TSTP Solution File: SCT200_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT200_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:51:14 EDT 2023
% Result : Theorem 61.30s 45.84s
% Output : Refutation 61.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 129
% Syntax : Number of formulae : 231 ( 85 unt; 29 typ; 0 def)
% Number of atoms : 2178 ( 255 equ; 0 cnn)
% Maximal formula atoms : 77 ( 10 avg)
% Number of connectives : 10156 ( 113 ~; 9 |; 59 &;9772 @)
% ( 15 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 12 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 9 con; 0-6 aty)
% Number of variables : 1171 ( 0 ^;1114 !; 18 ?;1171 :)
% ( 39 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(bool_type,type,
bool: $tType ).
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(in_rel_type,type,
in_rel:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TA ) @ bool ) > TB > TA > $o ) ).
thf(comp_type,type,
comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(refl_type,type,
refl:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $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(product_fst_type,type,
product_fst:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TB ) ).
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(product_snd_type,type,
product_snd:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TA ) ).
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(r_type,type,
r: 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(84,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ),C: product_prod @ TC @ TB] :
( ! [D: TC,E: TB] :
( ( ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ D ) @ E )
= C )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( aa @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ B @ D ) @ E ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TC @ TB @ ( fun @ TA @ bool ) ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_splitI2_H) ).
thf(457,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)],[84]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ D ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ E ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_prod__cases5) ).
thf(149,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)],[18]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( comp @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_o__apply) ).
thf(175,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( comp @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(139,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ B )
= ( product_fst @ TA @ TB @ A ) )
=> ( ( ( product_snd @ TA @ TB @ B )
= ( product_snd @ TA @ TB @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_prod__eqI) ).
thf(136,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ B )
= ( product_fst @ TA @ TB @ A ) )
=> ( ( ( product_snd @ TA @ TB @ B )
= ( product_snd @ TA @ TB @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_62_scomp__Pair) ).
thf(365,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)],[61]) ).
thf(87,axiom,
~ ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
~ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096_B_Bthesis_O_A_I_B_BR_O_AR_A_058_ALin_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(468,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)],[87]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_split__paired__All) ).
thf(481,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)],[90]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) ) @ D ) @ ( aa @ TD @ ( product_prod @ TC @ TD ) @ ( aa @ TC @ ( fun @ TD @ ( product_prod @ TC @ TD ) ) @ ( product_Pair @ TC @ TD ) @ E ) @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_prod__induct4) ).
thf(170,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)],[25]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ TC] :
( ( product_snd @ TA @ TC @ ( product_apsnd @ TB @ TC @ TA @ B @ A ) )
= ( aa @ TB @ TC @ B @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_snd__apsnd) ).
thf(523,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ TC] :
( ( product_snd @ TA @ TC @ ( product_apsnd @ TB @ TC @ TA @ B @ A ) )
= ( aa @ TB @ TC @ B @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',fact_44_apsnd__apfst__commute) ).
thf(115,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)],[7]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ D ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ C ) @ B ) ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_splitD_H) ).
thf(269,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)],[51]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ B ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_prod__cases3) ).
thf(202,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)],[36]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ),C: TB] :
( ( member @ TB @ C @ ( aa @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) ) @ ( product_prod_case @ TC @ TA @ ( fun @ TB @ bool ) ) @ B ) @ A ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( member @ TB @ C @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ B @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_mem__splitE) ).
thf(384,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)],[66]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_prod__caseI) ).
thf(142,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)],[15]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ TB ),C: fun @ TB @ bool] :
( ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TB @ bool @ C @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_splitE2) ).
thf(472,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)],[88]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',fact_63_Pair__scomp) ).
thf(436,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)],[76]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_curryD) ).
thf(257,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)],[47]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: product_prod @ TB @ TC,C: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ C ) @ B ) @ A ) )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ C @ D ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_splitE_H) ).
thf(184,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)],[30]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ TB,B: fun @ TB @ TC,C: TA] :
( ( aa @ TA @ TC @ ( comp @ TB @ TC @ TA @ B @ A ) @ C )
= ( aa @ TB @ TC @ B @ ( aa @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_o__def) ).
