TSTP Solution File: SCT202_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT202_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 11:51:14 EDT 2023
% Result : Theorem 179.05s 125.44s
% Output : Refutation 179.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 163
% Syntax : Number of formulae : 284 ( 87 unt; 44 typ; 0 def)
% Number of atoms : 3005 ( 213 equ; 0 cnn)
% Maximal formula atoms : 154 ( 12 avg)
% Number of connectives : 12148 ( 127 ~; 22 |; 62 &;11676 @)
% ( 21 <=>; 240 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 11 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 16 con; 0-6 aty)
% Number of variables : 1041 ( 0 ^; 989 !; 15 ?;1041 :)
% ( 37 !>; 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(top_type,type,
top:
!>[TA: $tType] : $o ).
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(pi_type,type,
pi:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ bool ) > ( fun @ TB @ ( fun @ TA @ bool ) ) > ( fun @ ( fun @ TB @ TA ) @ bool ) ) ).
thf(the_type,type,
the:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(order_215145569der_on_type,type,
order_215145569der_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) ) ).
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] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
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(a_type,type,
a: arrow_411405190le_alt ).
thf(a1_type,type,
a1: arrow_411405190le_alt ).
thf(b_type,type,
b: arrow_411405190le_alt ).
thf(b1_type,type,
b1: arrow_411405190le_alt ).
thf(40,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(261,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)],[40]) ).
thf(102,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( 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_12_const__Lin__Prof) ).
thf(527,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( 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)],[102]) ).
thf(88,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(449,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)],[88]) ).
thf(35,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_54_curry__conv) ).
thf(247,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)],[35]) ).
thf(43,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(269,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)],[43]) ).
thf(80,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_top1I) ).
thf(408,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(23,axiom,
! [TA: $tType,A: fun @ TA @ 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_36_funcset__id) ).
thf(170,plain,
! [TA: $tType,A: fun @ TA @ 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)],[23]) ).
thf(94,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_72_splitD) ).
thf(500,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)],[94]) ).
thf(106,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_46_prod__cases5) ).
thf(538,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)],[106]) ).
thf(14,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_61_internal__split__def) ).
thf(153,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)],[14]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( the @ ( 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 ) @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( fequal @ TB ) @ B ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) ) )
= ( 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_96_The__split__eq) ).
thf(174,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( the @ ( 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 ) @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( fequal @ TB ) @ B ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) ) )
= ( 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)],[25]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ( member @ TA @ A @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Pi__mem) ).
thf(185,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ( member @ TA @ A @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(301,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(84,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( fun @ TA @ bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_UNIV__eq__I) ).
thf(436,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( fun @ TA @ bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(91,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_79_inv__imagep__def) ).
thf(460,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)],[91]) ).
thf(4,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(125,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
( ( member @ TC @ D @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) )
=> ( 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_64_mem__splitI) ).
thf(344,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
( ( member @ TC @ D @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) )
=> ( 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)],[60]) ).
thf(20,axiom,
a1 != b1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_d1_I1_J) ).
thf(164,plain,
a1 != b1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
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',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ q @ arrow_610318064e_Prof ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(121,plain,
~ ( 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)],[2]) ).
thf(62,axiom,
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_15_assms_I1_J) ).
thf(348,plain,
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)],[62]) ).
thf(65,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 )] :
( ( 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 )] :
( ( 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 )
=> ( ( 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 ) )
=> ( 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_26_dictatorI) ).
thf(353,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 )] :
( ( 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 )] :
( ( 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 )
=> ( ( 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 ) )
=> ( 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)],[65]) ).
thf(89,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
& ( 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_22_complete__Lin) ).
thf(452,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
& ( 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)],[89]) ).
thf(69,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_50_prod__induct3) ).
thf(380,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)],[69]) ).
thf(103,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_47_prod__induct5) ).
thf(529,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)],[103]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ),C: TB] :
( ( 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 ) )
=> ~ ( 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_85_mem__splitE) ).
thf(534,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ),C: TB] :
( ( 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 ) )
=> ~ ( 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)],[105]) ).
thf(98,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_38_prod_Oexhaust) ).
thf(512,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)],[98]) ).
thf(85,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_the__sym__eq__trivial) ).
thf(439,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(63,axiom,
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_3__096P_H_A_058_AProf_096) ).
thf(349,plain,
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)],[63]) ).
thf(74,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_74_curry__split) ).
thf(392,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)],[74]) ).
