__curry) ).
thf(187,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( product_curry @ TA @ TB @ TC @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(76,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
!= ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ D ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ E ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_prod__cases5) ).
thf(406,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
!= ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ D ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ E ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(87,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(477,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(105,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( refl @ TA @ A )
<=> ! [B: TA] : ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Nitpick_Orefl_H__def) ).
thf(535,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( ( refl @ TA @ A )
=> ! [B: TA] : ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) ) @ A ) ) )
& ( ! [B: TA] : ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) ) @ A ) )
=> ( refl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(118,axiom,
arrow_2069624013nimity @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_u) ).
thf(609,plain,
arrow_2069624013nimity @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(89,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) )
=> ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Lin__irrefl) ).
thf(483,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) )
=> ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ TC ),C: fun @ TA @ ( fun @ TB @ TC ),D: product_prod @ TA @ TB] :
( ! [E: TA,F: TB] :
( ( ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ E ) @ F )
= D )
=> ( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ E ) @ F )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ E ) @ F ) ) )
=> ( ( A = D )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ C ) @ A )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_split__cong) ).
thf(155,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ TC ),C: fun @ TA @ ( fun @ TB @ TC ),D: product_prod @ TA @ TB] :
( ! [E: TA,F: TB] :
( ( ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ E ) @ F )
= D )
=> ( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ E ) @ F )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ E ) @ F ) ) )
=> ( ( A = D )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ C ) @ A )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Pair__inject) ).
thf(330,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(8,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(135,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( produc1605651328_split @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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_59_internal__split__conv) ).
thf(505,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( produc1605651328_split @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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)],[98]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ D ) @ ( pi @ TA @ TB @ C @ B ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_PiE) ).
thf(490,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ D ) @ ( pi @ TA @ TB @ C @ B ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( fequal @ TA @ B @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(162,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( fequal @ TA @ B @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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_72_split__conv) ).
thf(548,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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)],[110]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: product_prod @ TB @ TC,C: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ C ) @ B ) @ A ) )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ C @ D ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_splitE_H) ).
thf(374,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: product_prod @ TB @ TC,C: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ C ) @ B ) @ A ) )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ C @ D ) @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(33,axiom,
pp @ ( aa @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ f ) @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_assms_I1_J) ).
thf(209,plain,
pp @ ( aa @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ f ) @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(123,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: bool,C: product_prod @ TA @ TB] :
( ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( combb @ bool @ bool @ TB ) @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) ) ) @ A ) ) @ C ) )
<=> ( ( pp @ B )
& ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_split__part) ).
thf(355,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: bool,C: product_prod @ TA @ TB] :
( ( ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( combb @ bool @ bool @ TB ) @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) ) ) @ A ) ) @ C ) )
=> ( ( pp @ B )
& ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ C ) ) ) )
& ( ( ( pp @ B )
& ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ C ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( combb @ bool @ bool @ TB ) @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) ) ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(49,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ A ) @ arrow_610318064e_Prof ) )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ E ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096) ).
thf(282,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ A ) @ arrow_610318064e_Prof ) )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ E ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ E ) ) ) ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool] :
( ( pi @ TA @ TB @ A @ ( combk @ ( fun @ TB @ bool ) @ TA @ ( top_top @ ( fun @ TB @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ TA @ TB ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pi__UNIV) ).
thf(409,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool] :
( ( pi @ TA @ TB @ A @ ( combk @ ( fun @ TB @ bool ) @ TA @ ( top_top @ ( fun @ TB @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ TA @ TB ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(28,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(199,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ C ) @ B ) @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_curry__conv) ).
thf(338,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ C ) @ B ) @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(66,axiom,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ q ) @ arrow_610318064e_Prof ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096Q_A_058_AProf_096) ).
thf(359,plain,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ q ) @ arrow_610318064e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(21,axiom,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ p ) @ arrow_610318064e_Prof ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__096P_H_A_058_AProf_096) ).
thf(177,plain,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ p ) @ arrow_610318064e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
& ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_complete__Lin) ).
thf(182,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
& ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(115,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TA ) @ ( fun @ ( fun @ ( fun @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TA ) ) @ ( combi @ TA ) ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_funcset__id) ).
thf(600,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TA ) @ ( fun @ ( fun @ ( fun @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TA ) ) @ ( combi @ TA ) ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ),C: fun @ TE @ ( fun @ TD @ TC )] :
( ( aa @ ( product_prod @ TE @ TD ) @ TC @ ( aa @ ( fun @ TE @ ( fun @ TD @ TC ) ) @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( product_prod_case @ TE @ TD @ TC ) @ C ) @ ( aa @ ( product_prod @ TA @ TB ) @ ( product_prod @ TE @ TD ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( product_prod @ TE @ TD ) ) @ ( product_prod_case @ TA @ TB @ ( product_prod @ TE @ TD ) ) @ B ) @ A ) )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( fun @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) ) @ ( combb @ ( product_prod @ TE @ TD ) @ TC @ TB ) @ ( aa @ ( fun @ TE @ ( fun @ TD @ TC ) ) @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( product_prod_case @ TE @ TD @ TC ) @ C ) ) ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_split__twice) ).