thf(504,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ TB,B: fun @ TB @ TC,C: TA] :
( ( aa @ TA @ TC @ ( comp @ TB @ TC @ TA @ B @ A ) @ C )
= ( aa @ TB @ TC @ B @ ( aa @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_prod_Osimps_I2_J) ).
thf(157,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)],[20]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_60_scomp__apply) ).
thf(416,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)],[70]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ TC,B: product_prod @ TA @ TB,C: fun @ TB @ TC] :
( ( ( product_apsnd @ TB @ TC @ TA @ C @ B )
= ( product_apsnd @ TB @ TC @ TA @ A @ B ) )
<=> ( ( aa @ TB @ TC @ C @ ( product_snd @ TA @ TB @ B ) )
= ( aa @ TB @ TC @ A @ ( product_snd @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_apsnd__eq__conv) ).
thf(152,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ TC,B: product_prod @ TA @ TB,C: fun @ TB @ TC] :
( ( ( ( product_apsnd @ TB @ TC @ TA @ C @ B )
= ( product_apsnd @ TB @ TC @ TA @ A @ B ) )
=> ( ( aa @ TB @ TC @ C @ ( product_snd @ TA @ TB @ B ) )
= ( aa @ TB @ TC @ A @ ( product_snd @ TA @ TB @ B ) ) ) )
& ( ( ( aa @ TB @ TC @ C @ ( product_snd @ TA @ TB @ B ) )
= ( aa @ TB @ TC @ A @ ( product_snd @ TA @ TB @ B ) ) )
=> ( ( product_apsnd @ TB @ TC @ TA @ C @ B )
= ( product_apsnd @ TB @ TC @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',fact_66_in__lex__prod) ).
thf(376,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)],[65]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Pair__eq) ).
thf(485,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)],[91]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ TC] :
( ( product_fst @ TA @ TC @ ( product_apsnd @ TB @ TC @ TA @ B @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fst__apsnd) ).
thf(106,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ TC] :
( ( product_fst @ TA @ TC @ ( product_apsnd @ TB @ TC @ TA @ B @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',fact_59_apfst__convE) ).
thf(353,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)],[58]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( aa @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( aa @ TF @ ( fun @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) ) @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ E ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_prod__cases6) ).
thf(221,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)],[41]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TD,C: fun @ TD @ TC] :
( ( product_apfst @ TD @ TC @ TB @ C @ ( product_apfst @ TA @ TD @ TB @ B @ A ) )
= ( product_apfst @ TA @ TC @ TB @ ( comp @ TD @ TC @ TA @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_apfst__compose) ).
thf(133,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TD,C: fun @ TD @ TC] :
( ( product_apfst @ TD @ TC @ TB @ C @ ( product_apfst @ TA @ TD @ TB @ B @ A ) )
= ( product_apfst @ TA @ TC @ TB @ ( comp @ TD @ TC @ TA @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ TC,B: product_prod @ TA @ TB,C: fun @ TA @ TC] :
( ( ( product_apfst @ TA @ TC @ TB @ C @ B )
= ( product_apfst @ TA @ TC @ TB @ A @ B ) )
<=> ( ( aa @ TA @ TC @ C @ ( product_fst @ TA @ TB @ B ) )
= ( aa @ TA @ TC @ A @ ( product_fst @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_apfst__eq__conv) ).
thf(428,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ TC,B: product_prod @ TA @ TB,C: fun @ TA @ TC] :
( ( ( ( product_apfst @ TA @ TC @ TB @ C @ B )
= ( product_apfst @ TA @ TC @ TB @ A @ B ) )
=> ( ( aa @ TA @ TC @ C @ ( product_fst @ TA @ TB @ B ) )
= ( aa @ TA @ TC @ A @ ( product_fst @ TA @ TB @ B ) ) ) )
& ( ( ( aa @ TA @ TC @ C @ ( product_fst @ TA @ TB @ B ) )
= ( aa @ TA @ TC @ A @ ( product_fst @ TA @ TB @ B ) ) )
=> ( ( product_apfst @ TA @ TC @ TB @ C @ B )
= ( product_apfst @ TA @ TC @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ TC,D: fun @ TC @ TB] :
( ( ( comp @ TC @ TB @ TA @ D @ C )
= B )
=> ( ( aa @ TC @ TB @ D @ ( aa @ TA @ TC @ C @ A ) )
= ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_o__eq__dest__lhs) ).