thf(45,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_73_split__eta) ).
thf(275,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)],[45]) ).
thf(8,axiom,
b1 != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_d2_I2_J) ).
thf(137,plain,
b1 != a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,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_78_split__curry) ).
thf(252,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)],[37]) ).
thf(54,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_60_in__inv__imagep) ).
thf(329,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)],[54]) ).
thf(118,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( 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 )
=> ( 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_32_in__mktop) ).
thf(578,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( 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 )
=> ( 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 )
=> ( 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 ) ) )
=> ( 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)],[118]) ).
thf(15,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(156,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(78,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(403,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)],[78]) ).
thf(72,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_56_curryI) ).
thf(388,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)],[72]) ).
thf(22,axiom,
top @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(169,plain,
top @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ~ ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_PiE) ).
thf(339,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ~ ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Pi__I_H) ).
thf(554,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(99,axiom,
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 @ ( 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_13__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) ).
thf(515,plain,
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 @ ( 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)],[99]) ).
thf(90,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_51_prod__cases3) ).
thf(457,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)],[90]) ).
thf(7,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(134,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)],[7]) ).
thf(42,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_53_internal__split__conv) ).
thf(266,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)],[42]) ).
thf(107,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_84_splitE_H) ).
thf(541,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)],[107]) ).
thf(5,axiom,
a1 != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_d2_I1_J) ).
thf(128,plain,
a1 != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,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(237,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)],[31]) ).
thf(82,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( 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 )
=> ( 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_30_in__mkbot) ).
thf(412,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( 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 )
=> ( 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 )
=> ( 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 ) ) )
=> ( 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)],[82]) ).
thf(17,axiom,
arrow_2069624013nimity @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_u) ).
thf(161,plain,
arrow_2069624013nimity @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Pi__I) ).
thf(296,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(12,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(149,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(113,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_57_curryD) ).
thf(562,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)],[113]) ).
thf(48,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_67_Pi__UNIV) ).
thf(291,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)],[48]) ).
thf(108,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( 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_19_below__Lin) ).
thf(545,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( 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)],[108]) ).
thf(70,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_81_splitE) ).
thf(382,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)],[70]) ).
thf(116,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_48_prod__cases4) ).
thf(572,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)],[116]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( member @ ( fun @ TB @ TA ) @ D @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) )
=> ( ( member @ TB @ A @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_funcset__mem) ).
thf(498,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( member @ ( fun @ TB @ TA ) @ D @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) )
=> ( ( member @ TB @ A @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(56,axiom,
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_0__096P_A_058_AProf_096) ).
thf(335,plain,
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)],[56]) ).
thf(27,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_83_split__part) ).
thf(181,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)],[27]) ).
thf(64,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(350,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)],[64]) ).
thf(16,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(159,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(29,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 )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( 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 )
=> ( 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 )
| ( 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 )
=> ( 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_17_in__below) ).
thf(187,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 )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( ( 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 )
=> ( 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 )
| ( 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 )
=> ( 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 )
=> ( 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 )
| ( 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 )
=> ( 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 ) ) ) ) )
=> ( 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)],[29]) ).
thf(24,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_58_curryE) ).
thf(172,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)],[24]) ).
thf(34,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( 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 )
=> ~ ( 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_21_Lin__irrefl) ).
thf(245,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( 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 )
=> ~ ( 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)],[34]) ).
thf(97,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 ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ b1 ) @ b ) @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ a1 ) @ a ) @ ( 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 ) @ a @ a1 ) ) @ ( arrow_1158827142_above @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ a1 ) @ a ) @ ( 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 ) @ a @ a1 ) ) @ b1 @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Q__def) ).
thf(509,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 ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ b1 ) @ b ) @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ a1 ) @ a ) @ ( 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 ) @ a @ a1 ) ) @ ( arrow_1158827142_above @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ a1 ) @ a ) @ ( 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 ) @ a @ a1 ) ) @ b1 @ b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(83,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_71_splitD_H) ).
thf(434,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)],[83]) ).
thf(110,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( 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(552,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( 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)],[110]) ).
thf(9,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(140,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)],[9]) ).
thf(76,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_UNIV__I) ).
thf(399,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(46,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 )] :
( ( 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] : ( 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 ) )
=> ( 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_9_unanimity__def) ).
