TSTP Solution File: SCT229_5 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT229_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 11:51:19 EDT 2023
% Result : Theorem 53.76s 38.03s
% Output : Refutation 54.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 132
% Syntax : Number of formulae : 232 ( 56 unt; 34 typ; 0 def)
% Number of atoms : 1811 ( 222 equ; 0 cnn)
% Maximal formula atoms : 106 ( 9 avg)
% Number of connectives : 8441 ( 138 ~; 9 |; 71 &;7887 @)
% ( 31 <=>; 305 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 13 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 11 con; 0-5 aty)
% Number of variables : 1025 ( 0 ^; 982 !; 13 ?;1025 :)
% ( 30 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(arrow_159774573e_indi_type,type,
arrow_159774573e_indi: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(arrow_1958449194le_IIA_type,type,
arrow_1958449194le_IIA: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(arrow_1985332922le_Lin_type,type,
arrow_1985332922le_Lin: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ).
thf(arrow_610318064e_Prof_type,type,
arrow_610318064e_Prof: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ).
thf(arrow_1158827142_above_type,type,
arrow_1158827142_above: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_319942042_below_type,type,
arrow_319942042_below: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_987702531ctator_type,type,
arrow_987702531ctator: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > arrow_159774573e_indi > $o ).
thf(arrow_276188178_mkbot_type,type,
arrow_276188178_mkbot: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_424895264_mktop_type,type,
arrow_424895264_mktop: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_2069624013nimity_type,type,
arrow_2069624013nimity: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(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(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_curry_type,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ ( product_prod @ TC @ TB ) @ TA ) > ( fun @ TC @ ( fun @ TB @ TA ) ) ) ).
thf(produc1605651328_split_type,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TA ) ) ).
thf(product_prod_case_type,type,
product_prod_case:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TA ) ) ).
thf(product_prod_rec_type,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(id_on_type,type,
id_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).
thf(antisym_type,type,
antisym:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(converse_type,type,
converse:
!>[TA: $tType,TB: $tType] : ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) ).
thf(inv_image_type,type,
inv_image:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TB ) @ bool ) > ( fun @ TA @ TB ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).
thf(irrefl_type,type,
irrefl:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(total_on_type,type,
total_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(f_type,type,
f: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(p_type,type,
p: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(p1_type,type,
p1: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(a_type,type,
a: arrow_411405190le_alt ).
thf(b_type,type,
b: arrow_411405190le_alt ).
thf(c_type,type,
c: arrow_411405190le_alt ).
thf(42,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 ) @ ( 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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( member @ ( 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_60_in__below) ).
thf(279,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 ) @ ( 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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( member @ ( 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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( member @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( arrow_319942042_below @ C @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(54,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 ) @ ( 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_73_split__conv) ).
thf(351,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 ) @ ( 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)],[54]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_prod__cases6) ).
thf(479,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(73,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_23_o__eq__elim) ).
thf(468,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)],[73]) ).
thf(41,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( irrefl @ TA @ A )
<=> ! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_irrefl__def) ).
thf(276,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( ( irrefl @ TA @ A )
=> ! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A ) )
& ( ! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A )
=> ( irrefl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_prod__cases4) ).
thf(202,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19__C1_C) ).
thf(385,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_prod__cases5) ).
thf(550,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(87,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_24_o__eq__dest) ).
thf(538,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)],[87]) ).
thf(20,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ! [B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A )
=> ( B = C ) ) )
=> ( antisym @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_antisymI) ).
thf(185,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ! [B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A )
=> ( B = C ) ) )
=> ( antisym @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TA,C: TB] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ C @ B ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) )
<=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_converse__iff) ).
thf(320,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TA,C: TB] :
( ( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ C @ B ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A )
=> ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ C @ B ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(7,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( antisym @ TA @ A )
<=> ! [B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_antisym__def) ).
thf(110,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( ( antisym @ TA @ A )
=> ! [B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A )
=> ( B = C ) ) ) )
& ( ! [B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A )
=> ( B = C ) ) )
=> ( antisym @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(53,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] :
( ( ( 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_96_split__cong) ).