thf(265,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ TC,D: fun @ TC @ TB] :
( ( ( comp @ TC @ TB @ TA @ D @ C )
= B )
=> ( ( aa @ TC @ TB @ D @ ( aa @ TA @ TC @ C @ A ) )
= ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_prod__cases4) ).
thf(507,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)],[96]) ).
thf(82,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_424895264_mktop @ B @ A ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_mktop__Lin) ).
thf(452,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)],[82]) ).
thf(1,conjecture,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
& ( member @ ( 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 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
& ( member @ ( 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 ) @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(102,plain,
~ ? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
& ( member @ ( 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 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ B ) )
= A )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_fst__eqD) ).
thf(512,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ B ) )
= A )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_surj__pair) ).
thf(439,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)],[77]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_split__conv) ).
thf(160,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)],[21]) ).
thf(23,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(165,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)],[23]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) ) @ C ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_prod__induct3) ).
thf(197,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)],[34]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC ),B: product_prod @ TA @ TB,C: product_prod @ TA @ TB] :
( ( C = B )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ C )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_split__weak__cong) ).
thf(461,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)],[85]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Pair__inject) ).
thf(493,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)],[92]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_PairE) ).
thf(224,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)],[42]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',fact_36_apsnd__conv) ).
thf(188,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)],[31]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_snd @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_snd__conv) ).
thf(388,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_snd @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc1605651328_split @ TA @ TB @ TC )
= ( product_prod_case @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_internal__split__def) ).
thf(109,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)],[5]) ).
thf(89,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( B != A )
=> ( ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) @ C )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_notin__Lin__iff) ).
thf(476,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)],[89]) ).
thf(38,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 ) )
= ( aa @ TC @ ( product_prod @ TD @ TC ) @ ( aa @ TD @ ( fun @ TC @ ( product_prod @ TD @ TC ) ) @ ( product_Pair @ TD @ TC ) @ ( aa @ TA @ TD @ B @ ( product_fst @ TA @ TB @ A ) ) ) @ ( aa @ TB @ TC @ C @ ( product_snd @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_apsnd__apfst) ).
thf(212,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 ) )
= ( aa @ TC @ ( product_prod @ TD @ TC ) @ ( aa @ TD @ ( fun @ TC @ ( product_prod @ TD @ TC ) ) @ ( product_Pair @ TD @ TC ) @ ( aa @ TA @ TD @ B @ ( product_fst @ TA @ TB @ A ) ) ) @ ( aa @ TB @ TC @ C @ ( product_snd @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(59,axiom,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_linear__alt) ).
thf(360,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)],[59]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ TC ),C: fun @ TA @ ( fun @ TB @ TC ),D: product_prod @ TA @ TB] :
( ! [E: TA,F: TB] :
( ( ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ E ) @ F )
= D )
=> ( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ E ) @ F )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ E ) @ F ) ) )
=> ( ( A = D )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ C ) @ A )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_split__cong) ).
thf(205,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)],[37]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB] :
( ( ( product_snd @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ B ) )
= A )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_snd__eqD) ).
thf(311,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB] :
( ( ( product_snd @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ B ) )
= A )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ),B: TC,C: product_prod @ TA @ TB] :
( ! [D: TA,E: TB] :
( ( C
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ D ) @ E ) )
=> ( member @ TC @ B @ ( aa @ TB @ ( fun @ TC @ bool ) @ ( aa @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) @ A @ D ) @ E ) ) )
=> ( member @ TC @ B @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TA @ TB @ ( fun @ TC @ bool ) ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_mem__splitI2) ).
thf(423,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)],[72]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_61_scomp__def) ).
thf(191,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)],[32]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( B = A )
<=> ( ( ( product_fst @ TA @ TB @ B )
= ( product_fst @ TA @ TB @ A ) )
& ( ( product_snd @ TA @ TB @ B )
= ( product_snd @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_prod__eq__iff) ).
thf(118,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( B = A )
=> ( ( ( product_fst @ TA @ TB @ B )
= ( product_fst @ TA @ TB @ A ) )
& ( ( product_snd @ TA @ TB @ B )
= ( product_snd @ TA @ TB @ A ) ) ) )
& ( ( ( ( product_fst @ TA @ TB @ B )
= ( product_fst @ TA @ TB @ A ) )
& ( ( product_snd @ TA @ TB @ B )
= ( product_snd @ TA @ TB @ A ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ TC )] :
( ( 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 ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ ( product_fst @ TA @ TB @ A ) ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_prod__case__beta) ).