thf(278,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 )] :
( ( 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] : ( 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 ) )
=> ( 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 )] :
( ( 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] : ( 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 ) )
=> ( 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)],[46]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(299,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(96,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_33_split__paired__Ex) ).
thf(505,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)],[96]) ).
thf(21,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_63_prod__caseI) ).
thf(167,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)],[21]) ).
thf(109,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_23_split__paired__All) ).
thf(548,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)],[109]) ).
thf(38,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(255,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(100,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_24_Pair__eq) ).
thf(516,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)],[100]) ).
thf(18,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(162,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
( ! [D: TB] :
( ( member @ TB @ D @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) )
=> ( member @ ( fun @ TB @ TA ) @ B @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_funcsetI) ).
thf(531,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
( ! [D: TB] :
( ( member @ TB @ D @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) )
=> ( member @ ( fun @ TB @ TA ) @ B @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(112,axiom,
! [A: arrow_159774573e_indi] :
( ( 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 ) @ p1 @ A ) )
<=> ( 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 ) @ p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__C1_C) ).
thf(557,plain,
! [A: arrow_159774573e_indi] :
( ( ( 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 ) @ p1 @ A ) )
=> ( 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 ) @ p @ A ) ) )
& ( ( 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 ) @ p @ A ) )
=> ( 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 ) @ p1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(13,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(150,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(41,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_66_split__conv) ).
thf(263,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)],[41]) ).
thf(26,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_68_split__weak__cong) ).
thf(177,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)],[26]) ).
thf(95,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_55_curry__def) ).
thf(502,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)],[95]) ).
thf(92,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 )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( 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 )
=> ( 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 )
| ( 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 )
=> ( 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_16_in__above) ).
thf(463,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 )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( ( 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 )
=> ( 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 )
| ( 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 )
=> ( 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 )
=> ( 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 )
| ( 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 )
=> ( 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 ) ) ) ) )
=> ( 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)],[92]) ).
thf(66,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( B != A )
=> ( ~ ( 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 )
<=> ( 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_20_notin__Lin__iff) ).
thf(359,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( B != A )
=> ( ( ~ ( 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 )
=> ( 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 ) )
& ( ( 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 )
=> ~ ( 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)],[66]) ).
thf(57,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( 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_18_above__Lin) ).
thf(336,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( 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)],[57]) ).
thf(119,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_87_cond__split__eta) ).
thf(600,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)],[119]) ).
thf(71,axiom,
( arrow_1985332922le_Lin
= ( collect @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( order_215145569der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Lin__def) ).
thf(386,plain,
( arrow_1985332922le_Lin
= ( collect @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( order_215145569der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(10,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(143,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,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_59_Prof__def) ).
thf(250,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)],[36]) ).
thf(101,axiom,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_UNIV__def) ).
thf(524,plain,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(39,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_70_prod_Osimps_I2_J) ).
thf(258,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)],[39]) ).
thf(73,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_62_splitI) ).
thf(390,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)],[73]) ).
thf(77,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_49_prod__induct4) ).
thf(401,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)],[77]) ).
thf(115,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_80_splitI2) ).
thf(568,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)],[115]) ).
thf(44,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_69_split__twice) ).
thf(272,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)],[44]) ).
thf(61,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_iso__tuple__UNIV__I) ).
thf(346,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(47,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 ) )
=> ( member @ TC @ B @ ( aa @ TB @ ( fun @ TC @ bool ) @ ( aa @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) @ A @ D ) @ E ) ) )
=> ( 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_82_mem__splitI2) ).
thf(287,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 ) )
=> ( member @ TC @ B @ ( aa @ TB @ ( fun @ TC @ bool ) @ ( aa @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) @ A @ D ) @ E ) ) )
=> ( 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)],[47]) ).
thf(87,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_UNIV__witness) ).
thf(447,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(81,axiom,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_linear__alt) ).
thf(410,plain,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(11,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(146,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( top_top @ ( fun @ TB @ TA ) ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_top__apply) ).
thf(405,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( top_top @ ( fun @ TB @ TA ) ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(68,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] :
( ( member @ TA @ E @ D )
=> ( ( aa @ TA @ TB @ C @ E )
= ( aa @ TA @ TB @ B @ E ) ) )
=> ( ( member @ ( fun @ TA @ TB ) @ C @ ( pi @ TA @ TB @ D @ A ) )
<=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Pi__cong) ).
