TSTP Solution File: SCT193_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT193_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 11:51:12 EDT 2023
% Result : Theorem 132.30s 80.85s
% Output : Refutation 132.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 131
% Syntax : Number of formulae : 226 ( 59 unt; 38 typ; 0 def)
% Number of atoms : 2331 ( 187 equ; 0 cnn)
% Maximal formula atoms : 77 ( 12 avg)
% Number of connectives : 9914 ( 111 ~; 14 |; 75 &;9482 @)
% ( 17 <=>; 215 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 13 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 10 con; 0-6 aty)
% Number of variables : 960 ( 0 ^; 903 !; 13 ?; 960 :)
% ( 44 !>; 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_1985332922le_Lin_type,type,
arrow_1985332922le_Lin: fun @ ( 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_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(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(in_rel_type,type,
in_rel:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TA ) @ bool ) > TB > TA > $o ) ).
thf(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_apfst_type,type,
product_apfst:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( product_prod @ TC @ TA ) > ( product_prod @ TB @ TA ) ) ).
thf(product_apsnd_type,type,
product_apsnd:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( product_prod @ TA @ TC ) > ( product_prod @ TA @ TB ) ) ).
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(product_scomp_type,type,
product_scomp:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( fun @ TD @ ( product_prod @ TC @ TB ) ) > ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TD @ TA ) ) ).
thf(inv_image_type,type,
inv_image:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TB ) @ bool ) > ( fun @ TA @ TB ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).
thf(irrefl_type,type,
irrefl:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(total_on_type,type,
total_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(trans_type,type,
trans:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(lex_prod_type,type,
lex_prod:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TB ) @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > ( fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ 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(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(f_type,type,
f: ( 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(a_type,type,
a: arrow_411405190le_alt ).
thf(b_type,type,
b: arrow_411405190le_alt ).
thf(i_type,type,
i: arrow_159774573e_indi ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',fact_60_splitD) ).
thf(320,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)],[58]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',fact_12_Pair__inject) ).
thf(133,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)],[18]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( product_Pair @ TD @ TE ) @ F ) @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_prod__induct5) ).
thf(205,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( product_Pair @ TD @ TE ) @ F ) @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(69,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ! [B: arrow_159774573e_indi] :
( ( trans @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
& ( irrefl @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
& ( total_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) )
=> ! [B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( 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 ) @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ i ) )
=> ( 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 ) @ C ) @ ( f @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(350,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ! [B: arrow_159774573e_indi] :
( ( trans @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
& ( irrefl @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
& ( total_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) )
=> ! [B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( 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 ) @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ i ) )
=> ( 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 ) @ C ) @ ( f @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',fact_46_curryD) ).
thf(342,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)],[66]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',fact_30_prod__induct4) ).
thf(138,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)],[19]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( trans @ TB @ B )
=> ( trans @ TA @ ( inv_image @ TB @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_trans__inv__image) ).
thf(101,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( trans @ TB @ B )
=> ( trans @ TA @ ( inv_image @ TB @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',fact_65_splitE_H) ).
thf(479,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)],[92]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',fact_63_splitE) ).
thf(333,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)],[63]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',fact_68_splitI2_H) ).
thf(115,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)],[12]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ TB] :
( ( product_apfst @ TC @ TB @ TA @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ ( aa @ TC @ TB @ C @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_apfst__conv) ).
thf(449,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ TB] :
( ( product_apfst @ TC @ TB @ TA @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ ( aa @ TC @ TB @ C @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',fact_27_prod__cases6) ).
thf(202,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)],[35]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',fact_11_in__mkbot) ).
thf(142,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)],[21]) ).
thf(89,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_UNIV__I) ).
thf(472,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',fact_26_prod__induct6) ).
thf(184,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)],[28]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',fact_55_split__conv) ).
thf(372,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)],[75]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',fact_32_prod__induct3) ).
thf(344,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)],[67]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',fact_69_splitE2) ).
thf(357,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)],[71]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',fact_37_below__Lin) ).
thf(196,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)],[33]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',fact_62_split__curry) ).
thf(284,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)],[49]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( trans @ TA @ D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ A ) @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_transD) ).
thf(325,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( trans @ TA @ D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ A ) @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TC @ TB ),B: TA] :
( ( product_scomp @ TC @ TA @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ ( product_prod @ TA @ TC ) ) @ ( product_Pair @ TA @ TC ) @ B ) @ A )
= ( aa @ TA @ ( fun @ TC @ TB ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Pair__scomp) ).