thf(259,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ TC )] :
( ( 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 ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ ( product_fst @ TA @ TB @ A ) ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ ( product_fst @ TA @ TB @ A ) ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_surjective__pairing) ).
thf(413,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ ( product_fst @ TA @ TB @ A ) ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(68,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) @ ( arrow_424895264_mktop @ B @ A ) )
<=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_in__mktop) ).
thf(391,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)],[68]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( product_Pair @ TD @ TE ) @ F ) @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_prod__induct5) ).
thf(445,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)],[79]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_splitI) ).
thf(144,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)],[16]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TC] :
( ( product_fst @ TC @ TB @ ( product_apfst @ TA @ TC @ TB @ B @ A ) )
= ( aa @ TA @ TC @ B @ ( product_fst @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_fst__apfst) ).
thf(498,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TC] :
( ( product_fst @ TC @ TB @ ( product_apfst @ TA @ TC @ TB @ B @ A ) )
= ( aa @ TA @ TC @ B @ ( product_fst @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC,D: fun @ TA @ TD,E: fun @ TD @ TC] :
( ( ( comp @ TD @ TC @ TA @ E @ D )
= ( comp @ TB @ TC @ TA @ C @ B ) )
=> ( ( aa @ TD @ TC @ E @ ( aa @ TA @ TD @ D @ A ) )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_o__eq__dest) ).
thf(181,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC,D: fun @ TA @ TD,E: fun @ TD @ TC] :
( ( ( comp @ TD @ TC @ TA @ E @ D )
= ( comp @ TB @ TC @ TA @ C @ B ) )
=> ( ( aa @ TD @ TC @ E @ ( aa @ TA @ TD @ D @ A ) )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TD,C: fun @ TD @ ( fun @ TB @ TC )] :
( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( comp @ TD @ ( fun @ TB @ TC ) @ TA @ C @ B ) ) @ A )
= ( aa @ TB @ TC @ ( aa @ TD @ ( fun @ TB @ TC ) @ C @ ( aa @ TA @ TD @ B @ ( product_fst @ TA @ TB @ A ) ) ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_split__comp) ).
thf(350,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TD,C: fun @ TD @ ( fun @ TB @ TC )] :
( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( comp @ TD @ ( fun @ TB @ TC ) @ TA @ C @ B ) ) @ A )
= ( aa @ TB @ TC @ ( aa @ TD @ ( fun @ TB @ TC ) @ C @ ( aa @ TA @ TD @ B @ ( product_fst @ TA @ TB @ A ) ) ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_prod_Orecs) ).
thf(172,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)],[26]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ B ) @ A ) )
=> ~ ! [C: TB,D: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_splitE) ).
thf(419,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)],[71]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_splitD) ).
thf(230,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)],[44]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ ( product_fst @ TA @ TB @ A ) ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_pair__collapse) ).
thf(362,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ ( product_fst @ TA @ TB @ A ) ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(52,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) @ ( arrow_1158827142_above @ C @ E @ D ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ E ) @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_in__above) ).
thf(271,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)],[52]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_curryI) ).
thf(140,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)],[14]) ).
thf(100,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( refl @ 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/sandbox/benchmark/theBenchmark.p',fact_39_Nitpick_Orefl_H__def) ).
thf(520,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( ( refl @ 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 )
=> ( refl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ TD,C: fun @ TD @ TC] :
( ( product_apsnd @ TD @ TC @ TA @ C @ ( product_apsnd @ TB @ TD @ TA @ B @ A ) )
= ( product_apsnd @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_apsnd__compose) ).
thf(130,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ TD,C: fun @ TD @ TC] :
( ( product_apsnd @ TD @ TC @ TA @ C @ ( product_apsnd @ TB @ TD @ TA @ B @ A ) )
= ( product_apsnd @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_prod_Oexhaust) ).
thf(306,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)],[53]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_curryE) ).