thf(373,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] :
( ( member @ TA @ E @ D )
=> ( ( aa @ TA @ TB @ C @ E )
= ( aa @ TA @ TB @ B @ E ) ) )
=> ( ( ( member @ ( fun @ TA @ TB ) @ C @ ( pi @ TA @ TB @ D @ A ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ D @ A ) ) )
& ( ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ D @ A ) )
=> ( member @ ( fun @ TA @ TB ) @ C @ ( pi @ TA @ TB @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(120,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_the__eq__trivial) ).
thf(603,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(114,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_86_splitI2_H) ).
thf(564,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)],[114]) ).
thf(53,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 )] :
( ( 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 )] :
( ( 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] :
( ( 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 ) )
<=> ( 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 ) ) )
=> ( ( 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 ) )
<=> ( 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_10_IIA__def) ).
thf(305,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 )] :
( ( 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 )] :
( ( 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] :
( ( ( 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 ) )
=> ( 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 ) ) )
& ( ( 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 ) )
=> ( 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 ) ) ) )
=> ( ( ( 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 ) )
=> ( 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 ) ) )
& ( ( 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 ) )
=> ( 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 )] :
( ( 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 )] :
( ( 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] :
( ( ( 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 ) )
=> ( 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 ) ) )
& ( ( 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 ) )
=> ( 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 ) ) ) )
=> ( ( ( 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 ) )
=> ( 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 ) ) )
& ( ( 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 ) )
=> ( 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)],[53]) ).
thf(49,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( 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(294,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( 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)],[49]) ).
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_52_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(32,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_35_prod_Orecs) ).
thf(239,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)],[32]) ).
thf(33,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_45_prod__cases6) ).
thf(242,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)],[33]) ).
thf(75,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_91_splitE2) ).
thf(395,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)],[75]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( the @ ( product_prod @ TA @ TB ) @ A )
= ( the @ ( product_prod @ TA @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( product_prod @ TA @ TB ) @ bool @ TB ) @ A ) ) @ ( product_Pair @ TA @ TB ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_split__paired__The) ).
thf(332,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( the @ ( product_prod @ TA @ TB ) @ A )
= ( the @ ( product_prod @ TA @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( product_prod @ TA @ TB ) @ bool @ TB ) @ A ) ) @ ( product_Pair @ TA @ TB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(117,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(575,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(6,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_d1_I2_J) ).
thf(131,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
arrow_1958449194le_IIA @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).
thf(163,plain,
arrow_1958449194le_IIA @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(86,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_31_Pair__inject) ).
thf(442,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)],[86]) ).
thf(3,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(122,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) @ B )
<=> ( 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_29_pred__equals__eq2) ).
thf(222,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ! [C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) @ B )
=> ( 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 ) )
& ( ( 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 )
=> ( 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] :
( ( ( 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 )
=> ( 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 ) )
& ( ( 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 )
=> ( 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)],[30]) ).
thf(67,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 )] :
( ( 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_4_dictator__def) ).
thf(364,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 )] :
( ( 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 )] :
( ( 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)],[67]) ).
thf(606,plain,
$false,
inference(cvc4,[status(thm)],[261,527,449,247,269,408,170,500,538,153,174,185,301,436,460,125,344,164,121,348,353,452,380,529,534,512,439,349,392,275,137,252,329,578,156,403,388,169,339,554,515,457,134,266,541,128,237,412,161,296,149,562,291,545,382,572,498,335,181,350,159,187,172,245,509,434,552,140,399,278,299,505,167,548,255,516,162,531,557,150,263,177,502,463,359,336,600,386,143,250,524,258,390,401,568,272,346,287,447,410,146,405,373,603,564,305,294,341,239,242,395,332,575,131,163,442,122,222,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SCT202_5 : TPTP v8.1.2. Released v6.0.0.
% 0.09/0.13 % Command : run_Leo-III %s %d
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu May 18 15:23:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.83/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.67/1.05 % [INFO] Parsing done (213ms).
% 1.67/1.05 % [INFO] Running in sequential loop mode.
% 2.11/1.25 % [INFO] eprover registered as external prover.
% 2.11/1.25 % [INFO] cvc4 registered as external prover.
% 2.11/1.25 % [INFO] Scanning for conjecture ...
% 2.66/1.36 % [INFO] Found a conjecture and 118 axioms. Running axiom selection ...
% 3.05/1.44 % [INFO] Axiom selection finished. Selected 118 axioms (removed 0 axioms).
% 3.63/1.62 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.63/1.64 % [INFO] Type checking passed.