thf(344,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] :
( ( ( 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)],[53]) ).
thf(56,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
= ( 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_95_splitE2) ).
thf(357,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ TB ),C: fun @ TB @ bool] :
( ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( 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)],[56]) ).
thf(71,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( id_on @ TA @ A ) )
<=> ( ( C = B )
& ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Id__on__iff) ).
thf(460,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( id_on @ TA @ A ) )
=> ( ( C = B )
& ( member @ TA @ C @ A ) ) )
& ( ( ( C = B )
& ( member @ TA @ C @ A ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( id_on @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( 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_74_splitD) ).
thf(559,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 ) @ ( product_Pair @ TB @ TA @ B @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(67,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 @ ( product_Pair @ TB @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_curry__conv) ).
thf(416,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 @ ( product_Pair @ TB @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(44,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
= ( 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_89_splitE) ).
thf(316,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
= ( 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)],[44]) ).
thf(35,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 ) @ ( product_Pair @ TB @ TC @ C @ B ) ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_splitD_H) ).
thf(261,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 ) @ ( 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)],[35]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( 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_45_curryI) ).
thf(475,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( 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)],[75]) ).
thf(80,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ B @ ( id_on @ TA @ A ) )
=> ~ ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B
!= ( product_Pair @ TA @ TA @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Id__onE) ).
thf(492,plain,
! [TA: $tType,A: fun @ TA @ bool,B: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ B @ ( id_on @ TA @ A ) )
=> ~ ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B
!= ( product_Pair @ TA @ TA @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(27,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
= ( 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_90_mem__splitI2) ).
thf(211,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
= ( 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)],[27]) ).
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_69_internal__split__def) ).
thf(106,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(98,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_A_I1_J) ).
thf(574,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(13,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] :
( ( ( 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_91_splitI2_H) ).
thf(132,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] :
( ( ( 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)],[13]) ).
thf(65,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_11_o__apply) ).
thf(411,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)],[65]) ).
thf(31,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_78_split__weak__cong) ).
thf(248,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)],[31]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_prod__induct4) ).
thf(117,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,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 ) @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_prod__caseI) ).
thf(270,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 ) @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,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_26_o__def) ).
thf(160,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)],[15]) ).
thf(95,axiom,
! [A: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( comp @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ p1 ) @ A ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062_Iconverse_Ao_AP_J_Ai_092_060_094esub_062_Aa_J_A_061_A_Ib_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ac_J_096) ).
thf(561,plain,
! [A: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( comp @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ p1 ) @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( comp @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ p1 ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(17,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)],[17]) ).
thf(72,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( comp @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ p1 ) @ arrow_610318064e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_cP) ).
thf(467,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( comp @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ p1 ) @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(96,axiom,
! [A: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_iff) ).
thf(566,plain,
! [A: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(32,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_62_above__Lin) ).
thf(252,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)],[32]) ).
thf(57,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_49_comp__cong) ).
thf(361,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)],[57]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( in_rel @ TA @ TB @ C @ B @ A )
<=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_in__rel__def) ).
thf(324,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ( in_rel @ TA @ TB @ C @ B @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C )
=> ( in_rel @ TA @ TB @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(29,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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_in__mktop) ).
thf(224,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 ) @ ( 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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) )
=> ( member @ ( 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)],[29]) ).
thf(51,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_61_below__Lin) ).
thf(339,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)],[51]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_PairE) ).
thf(547,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(6,axiom,
arrow_1958449194le_IIA @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_assms_I3_J) ).
thf(109,plain,
arrow_1958449194le_IIA @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(74,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
= ( 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_92_splitE_H) ).
thf(471,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
= ( 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)],[74]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: TA,C: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( antisym @ TA @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ A ) @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_antisymD) ).
thf(457,plain,
! [TA: $tType,A: TA,B: TA,C: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( antisym @ TA @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ A ) @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(12,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_82_curry__split) ).