thf(164,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TC @ TB ),B: TA] :
( ( product_scomp @ TC @ TA @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ ( product_prod @ TA @ TC ) ) @ ( product_Pair @ TA @ TC ) @ B ) @ A )
= ( aa @ TA @ ( fun @ TC @ TB ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(94,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( trans @ TA @ A )
<=> ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_trans__def) ).
thf(485,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( ( trans @ TA @ A )
=> ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) ) )
& ( ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) )
=> ( trans @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TD,C: fun @ TB @ TC] :
( ( product_apsnd @ TB @ TC @ TD @ C @ ( product_apfst @ TA @ TD @ TB @ B @ A ) )
= ( product_apfst @ TA @ TD @ TC @ B @ ( product_apsnd @ TB @ TC @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_apsnd__apfst__commute) ).
thf(106,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TD,C: fun @ TB @ TC] :
( ( product_apsnd @ TB @ TC @ TD @ C @ ( product_apfst @ TA @ TD @ TB @ B @ A ) )
= ( product_apfst @ TA @ TD @ TC @ B @ ( product_apsnd @ TB @ TC @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',fact_58_prod_Osimps_I2_J) ).
thf(121,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)],[14]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ TB,C: product_prod @ TB @ TA] :
( ( C
= ( product_apfst @ TC @ TB @ TA @ 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 ) )
=> ( C
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ ( aa @ TC @ TB @ B @ D ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_apfst__convE) ).
thf(292,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ TB,C: product_prod @ TB @ TA] :
( ( C
= ( product_apfst @ TC @ TB @ TA @ 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 ) )
=> ( C
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ ( aa @ TC @ TB @ B @ D ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(83,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_UNIV__witness) ).
thf(452,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(73,axiom,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_UNIV__def) ).
thf(366,plain,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ E ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C ) ) @ ( lex_prod @ TB @ TA @ B @ A ) )
<=> ( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ F ) @ D ) @ B )
| ( ( F = D )
& ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_in__lex__prod) ).
thf(302,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool,C: TA,D: TB,E: TA,F: TB] :
( ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ E ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C ) ) @ ( lex_prod @ TB @ TA @ B @ A ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ F ) @ D ) @ B )
| ( ( F = D )
& ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ E ) @ C ) @ A ) ) ) )
& ( ( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ F ) @ D ) @ B )
| ( ( F = D )
& ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ E ) @ C ) @ A ) ) )
=> ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ E ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C ) ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(80,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(424,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)],[80]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',fact_67_mem__splitI2) ).
thf(192,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)],[32]) ).
thf(72,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( order_215145569der_on @ TA @ B ) @ A ) )
<=> ( ( trans @ TA @ A )
& ( irrefl @ TA @ A )
& ( total_on @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_strict__linear__order__on__def) ).
thf(361,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( order_215145569der_on @ TA @ B ) @ A ) )
=> ( ( trans @ TA @ A )
& ( irrefl @ TA @ A )
& ( total_on @ TA @ B @ A ) ) )
& ( ( ( trans @ TA @ A )
& ( irrefl @ TA @ A )
& ( total_on @ TA @ B @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( order_215145569der_on @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',fact_4_split__paired__All) ).
thf(461,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)],[86]) ).
thf(85,axiom,
( ! [A: arrow_159774573e_indi] :
( ( trans @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
& ( irrefl @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
& ( total_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) )
=> ( ( trans @ arrow_411405190le_alt @ ( f @ p ) )
& ( irrefl @ arrow_411405190le_alt @ ( f @ p ) )
& ( total_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ ( f @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(456,plain,
( ! [A: arrow_159774573e_indi] :
( ( trans @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
& ( irrefl @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
& ( total_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) )
=> ( ( trans @ arrow_411405190le_alt @ ( f @ p ) )
& ( irrefl @ arrow_411405190le_alt @ ( f @ p ) )
& ( total_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ ( f @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',fact_22_prod__cases3) ).
thf(317,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)],[57]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( product_prod @ TB @ TC )] :
( ( product_scomp @ TA @ TB @ TC @ ( product_prod @ TB @ TC ) @ A @ ( product_Pair @ TB @ TC ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_scomp__Pair) ).
thf(188,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( product_prod @ TB @ TC )] :
( ( product_scomp @ TA @ TB @ TC @ ( product_prod @ TB @ TC ) @ A @ ( product_Pair @ TB @ TC ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',fact_41_curry__conv) ).