% 3.63/1.64 % [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 ...
% 4.21/1.80 % [INFO] [Domain constraints] Detected constraint on bool
% 4.21/1.81 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 4.21/1.82 % [INFO] [Domain constraints] Detected constraint on bool
% 4.21/1.82 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 179.05/125.44 % External prover 'cvc4' found a proof!
% 179.05/125.44 % [INFO] Killing All external provers ...
% 179.05/125.44 % Time passed: 124938ms (effective reasoning time: 124384ms)
% 179.05/125.44 % 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)>
% 179.05/125.44 % Axioms used in derivation (118): fact_41_funcsetI, fact_91_splitE2, fact_47_prod__induct5, fact_39_Pi__mem, fact_45_prod__cases6, fact_28_mktop__Lin, fact_48_prod__cases4, help_fconj_3_1_U, fact_3__096P_H_A_058_AProf_096, fact_85_mem__splitE, fact_57_curryD, fact_51_prod__cases3, fact_26_dictatorI, help_COMBI_1_1_U, fact_23_split__paired__All, fact_5_d1_I2_J, fact_96_The__split__eq, fact_63_prod__caseI, help_fTrue_1_1_T, fact_6_d2_I1_J, fact_16_in__above, fact_25_linear__alt, fact_34_PiE, fact_74_curry__split, fact_89_iso__tuple__UNIV__I, help_fTrue_1_1_U, fact_66_split__conv, fact_78_split__curry, fact_84_splitE_H, fact_38_prod_Oexhaust, fact_42_Pi__I_H, fact_94_UNIV__eq__I, fact_24_Pair__eq, fact_79_inv__imagep__def, fact_88_UNIV__I, fact_61_internal__split__def, fact_93_UNIV__witness, fact_13__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096, fact_64_mem__splitI, fact_37_funcset__mem, fact_20_notin__Lin__iff, fact_71_splitD_H, help_COMBB_1_1_U, help_If_1_1_T, fact_43_Pi__cong, fact_32_in__mktop, fact_73_split__eta, fact_55_curry__def, fact_8_d1_I1_J, fact_90_UNIV__def, fact_9_unanimity__def, fact_69_split__twice, fact_52_PairE, fact_82_mem__splitI2, fact_19_below__Lin, help_fconj_2_1_U, fact_86_splitI2_H, fact_44_prod__induct6, fact_7_d2_I2_J, fact_83_split__part, fact_4_dictator__def, arity_HOL_Obool___Orderings_Otop, fact_27_mkbot__Lin, fact_70_prod_Osimps_I2_J, help_fequal_1_1_T, fact_59_Prof__def, fact_21_Lin__irrefl, fact_76_mem__def, fact_0__096P_A_058_AProf_096, fact_60_in__inv__imagep, fact_56_curryI, fact_65_top1I, fact_58_curryE, help_If_3_1_T, fact_17_in__below, fact_40_Pi__I, help_If_2_1_T, help_COMBK_1_1_U, fact_1_assms_I3_J, fact_31_Pair__inject, fact_81_splitE, fact_46_prod__cases5, help_COMBC_1_1_U, fact_68_split__weak__cong, fact_95_Lin__def, fact_92_top__apply, fact_54_curry__conv, help_fequal_2_1_T, fact_67_Pi__UNIV, fact_33_split__paired__Ex, help_fconj_1_1_U, fact_18_above__Lin, fact_22_complete__Lin, fact_98_the__sym__eq__trivial, fact_72_splitD, fact_36_funcset__id, fact_29_pred__equals__eq2, fact_97_split__paired__The, fact_77_Collect__def, fact_15_assms_I1_J, fact_2_u, help_pp_1_1_U, fact_87_cond__split__eta, fact_10_IIA__def, fact_75_ext, help_pp_2_1_U, fact_50_prod__induct3, fact_30_in__mkbot, arity_fun___Orderings_Otop, fact_14__C1_C, fact_35_prod_Orecs, fact_99_the__eq__trivial, fact_11_Q__def, fact_12_const__Lin__Prof, fact_49_prod__induct4, fact_53_internal__split__conv, fact_80_splitI2, fact_62_splitI
% 179.05/125.44 % No. of inferences in proof: 240
% 179.05/125.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 124938 ms resp. 124384 ms w/o parsing
% 179.41/125.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 179.41/125.54 % [INFO] Killing All external provers ...
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