thf(129,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)],[12]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] :
( ( B
= ( 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_88_splitI2) ).
thf(266,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] :
( ( B
= ( 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)],[37]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_prod__cases3) ).
thf(205,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_prod_Orecs) ).
thf(541,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(99,axiom,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_A_I2_J) ).
thf(577,plain,
b != c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(34,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_56_mktop__Lin) ).
thf(259,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)],[34]) ).
thf(60,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_25_o__assoc) ).
thf(382,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)],[60]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Pair__eq) ).
thf(498,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_prod__induct3) ).
thf(274,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(68,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 ) @ ( 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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( 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_59_in__above) ).
thf(419,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 ) @ ( 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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( 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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( arrow_1158827142_above @ C @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( converse @ TB @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_converse__converse) ).
thf(208,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( converse @ TB @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(76,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 @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_curryE) ).
thf(477,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 @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(86,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(535,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)],[86]) ).
thf(3,axiom,
arrow_2069624013nimity @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_u) ).
thf(103,plain,
arrow_2069624013nimity @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(46,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p @ arrow_610318064e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_A_I5_J) ).
thf(323,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(23,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( C = B )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( id_on @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Id__on__eqI) ).
thf(198,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( C = B )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( id_on @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_split__paired__Ex) ).
thf(255,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(79,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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
<=> ( member @ ( 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_53_notin__Lin__iff) ).
thf(487,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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
=> ( member @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C )
=> ~ ( member @ ( 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)],[79]) ).
thf(92,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_81_split__curry) ).
thf(553,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)],[92]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_prod__induct5) ).
thf(342,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(10,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
= ( 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_93_mem__splitE) ).
thf(123,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
= ( 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)],[10]) ).
thf(66,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_63_linear__alt) ).
thf(414,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)],[66]) ).
thf(48,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_2069624013nimity @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_unanimity__def) ).
thf(327,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_2069624013nimity @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) )
=> ( arrow_2069624013nimity @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
( ( member @ TC @ D @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) )
=> ( member @ TC @ D @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TB @ TA @ ( fun @ TC @ bool ) ) @ C ) @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_mem__splitI) ).
thf(409,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 ) @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prod_Oexhaust) ).
thf(263,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(19,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ ( id_on @ TA @ A ) )
= ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_converse__Id__on) ).
thf(182,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ ( id_on @ TA @ A ) )
= ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_prod__induct6) ).
thf(127,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(89,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( antisym @ TA @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ A ) )
<=> ( antisym @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_antisym__converse) ).
thf(544,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( ( antisym @ TA @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ A ) )
=> ( antisym @ TA @ A ) )
& ( ( antisym @ TA @ A )
=> ( antisym @ TA @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(49,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p1 @ arrow_610318064e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_A_I4_J) ).
thf(336,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p1 @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(43,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 @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_curryD) ).
thf(314,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 @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(97,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_A_I3_J) ).
thf(571,plain,
a != c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(93,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 ) @ ( 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_79_prod_Osimps_I2_J) ).
thf(556,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 ) @ ( 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)],[93]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Pair__inject) ).
thf(482,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(4,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( antisym @ TA @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_antisym__Id__on) ).
thf(104,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( antisym @ TA @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(59,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( D != C )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [E: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ E ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__C3_C) ).
thf(368,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( D != C )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [E: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ E ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(9,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_50_o__eq__dest__lhs) ).
thf(119,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)],[9]) ).
thf(30,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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
=> ~ ( member @ ( 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_52_Lin__irrefl) ).
thf(246,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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
=> ~ ( member @ ( 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)],[30]) ).
thf(84,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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_in__mkbot) ).
thf(510,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 ) @ ( 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 ) @ ( 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 ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) )
=> ( member @ ( 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)],[84]) ).
thf(39,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_55_mkbot__Lin) ).
thf(272,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)],[39]) ).
thf(18,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__C2_C) ).
thf(168,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ arrow_1985332922le_Lin )
<=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_converse__in__Lin) ).