thf(595,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ),C: fun @ TE @ ( fun @ TD @ TC )] :
( ( aa @ ( product_prod @ TE @ TD ) @ TC @ ( aa @ ( fun @ TE @ ( fun @ TD @ TC ) ) @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( product_prod_case @ TE @ TD @ TC ) @ C ) @ ( aa @ ( product_prod @ TA @ TB ) @ ( product_prod @ TE @ TD ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( product_prod @ TE @ TD ) ) @ ( product_prod_case @ TA @ TB @ ( product_prod @ TE @ TD ) ) @ B ) @ A ) )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( fun @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) ) @ ( combb @ ( product_prod @ TE @ TD ) @ TC @ TB ) @ ( aa @ ( fun @ TE @ ( fun @ TD @ TC ) ) @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( product_prod_case @ TE @ TD @ TC ) @ C ) ) ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( pp @ ( aa @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TB @ TA ) ) @ D ) @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) ) )
=> ( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TB @ TA @ D @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_funcset__mem) ).
thf(250,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( pp @ ( aa @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TB @ TA ) ) @ D ) @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) ) )
=> ( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TB @ TA @ D @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(68,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_UNIV__I) ).
thf(363,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(94,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_1158827142_above @ A @ C @ B ) ) @ arrow_1985332922le_Lin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_above__Lin) ).
thf(495,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_1158827142_above @ A @ C @ B ) ) @ arrow_1985332922le_Lin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC ),B: product_prod @ TA @ TB,C: product_prod @ TA @ TB] :
( ( C = B )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ C )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_split__weak__cong) ).
thf(246,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC ),B: product_prod @ TA @ TB,C: product_prod @ TA @ TB] :
( ( C = B )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ C )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(32,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) ) @ D ) @ ( aa @ TD @ ( product_prod @ TC @ TD ) @ ( aa @ TC @ ( fun @ TD @ ( product_prod @ TC @ TD ) ) @ ( 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_50_prod__induct4) ).
thf(207,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) ) @ D ) @ ( aa @ TD @ ( product_prod @ TC @ TD ) @ ( aa @ TC @ ( fun @ TD @ ( product_prod @ TC @ TD ) ) @ ( 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)],[32]) ).
thf(88,axiom,
! [A: arrow_159774573e_indi] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a1 ) @ b1 ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__C1_C) ).
thf(478,plain,
! [A: arrow_159774573e_indi] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a1 ) @ b1 ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a1 ) @ b1 ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(36,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( 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_48_prod__induct5) ).
thf(214,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( 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)],[36]) ).
thf(50,axiom,
b != a1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_d2_I2_J) ).
thf(290,plain,
b != a1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1,conjecture,
pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ q ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(119,plain,
~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ q ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(73,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 @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_split__paired__Ex) ).
thf(378,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 @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( 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)],[73]) ).
thf(83,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( fequal @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(433,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( fequal @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_curryD) ).
thf(510,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_curryE) ).
thf(168,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_d1_I1_J) ).
thf(190,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(34,axiom,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_linear__alt) ).
thf(210,plain,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(5,axiom,
a1 != b1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_d1_I2_J) ).
thf(126,plain,
a1 != b1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_PairE) ).
thf(341,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ),C: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( aa @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) ) @ ( product_prod_case @ TC @ TA @ ( fun @ TB @ bool ) ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_mem__splitE) ).
thf(195,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ),C: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( aa @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) ) @ ( product_prod_case @ TC @ TA @ ( fun @ TB @ bool ) ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(437,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ D ) @ ( pi @ TA @ TB @ C @ B ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Pi__mem) ).
thf(200,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ D ) @ ( pi @ TA @ TB @ C @ B ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] :
( ( B
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ C ) @ D ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_splitI2) ).
thf(178,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] :
( ( B
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ C ) @ D ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ B @ D ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Pi__I_H) ).
thf(501,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ B @ D ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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_81_prod_Osimps_I2_J) ).
thf(369,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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)],[70]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) ) @ ( combb @ ( product_prod @ TA @ TB ) @ TC @ TB ) @ A ) ) @ ( product_Pair @ TA @ TB ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_split__eta) ).
thf(254,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) ) @ ( combb @ ( product_prod @ TA @ TB ) @ TC @ TB ) @ A ) ) @ ( product_Pair @ TA @ TB ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ D ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ C ) @ B ) ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_splitD_H) ).
thf(543,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ D ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ C ) @ B ) ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(610,plain,
$false,
inference(cvc4,[status(thm)],[141,347,234,352,365,138,170,120,440,202,384,538,417,301,257,372,504,344,325,152,228,216,475,492,485,348,602,147,293,132,243,428,512,534,260,598,297,165,252,551,488,225,193,212,515,173,129,605,360,508,530,586,298,412,425,430,149,204,545,382,144,498,335,236,350,540,187,406,477,535,609,483,155,330,135,505,490,162,548,374,209,123,355,282,409,199,338,359,177,182,600,595,250,363,495,246,207,478,214,290,119,378,433,510,168,190,210,126,341,195,437,200,178,501,369,254,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SCT205_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 15:26:07 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.88/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.44/1.05 % [INFO] Parsing done (232ms).