thf(374,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)],[64]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: fun @ TA @ TB,B: fun @ TB @ TD,C: fun @ TD @ TC] :
( ( comp @ TD @ TC @ TA @ C @ ( comp @ TB @ TD @ TA @ B @ A ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_o__assoc) ).
thf(112,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: fun @ TA @ TB,B: fun @ TB @ TD,C: fun @ TD @ TC] :
( ( comp @ TD @ TC @ TA @ C @ ( comp @ TB @ TD @ TA @ B @ A ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] :
( ( B
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ C ) @ D ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_splitI2) ).
thf(516,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)],[99]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( produc1605651328_split @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_internal__split__conv) ).
thf(194,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)],[33]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',fact_37_apfst__conv) ).
thf(199,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)],[35]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_split__paired__Ex) ).
thf(370,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)],[63]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TC] :
( ( product_snd @ TC @ TB @ ( product_apfst @ TA @ TC @ TB @ B @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_snd__apfst) ).
thf(127,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TC] :
( ( product_snd @ TC @ TB @ ( product_apfst @ TA @ TC @ TB @ B @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ TC,C: fun @ TA @ TD] :
( ( product_apfst @ TA @ TD @ TC @ C @ ( product_apsnd @ TB @ TC @ TA @ B @ A ) )
= ( aa @ TC @ ( product_prod @ TD @ TC ) @ ( aa @ TD @ ( fun @ TC @ ( product_prod @ TD @ TC ) ) @ ( product_Pair @ TD @ TC ) @ ( aa @ TA @ TD @ C @ ( product_fst @ TA @ TB @ A ) ) ) @ ( aa @ TB @ TC @ B @ ( product_snd @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_apfst__apsnd) ).
thf(465,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ TC,C: fun @ TA @ TD] :
( ( product_apfst @ TA @ TD @ TC @ C @ ( product_apsnd @ TB @ TC @ TA @ B @ A ) )
= ( aa @ TC @ ( product_prod @ TD @ TC ) @ ( aa @ TD @ ( fun @ TC @ ( product_prod @ TD @ TC ) ) @ ( product_Pair @ TD @ TC ) @ ( aa @ TA @ TD @ C @ ( product_fst @ TA @ TB @ A ) ) ) @ ( aa @ TB @ TC @ B @ ( product_snd @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
( ( member @ TC @ D @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) )
=> ( member @ TC @ D @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TB @ TA @ ( fun @ TC @ bool ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mem__splitI) ).
thf(450,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)],[81]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(218,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)],[40]) ).
thf(3,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(104,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(62,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_276188178_mkbot @ B @ A ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_mkbot__Lin) ).
thf(368,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)],[62]) ).
thf(46,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) @ ( arrow_276188178_mkbot @ B @ A ) )
<=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_in__mkbot) ).
thf(235,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)],[46]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ bool,C: TB,D: fun @ TB @ bool] :
( ( pp @ ( aa @ TB @ bool @ D @ C ) )
=> ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( pp @ ( aa @ TB @ bool @ D @ ( product_fst @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ A ) ) ) )
& ( pp @ ( aa @ TA @ bool @ B @ ( product_snd @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_conjI__realizer) ).
thf(433,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ bool,C: TB,D: fun @ TB @ bool] :
( ( pp @ ( aa @ TB @ bool @ D @ C ) )
=> ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( pp @ ( aa @ TB @ bool @ D @ ( product_fst @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ A ) ) ) )
& ( pp @ ( aa @ TA @ bool @ B @ ( product_snd @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ ( product_snd @ TA @ TB @ A ) ) @ ( product_fst @ TA @ TB @ A ) ) )
=> ~ ! [C: TA,D: TB] :
~ ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_exE__realizer_H) ).
thf(510,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ ( product_snd @ TA @ TB @ A ) ) @ ( product_fst @ TA @ TB @ A ) ) )
=> ~ ! [C: TA,D: TB] :
~ ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ C ) @ B ) @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_curry__conv) ).
thf(447,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)],[80]) ).
thf(56,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) @ ( arrow_319942042_below @ C @ E @ D ) )
<=> ( ( B != A )
& ( ( A = E )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ A ) @ C ) ) )
& ( ( B != E )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_in__below) ).
thf(315,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)],[56]) ).
thf(17,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms) ).