thf(190,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ arrow_1985332922le_Lin )
=> ( 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 ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_1958449194le_IIA @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_IIA__def) ).
thf(136,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_1958449194le_IIA @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) )
=> ( arrow_1958449194le_IIA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_split__paired__All) ).
thf(506,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TB,D: TB] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ D @ C ) @ ( inv_image @ TA @ TB @ B @ A ) )
<=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( aa @ TB @ TA @ A @ D ) @ ( aa @ TB @ TA @ A @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_in__inv__image) ).
thf(195,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TB,D: TB] :
( ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ D @ C ) @ ( inv_image @ TA @ TB @ B @ A ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( aa @ TB @ TA @ A @ D ) @ ( aa @ TB @ TA @ A @ C ) ) @ B ) )
& ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( aa @ TB @ TA @ A @ D ) @ ( aa @ TB @ TA @ A @ C ) ) @ B )
=> ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ D @ C ) @ ( inv_image @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(63,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( total_on @ TA @ B @ A )
<=> ! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_total__on__def) ).
thf(400,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( total_on @ TA @ B @ A )
=> ! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ A ) ) ) ) ) )
& ( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ A ) ) ) ) )
=> ( total_on @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(85,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 ) @ ( 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_41_internal__split__conv) ).
thf(532,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 ) @ ( 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)],[85]) ).
thf(62,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
& ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_complete__Lin) ).
thf(395,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
& ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TB,C: TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ B ) @ A )
=> ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ C ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_converseI) ).
thf(163,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TB,C: TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ B ) @ A )
=> ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ C ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TA,C: TB] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ C @ B ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_converseD) ).
thf(337,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TA,C: TB] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ C @ B ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ ( inv_image @ TB @ TA @ B @ A ) )
= ( inv_image @ TB @ TA @ ( aa @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ ( converse @ TB @ TB ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_converse__inv__image) ).
thf(354,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ ( inv_image @ TB @ TA @ B @ A ) )
= ( inv_image @ TB @ TA @ ( aa @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ ( converse @ TB @ TB ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(28,axiom,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_987702531ctator @ B @ A )
<=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_dictator__def) ).
thf(215,plain,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_987702531ctator @ B @ A )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) )
& ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: product_prod @ TB @ TA] :
( ( member @ ( product_prod @ TB @ TA ) @ B @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) )
=> ~ ! [C: TA,D: TB] :
( ( B
= ( product_Pair @ TB @ TA @ D @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_converseE) ).
thf(364,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: product_prod @ TB @ TA] :
( ( member @ ( product_prod @ TB @ TA ) @ B @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( converse @ TA @ TB ) @ A ) )
=> ~ ! [C: TA,D: TB] :
( ( B
= ( product_Pair @ TB @ TA @ D @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1,conjecture,
b != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_7) ).
thf(2,negated_conjecture,
b != a,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(100,plain,
b != a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_splitI) ).
thf(496,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 ) @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(69,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( total_on @ TA @ B @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ A ) )
<=> ( total_on @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_total__on__converse) ).
thf(454,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( total_on @ TA @ B @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ A ) )
=> ( total_on @ TA @ B @ A ) )
& ( ( total_on @ TA @ B @ A )
=> ( total_on @ TA @ B @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ ( converse @ TA @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(580,plain,
$false,
inference(e,[status(thm)],[279,351,479,468,276,202,385,550,538,185,320,110,344,357,460,559,416,316,261,475,492,211,106,574,132,411,248,117,270,160,561,165,467,566,252,361,324,224,339,547,109,471,457,129,266,205,541,577,259,382,498,274,419,208,477,535,103,323,198,255,487,553,342,123,414,327,409,263,182,127,544,336,314,571,556,482,104,368,119,246,510,272,168,190,136,506,195,400,532,395,163,337,354,215,364,100,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SCT229_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.13 % Command : run_Leo-III %s %d
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 18 15:29:31 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.94/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/1.10 % [INFO] Parsing done (224ms).
% 1.58/1.11 % [INFO] Running in sequential loop mode.