thf(169,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)],[24]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',fact_66_mem__splitE) ).
thf(420,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)],[79]) ).
thf(9,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(109,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(124,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_20_prod_Oexhaust) ).
thf(339,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)],[65]) ).
thf(91,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( irrefl @ TA @ A )
<=> ! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_irrefl__def) ).
thf(476,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( ( irrefl @ TA @ A )
=> ! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) @ A ) )
& ( ! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) @ A )
=> ( irrefl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc1605651328_split @ TA @ TB @ TC )
= ( product_prod_case @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_internal__split__def) ).
thf(96,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)],[3]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',fact_16_prod_Orecs) ).
thf(264,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)],[44]) ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',fact_34_in__above) ).
thf(375,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)],[76]) ).
thf(31,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 ) @ a ) @ b ) @ ( f @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(191,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 ) @ a ) @ b ) @ ( f @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(78,axiom,
! [A: arrow_159774573e_indi] :
( ( trans @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
& ( irrefl @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
& ( total_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(413,plain,
! [A: arrow_159774573e_indi] :
( ( trans @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
& ( irrefl @ arrow_411405190le_alt @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
& ( total_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',fact_21_PairE) ).
thf(172,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)],[25]) ).
thf(46,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_top1I) ).
thf(271,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(103,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',fact_53_splitI) ).
thf(140,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)],[20]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',fact_52_prod__caseI) ).
thf(213,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)],[39]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',fact_24_Lin__irrefl) ).
thf(483,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)],[93]) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',fact_40_internal__split__conv) ).
thf(330,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)],[62]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',fact_29_prod__cases5) ).
thf(130,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)],[17]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',fact_33_in__below) ).
thf(223,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)],[41]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( in_rel @ TA @ TB @ C @ B @ A )
<=> ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_in__rel__def) ).
thf(299,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ( in_rel @ TA @ TB @ C @ B @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) @ C ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) @ C )
=> ( in_rel @ TA @ TB @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(45,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) )
=> ( trans @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_transI) ).
thf(267,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) )
=> ( trans @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',fact_17_Lin__def) ).
thf(167,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)],[23]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(282,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1,conjecture,
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 @ i ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(2,negated_conjecture,
~ ( 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 @ i ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(95,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 ) @ a ) @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ i ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TB,D: TB] :
( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ D ) @ C ) @ ( inv_image @ TA @ TB @ B @ A ) )
<=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ ( aa @ TB @ TA @ A @ D ) ) @ ( aa @ TB @ TA @ A @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_in__inv__image) ).
thf(327,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TB,D: TB] :
( ( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ D ) @ C ) @ ( inv_image @ TA @ TB @ B @ A ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ ( aa @ TB @ TA @ A @ D ) ) @ ( aa @ TB @ TA @ A @ C ) ) @ B ) )
& ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ ( aa @ TB @ TA @ A @ D ) ) @ ( aa @ TB @ TA @ A @ C ) ) @ B )
=> ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ D ) @ C ) @ ( inv_image @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',fact_64_splitI2) ).
thf(310,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)],[55]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( top_top @ ( fun @ TB @ TA ) ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_top__apply) ).
thf(199,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)],[34]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ TC ),C: fun @ TA @ ( fun @ TB @ TC ),D: product_prod @ TA @ TB] :
( ! [E: TA,F: TB] :
( ( ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ E ) @ F )
= D )
=> ( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ E ) @ F )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ E ) @ F ) ) )
=> ( ( A = D )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ C ) @ A )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_split__cong) ).
thf(177,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ TC ),C: fun @ TA @ ( fun @ TB @ TC ),D: product_prod @ TA @ TB] :
( ! [E: TA,F: TB] :
( ( ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ E ) @ F )
= D )
=> ( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ E ) @ F )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ E ) @ F ) ) )
=> ( ( A = D )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ C ) @ A )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( fun @ TA @ bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_UNIV__eq__I) ).
thf(127,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)],[16]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',fact_57_splitD_H) ).
thf(470,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)],[88]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( trans @ TB @ B )
=> ( ( trans @ TA @ A )
=> ( trans @ ( product_prod @ TB @ TA ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_trans__lex__prod) ).