thf(146,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ E ) @ ( aa @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) ) @ F ) @ ( aa @ TF @ ( product_prod @ TE @ TF ) @ ( aa @ TE @ ( fun @ TF @ ( product_prod @ TE @ TF ) ) @ ( product_Pair @ TE @ TF ) @ G ) @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_prod__induct6) ).
thf(168,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)],[24]) ).
thf(49,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_319942042_below @ A @ C @ B ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_below__Lin) ).
thf(262,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)],[49]) ).
thf(73,axiom,
member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ r @ arrow_1985332922le_Lin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096R_A_058_ALin_096) ).
thf(427,plain,
member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ r @ arrow_1985332922le_Lin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(22,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) @ C )
=> ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Lin__irrefl) ).
thf(163,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)],[22]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',fact_35_in__rel__def) ).
thf(178,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)],[28]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC )] :
( ( product_curry @ TA @ TB @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_curry__split) ).
thf(442,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)],[78]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( product_curry @ TA @ TB @ TC @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_split__curry) ).
thf(501,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)],[94]) ).
thf(43,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_1158827142_above @ A @ C @ B ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_above__Lin) ).
thf(227,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)],[43]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( fun @ TB @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ C @ ( product_snd @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ A ) @ B ) ) ) @ ( product_fst @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_exI__realizer) ).
thf(309,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( fun @ TB @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ C @ ( product_snd @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ A ) @ B ) ) ) @ ( product_fst @ TB @ TA @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: fun @ TA @ TB,B: fun @ TB @ TC,C: fun @ TA @ TD,D: fun @ TD @ TC] :
( ( ( comp @ TD @ TC @ TA @ D @ C )
= ( comp @ TB @ TC @ TA @ B @ A ) )
=> ! [E: TA] :
( ( aa @ TD @ TC @ D @ ( aa @ TA @ TD @ C @ E ) )
= ( aa @ TB @ TC @ B @ ( aa @ TA @ TB @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_o__eq__elim) ).
thf(215,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: fun @ TA @ TB,B: fun @ TB @ TC,C: fun @ TA @ TD,D: fun @ TD @ TC] :
( ( ( comp @ TD @ TC @ TA @ D @ C )
= ( comp @ TB @ TC @ TA @ B @ A ) )
=> ! [E: TA] :
( ( aa @ TD @ TC @ D @ ( aa @ TA @ TD @ C @ E ) )
= ( aa @ TB @ TC @ B @ ( aa @ TA @ TB @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA,B: fun @ TA @ TC,C: fun @ TC @ TB,D: TE,E: fun @ TE @ TD,F: fun @ TD @ TB] :
( ( ( aa @ TD @ TB @ F @ ( aa @ TE @ TD @ E @ D ) )
= ( aa @ TC @ TB @ C @ ( aa @ TA @ TC @ B @ A ) ) )
=> ( ( aa @ TE @ TB @ ( comp @ TD @ TB @ TE @ F @ E ) @ D )
= ( aa @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_comp__cong) ).
thf(454,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA,B: fun @ TA @ TC,C: fun @ TC @ TB,D: TE,E: fun @ TE @ TD,F: fun @ TD @ TB] :
( ( ( aa @ TD @ TB @ F @ ( aa @ TE @ TD @ E @ D ) )
= ( aa @ TC @ TB @ C @ ( aa @ TA @ TC @ B @ A ) ) )
=> ( ( aa @ TE @ TB @ ( comp @ TD @ TB @ TE @ F @ E ) @ D )
= ( aa @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_fst @ TA @ TB @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_fst__conv) ).
thf(232,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_fst @ TA @ TB @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(526,plain,
$false,
inference(e,[status(thm)],[457,149,175,139,136,365,468,481,170,523,115,269,202,384,142,472,436,257,184,504,157,416,152,376,485,106,353,221,133,428,265,507,452,102,512,439,160,165,197,461,493,224,188,388,109,476,212,360,205,311,423,191,118,259,413,391,445,144,498,181,350,172,419,230,362,271,140,520,130,306,374,112,516,194,199,370,127,465,450,218,104,368,235,433,510,447,315,146,168,262,427,163,178,442,501,227,309,215,454,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SCT200_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n021.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Thu May 18 15:26:43 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.99/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.77/1.23 % [INFO] Parsing done (306ms).