% 1.78/1.06 % [INFO] Running in sequential loop mode.
% 2.42/1.29 % [INFO] eprover registered as external prover.
% 2.42/1.29 % [INFO] cvc4 registered as external prover.
% 2.42/1.30 % [INFO] Scanning for conjecture ...
% 2.84/1.43 % [INFO] Found a conjecture and 116 axioms. Running axiom selection ...
% 3.31/1.53 % [INFO] Axiom selection finished. Selected 116 axioms (removed 0 axioms).
% 3.95/1.73 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.01/1.76 % [INFO] Type checking passed.
% 4.01/1.76 % [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 ...
% 4.54/1.95 % [INFO] [Domain constraints] Detected constraint on bool
% 4.87/1.95 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 4.99/1.99 % [INFO] [Domain constraints] Detected constraint on bool
% 4.99/1.99 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 92.41/46.63 % External prover 'cvc4' found a proof!
% 92.41/46.63 % [INFO] Killing All external provers ...
% 92.41/46.63 % Time passed: 46121ms (effective reasoning time: 45568ms)
% 92.41/46.63 % 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)>
% 92.41/46.63 % Axioms used in derivation (116): fact_4_d1_I1_J, fact_61_curryI, fact_53_prod__cases3, fact_46_prod__cases6, fact_77_Collect__def, fact_68_mem__splitI, fact_22__096P_H_A_058_AProf_096, fact_79_splitD, fact_28_mktop__Lin, fact_54_funcsetI, fact_62_curryE, fact_60_curry__conv, fact_48_prod__induct5, help_fconj_3_1_U, fact_49_Pi__I, fact_13_d1_I2_J, help_COMBI_1_1_U, fact_69_prod__caseI, fact_57_prod_Oexhaust, fact_93_Nitpick_Oprod__def, fact_92_splitI2_H, help_fTrue_1_1_T, fact_73_Pi__UNIV, fact_97_iso__tuple__UNIV__I, fact_41_PiE, fact_59_internal__split__conv, fact_72_split__conv, fact_36_prod_Orecs, fact_47_prod__cases5, fact_10__C1_C, fact_9__096F_AQ_A_058_ALin_096, fact_51_prod__cases4, help_fTrue_1_1_U, fact_98_split__cong, fact_23_assms_I1_J, fact_65_in__inv__imagep, fact_90_splitE_H, fact_66_Prof__def, fact_91_mem__splitE, fact_81_prod_Osimps_I2_J, help_COMBB_1_1_U, help_If_1_1_T, fact_33_IIA__def, fact_12_Pair__eq, fact_43_funcset__mem, fact_24_above__Lin, fact_82_split__weak__cong, help_fconj_2_1_U, fact_40_dictatorI, fact_44_prod__induct6, fact_63_curryD, fact_19_Q__def, fact_21__096P_A_058_AProf_096, fact_11_split__paired__All, fact_27_mkbot__Lin, fact_14_in__mkbot, help_fequal_1_1_T, fact_3__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096, fact_99_splitE2, fact_83_split__twice, fact_25_below__Lin, fact_35_complete__Lin, fact_7__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096, fact_18_split__paired__Ex, fact_67_internal__split__def, fact_76_mem__def, fact_71_top1I, fact_56_Pi__cong, fact_85_inv__imagep__def, help_If_3_1_T, fact_32_notin__Lin__iff, fact_96_UNIV__def, fact_87_splitE, fact_78_curry__split, fact_15_in__mktop, help_If_2_1_T, help_COMBK_1_1_U, fact_1_assms_I3_J, fact_6_d2_I2_J, fact_37_linear__alt, fact_20_Nitpick_Orefl_H__def, help_COMBC_1_1_U, fact_5_d2_I1_J, fact_16_Pair__inject, help_fequal_2_1_T, fact_74_split__curry, fact_39_pred__equals__eq2, help_fconj_1_1_U, fact_70_splitI, fact_88_mem__splitI2, fact_80_splitD_H, fact_8__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096, fact_42_funcset__id, fact_38_dictator__def, fact_17_in__rel__def, fact_45_Pi__mem, fact_0__096Q_A_058_AProf_096, fact_26_const__Lin__Prof, fact_94_cond__split__eta, fact_55_Pi__I_H, fact_2_u, help_pp_1_1_U, fact_29_in__below, fact_89_split__part, fact_95_UNIV__I, fact_30_in__above, fact_75_ext, fact_86_splitI2, fact_52_prod__induct3, fact_84_split__eta, fact_64_curry__def, fact_34_unanimity__def, fact_50_prod__induct4, help_pp_2_1_U, fact_58_PairE, fact_31_Lin__irrefl
% 92.41/46.63 % No. of inferences in proof: 236
% 92.41/46.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 46121 ms resp. 45568 ms w/o parsing
% 93.18/46.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 93.18/46.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------