thf(175,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( trans @ TB @ B )
=> ( ( trans @ TA @ A )
=> ( trans @ ( product_prod @ TB @ TA ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TA @ TB] :
( ( product_apsnd @ TA @ TB @ TC @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ B ) @ ( aa @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_apsnd__conv) ).
thf(314,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TA @ TB] :
( ( product_apsnd @ TA @ TB @ TC @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ B ) @ ( aa @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',fact_23_notin__Lin__iff) ).
thf(465,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)],[87]) ).
thf(4,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(99,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',fact_59_split__weak__cong) ).
thf(258,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)],[42]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_42_curryI) ).
thf(186,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)],[29]) ).
thf(11,axiom,
top @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(114,plain,
top @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',fact_36_above__Lin) ).
thf(207,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)],[37]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',fact_14_split__paired__Ex) ).
thf(346,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)],[68]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ TD ),C: fun @ TA @ ( product_prod @ TC @ TB )] :
( ( aa @ TA @ TD @ ( product_scomp @ TA @ TC @ TB @ TD @ C @ B ) @ A )
= ( aa @ ( product_prod @ TC @ TB ) @ TD @ ( aa @ ( fun @ TC @ ( fun @ TB @ TD ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TD ) @ ( product_prod_case @ TC @ TB @ TD ) @ B ) @ ( aa @ TA @ ( product_prod @ TC @ TB ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_scomp__apply) ).
thf(287,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ TD ),C: fun @ TA @ ( product_prod @ TC @ TB )] :
( ( aa @ TA @ TD @ ( product_scomp @ TA @ TC @ TB @ TD @ C @ B ) @ A )
= ( aa @ ( product_prod @ TC @ TB ) @ TD @ ( aa @ ( fun @ TC @ ( fun @ TB @ TD ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TD ) @ ( product_prod_case @ TC @ TB @ TD ) @ B ) @ ( aa @ TA @ ( product_prod @ TC @ TB ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_45_curryE) ).
thf(290,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)],[51]) ).
thf(13,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_iso__tuple__UNIV__I) ).
thf(119,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',fact_61_curry__split) ).
thf(410,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)],[77]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',fact_35_linear__alt) ).
thf(262,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)],[43]) ).
thf(47,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( total_on @ TA @ B @ A )
<=> ! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
| ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_total__on__def) ).
thf(273,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( total_on @ TA @ B @ A )
=> ! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
| ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ D ) @ C ) @ A ) ) ) ) ) )
& ( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
| ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ D ) @ C ) @ A ) ) ) ) )
=> ( total_on @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: fun @ TC @ ( fun @ TB @ TD ),B: fun @ TA @ ( product_prod @ TC @ TB ),C: TA] :
( ( aa @ TA @ TD @ ( product_scomp @ TA @ TC @ TB @ TD @ B @ A ) @ C )
= ( aa @ ( product_prod @ TC @ TB ) @ TD @ ( aa @ ( fun @ TC @ ( fun @ TB @ TD ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TD ) @ ( product_prod_case @ TC @ TB @ TD ) @ A ) @ ( aa @ TA @ ( product_prod @ TC @ TB ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_scomp__def) ).
thf(210,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: fun @ TC @ ( fun @ TB @ TD ),B: fun @ TA @ ( product_prod @ TC @ TB ),C: TA] :
( ( aa @ TA @ TD @ ( product_scomp @ TA @ TC @ TB @ TD @ B @ A ) @ C )
= ( aa @ ( product_prod @ TC @ TB ) @ TD @ ( aa @ ( fun @ TC @ ( fun @ TB @ TD ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TD ) @ ( product_prod_case @ TC @ TB @ TD ) @ A ) @ ( aa @ TA @ ( product_prod @ TC @ TB ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',fact_25_mkbot__Lin) ).
thf(474,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)],[90]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',fact_39_in__mktop) ).
thf(427,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)],[81]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_43_in__inv__imagep) ).
thf(369,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)],[74]) ).
thf(10,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(111,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',fact_31_prod__cases4) ).
thf(322,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)],[59]) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',fact_54_mem__splitI) ).
thf(337,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)],[64]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(354,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)],[70]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',fact_5_Pair__eq) ).
thf(215,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)],[40]) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',fact_38_mktop__Lin) ).
thf(454,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)],[84]) ).
thf(5,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(100,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(490,plain,
$false,
inference(cvc4,[status(thm)],[320,133,205,350,342,138,101,479,333,115,449,202,142,472,184,372,344,357,196,284,325,164,485,106,121,292,452,366,302,424,192,361,461,456,317,188,169,420,109,124,339,476,96,264,375,191,413,172,271,103,140,213,483,330,130,223,299,267,167,282,95,327,310,199,177,127,470,175,314,465,99,258,186,114,207,346,287,290,119,410,262,273,210,474,427,369,111,322,337,354,215,454,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT193_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 15:49:08 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.58/1.06 % [INFO] Parsing done (210ms).