% 1.98/1.24 % [INFO] Running in sequential loop mode.
% 2.62/1.48 % [INFO] eprover registered as external prover.
% 2.62/1.48 % [INFO] cvc4 registered as external prover.
% 2.62/1.48 % [INFO] Scanning for conjecture ...
% 2.93/1.60 % [INFO] Found a conjecture and 99 axioms. Running axiom selection ...
% 3.46/1.69 % [INFO] Axiom selection finished. Selected 99 axioms (removed 0 axioms).
% 3.95/1.90 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.17/1.92 % [INFO] Type checking passed.
% 4.17/1.92 % [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 ...
% 61.30/45.84 % External prover 'e' found a proof!
% 61.30/45.84 % [INFO] Killing All external provers ...
% 61.30/45.84 % Time passed: 45303ms (effective reasoning time: 44597ms)
% 61.30/45.84 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 61.30/45.84 % Axioms used in derivation (99): fact_33_curryD, fact_74_snd__eqD, fact_70_snd__apfst, fact_32_curryE, fact_83_fst__conv, fact_29_internal__split__conv, fact_10_above__Lin, fact_92_o__eq__elim, fact_78_surjective__pairing, fact_90_comp__cong, fact_93_o__def, fact_67_apfst__eq__conv, fact_48_prod_Osimps_I2_J, fact_59_apfst__convE, fact_89_apfst__compose, fact_81_prod__eqI, fact_11_below__Lin, fact_46_splitD, fact_5_split__paired__All, fact_47_splitD_H, fact_56_splitE_H, fact_61_scomp__def, fact_77_snd__conv, fact_96_o__eq__dest__lhs, fact_72_apsnd__eq__conv, fact_28_prod__cases5, fact_21_prod__cases3, fact_65_apfst__apsnd, fact_18_prod_Orecs, fact_41_prod__caseI, fact_8_in__below, fact_71_snd__apsnd, fact_24_prod__induct4, fact_12_mkbot__Lin, fact_20_PairE, fact_22_prod__induct3, fact_7_in__above, fact_36_apsnd__conv, fact_88_apsnd__compose, fact_95_o__eq__dest, fact_55_mem__splitE, fact_40_splitI, fact_19_prod_Oexhaust, fact_34_internal__split__def, fact_58_split__cong, fact_2_assms, fact_14_in__mkbot, fact_63_Pair__scomp, fact_31_curryI, fact_6_Pair__eq, fact_66_in__lex__prod, fact_45_split__weak__cong, fact_76_mem__def, fact_53_mem__splitI2, fact_39_Nitpick_Orefl_H__def, fact_91_o__apply, fact_73_prod__case__beta, fact_38_surj__pair, fact_0__096R_A_058_ALin_096, fact_86_exE__realizer_H, fact_52_splitI2, fact_15_in__mktop, fact_82_fst__eqD, fact_54_splitI2_H, fact_60_scomp__apply, fact_87_split__comp, fact_9_linear__alt, fact_68_fst__apfst, fact_84_conjI__realizer, fact_26_prod__cases6, fact_16_Pair__inject, fact_1__096_B_Bthesis_O_A_I_B_BR_O_AR_A_058_ALin_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_27_prod__induct5, fact_42_mem__splitI, fact_17_split__paired__Ex, fact_64_apsnd__apfst, fact_4_Lin__irrefl, fact_57_splitE2, fact_85_exI__realizer, fact_25_prod__induct6, fact_80_prod__eq__iff, fact_30_curry__conv, fact_13_mktop__Lin, fact_35_in__rel__def, fact_50_split__curry, fact_94_o__assoc, help_pp_1_1_U, fact_51_splitE, fact_62_scomp__Pair, fact_44_apsnd__apfst__commute, fact_69_fst__apsnd, fact_37_apfst__conv, fact_75_ext, fact_43_split__conv, fact_3_notin__Lin__iff, fact_23_prod__cases4, help_pp_2_1_U, fact_49_curry__split, fact_79_pair__collapse
% 61.30/45.84 % No. of inferences in proof: 202
% 61.30/45.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 45303 ms resp. 44597 ms w/o parsing
% 61.74/45.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 61.74/45.94 % [INFO] Killing All external provers ...
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