% 2.39/1.33 % [INFO] eprover registered as external prover.
% 2.39/1.33 % [INFO] cvc4 registered as external prover.
% 2.39/1.33 % [INFO] Scanning for conjecture ...
% 2.55/1.44 % [INFO] Found a conjecture and 106 axioms. Running axiom selection ...
% 2.94/1.52 % [INFO] Axiom selection finished. Selected 97 axioms (removed 9 axioms).
% 3.51/1.70 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.51/1.73 % [INFO] Type checking passed.
% 3.51/1.73 % [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 ...
% 53.65/38.02 % External prover 'e' found a proof!
% 53.65/38.02 % [INFO] Killing All external provers ...
% 53.65/38.03 % Time passed: 37500ms (effective reasoning time: 36916ms)
% 53.65/38.03 % 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)>
% 53.76/38.03 % Axioms used in derivation (97): fact_65_irrefl__def, fact_26_o__def, fact_82_curry__split, fact_32_PairE, fact_16_dictator__def, fact_23_o__eq__elim, fact_60_in__below, fact_59_in__above, fact_75_ext, fact_93_mem__splitE, fact_91_splitI2_H, fact_25_o__assoc, fact_70_prod__caseI, fact_58_complete__Lin, fact_79_prod_Osimps_I2_J, fact_73_split__conv, fact_86_Id__on__iff, fact_24_o__eq__dest, fact_30_prod_Orecs, fact_17_converseE, fact_67_antisym__converse, fact_72_mem__splitI, fact_3_A_I2_J, fact_84_antisym__def, fact_31_prod_Oexhaust, fact_52_Lin__irrefl, fact_14_converseI, fact_37_prod__induct5, fact_10_converse__iff, fact_36_prod__cases6, fact_63_linear__alt, fact_6_cP, fact_95_splitE2, fact_34_prod__induct3, fact_38_prod__cases5, fact_88_splitI2, fact_1_A_I5_J, fact_44_in__mkbot, fact_7_assms_I3_J, fact_11_o__apply, fact_21_unanimity__def, fact_15_converseD, fact_64_converse__inv__image, fact_90_mem__splitI2, fact_8_u, fact_57_in__rel__def, fact_49_comp__cong, fact_20__C3_C, fact_94_antisymI, fact_29_split__paired__Ex, fact_4_A_I3_J, fact_78_split__weak__cong, fact_27_converse__converse, fact_19__C1_C, fact_5_iff, fact_41_internal__split__conv, fact_13_Pair__eq, fact_55_mkbot__Lin, fact_46_curryD, fact_43_in__mktop, fact_35_prod__induct6, fact_76_mem__def, fact_2_A_I1_J, fact_83_antisymD, fact_28_IIA__def, fact_71_splitI, fact_74_splitD, fact_61_below__Lin, fact_12_split__paired__All, fact_81_split__curry, fact_47_curryE, fact_53_notin__Lin__iff, fact_9__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062_Iconverse_Ao_AP_J_Ai_092_060_094esub_062_Aa_J_A_061_A_Ib_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ac_J_096, fact_66_in__inv__image, fact_51_total__on__converse, fact_54_total__on__def, fact_80_splitD_H, fact_48_converse__in__Lin, fact_18__C2_C, fact_22_Pair__inject, fact_69_internal__split__def, fact_96_split__cong, fact_33_prod__cases3, fact_85_Id__on__eqI, fact_56_mktop__Lin, fact_87_Id__onE, fact_40_prod__cases4, fact_89_splitE, fact_42_curry__conv, fact_92_splitE_H, fact_77_antisym__Id__on, fact_62_above__Lin, fact_68_converse__Id__on, fact_0_A_I4_J, fact_50_o__eq__dest__lhs, fact_45_curryI, fact_39_prod__induct4
% 53.76/38.03 % No. of inferences in proof: 198
% 53.76/38.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 37500 ms resp. 36916 ms w/o parsing
% 54.14/38.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 54.14/38.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------