% 1.58/1.06 % [INFO] Running in sequential loop mode.
% 2.23/1.27 % [INFO] eprover registered as external prover.
% 2.23/1.27 % [INFO] cvc4 registered as external prover.
% 2.23/1.27 % [INFO] Scanning for conjecture ...
% 2.70/1.39 % [INFO] Found a conjecture and 92 axioms. Running axiom selection ...
% 2.70/1.46 % [INFO] Axiom selection finished. Selected 92 axioms (removed 0 axioms).
% 3.50/1.63 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.50/1.65 % [INFO] Type checking passed.
% 3.50/1.65 % [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 ...
% 4.15/1.81 % [INFO] [Domain constraints] Detected constraint on bool
% 4.15/1.81 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 132.30/80.85 % External prover 'cvc4' found a proof!
% 132.30/80.85 % [INFO] Killing All external provers ...
% 132.30/80.85 % Time passed: 80331ms (effective reasoning time: 79783ms)
% 132.30/80.85 % 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)>
% 132.30/80.85 % Axioms used in derivation (92): fact_36_above__Lin, help_fTrue_1_1_T, fact_42_curryI, fact_7_trans__def, fact_68_splitI2_H, fact_50_in__rel__def, fact_23_notin__Lin__iff, fact_34_in__above, fact_29_prod__cases5, fact_32_prod__induct3, fact_62_split__curry, fact_14_split__paired__Ex, fact_35_linear__alt, fact_25_mkbot__Lin, fact_18_UNIV__eq__I, fact_55_split__conv, fact_21_PairE, fact_5_Pair__eq, fact_54_mem__splitI, fact_47_trans__inv__image, fact_80_apfst__convE, conj_3, fact_61_curry__split, fact_71_scomp__apply, fact_33_in__below, fact_37_below__Lin, fact_60_splitD, fact_49_trans__lex__prod, help_fTrue_1_1_U, fact_4_split__paired__All, fact_27_prod__cases6, fact_67_mem__splitI2, fact_58_prod_Osimps_I2_J, fact_79_scomp__Pair, fact_11_in__mkbot, fact_74_apsnd__apfst__commute, fact_10_top__apply, fact_40_internal__split__conv, conj_2, fact_78_Pair__scomp, fact_66_mem__splitE, fact_26_prod__induct6, fact_19_UNIV__witness, fact_20_prod_Oexhaust, fact_70_split__cong, fact_13_UNIV__def, fact_41_curry__conv, arity_HOL_Obool___Orderings_Otop, fact_16_prod_Orecs, fact_46_curryD, fact_59_split__weak__cong, fact_56_in__lex__prod, fact_63_splitE, fact_9_strict__linear__order__on__def, fact_76_mem__def, fact_38_mktop__Lin, fact_44_in__inv__image, help_COMBK_1_1_U, fact_39_in__mktop, fact_22_prod__cases3, fact_6_total__on__def, fact_53_splitI, fact_31_prod__cases4, fact_28_prod__induct5, fact_3_iso__tuple__UNIV__I, fact_72_apfst__conv, fact_0_irrefl__def, fact_51_apsnd__conv, fact_52_prod__caseI, conj_1, fact_64_splitI2, fact_1_top1I, fact_17_Lin__def, fact_73_scomp__def, fact_69_splitE2, fact_43_in__inv__imagep, fact_57_splitD_H, fact_48_internal__split__def, fact_77_Collect__def, fact_8_transD, fact_65_splitE_H, help_pp_1_1_U, fact_2_UNIV__I, fact_75_ext, arity_fun___Orderings_Otop, fact_15_transI, fact_45_curryE, conj_0, help_pp_2_1_U, fact_24_Lin__irrefl, fact_30_prod__induct4, fact_12_Pair__inject
% 132.30/80.85 % No. of inferences in proof: 188
% 132.30/80.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 80331 ms resp. 79783 ms w/o parsing
% 132.61/80.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 132.61/80.94 % [INFO] Killing All external provers ...
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