TSTP Solution File: ITP139^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP139^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 : Tue May 7 07:48:10 EDT 2024
% Result : Theorem 16.65s 5.11s
% Output : Refutation 17.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 439
% Syntax : Number of formulae : 761 ( 180 unt; 119 typ; 0 def)
% Number of atoms : 2176 ( 914 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 5227 ( 60 ~; 2 |; 58 &;4059 @)
% ( 0 <=>;1048 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 895 ( 895 >; 0 *; 0 +; 0 <<)
% Number of symbols : 107 ( 105 usr; 8 con; 0-3 aty)
% Number of variables : 1906 ( 74 ^1764 !; 68 ?;1906 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr2014382200lle_tv_type,type,
set_Pr2014382200lle_tv: $tType ).
thf(produc1647334210lle_tv_type,type,
produc1647334210lle_tv: $tType ).
thf(set_Pr1725653840tv_nat_type,type,
set_Pr1725653840tv_nat: $tType ).
thf(set_Pr13445366lle_tv_type,type,
set_Pr13445366lle_tv: $tType ).
thf(produc194167194tv_nat_type,type,
produc194167194tv_nat: $tType ).
thf(produc270694976lle_tv_type,type,
produc270694976lle_tv: $tType ).
thf(set_se800614875lle_tv_type,type,
set_se800614875lle_tv: $tType ).
thf(set_Pr1986765409at_nat_type,type,
set_Pr1986765409at_nat: $tType ).
thf(set_Pa1764573435lle_tv_type,type,
set_Pa1764573435lle_tv: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(paraco1605129243lle_tv_type,type,
paraco1605129243lle_tv: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(inj_on_nat_nat_type,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(inj_on1955349912lle_tv_type,type,
inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
thf(inj_on1179712058tv_nat_type,type,
inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
thf(inj_on772319074lle_tv_type,type,
inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
thf(inj_on642995232at_nat_type,type,
inj_on642995232at_nat: ( product_prod_nat_nat > nat ) > set_Pr1986765409at_nat > $o ).
thf(inj_on520021963lle_tv_type,type,
inj_on520021963lle_tv: ( product_prod_nat_nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat > $o ).
thf(inj_on26176689at_nat_type,type,
inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
thf(inj_on1840679568lle_tv_type,type,
inj_on1840679568lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > $o ).
thf(inj_on1764151786tv_nat_type,type,
inj_on1764151786tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > $o ).
thf(inj_on936843139tv_nat_type,type,
inj_on936843139tv_nat: ( produc270694976lle_tv > nat ) > set_Pr13445366lle_tv > $o ).
thf(inj_on394919723lle_tv_type,type,
inj_on394919723lle_tv: ( produc270694976lle_tv > paraco1605129243lle_tv ) > set_Pr13445366lle_tv > $o ).
thf(inj_on1745913142lle_tv_type,type,
inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
thf(inj_on808253149at_nat_type,type,
inj_on808253149at_nat: ( produc194167194tv_nat > nat ) > set_Pr1725653840tv_nat > $o ).
thf(inj_on1612474245lle_tv_type,type,
inj_on1612474245lle_tv: ( produc194167194tv_nat > paraco1605129243lle_tv ) > set_Pr1725653840tv_nat > $o ).
thf(inj_on1971554740at_nat_type,type,
inj_on1971554740at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > $o ).
thf(inj_on552895452tv_nat_type,type,
inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
thf(inj_on967082628lle_tv_type,type,
inj_on967082628lle_tv: ( produc194167194tv_nat > produc1647334210lle_tv ) > set_Pr1725653840tv_nat > $o ).
thf(inj_on2112487900lle_tv_type,type,
inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
thf(strict2146030304at_nat_type,type,
strict2146030304at_nat: ( nat > nat ) > set_nat > $o ).
thf(strict1310998166et_nat_type,type,
strict1310998166et_nat: ( nat > set_nat ) > set_nat > $o ).
thf(strict1658340843lle_tv_type,type,
strict1658340843lle_tv: ( nat > set_Pa1764573435lle_tv ) > set_nat > $o ).
thf(the_inv_into_nat_nat_type,type,
the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
thf(the_in138087638lle_tv_type,type,
the_in138087638lle_tv: set_nat > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > nat ).
thf(the_in1509933432tv_nat_type,type,
the_in1509933432tv_nat: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > nat ) > nat > paraco1605129243lle_tv ).
thf(the_in452116896lle_tv_type,type,
the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(the_in2068894451at_nat_type,type,
the_in2068894451at_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(the_in667485224tv_nat_type,type,
the_in667485224tv_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > produc194167194tv_nat ) > produc194167194tv_nat > product_prod_nat_nat ).
thf(the_in1388677748lle_tv_type,type,
the_in1388677748lle_tv: set_Pr13445366lle_tv > ( produc270694976lle_tv > produc270694976lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
thf(the_in874888178at_nat_type,type,
the_in874888178at_nat: set_Pr1725653840tv_nat > ( produc194167194tv_nat > product_prod_nat_nat ) > product_prod_nat_nat > produc194167194tv_nat ).
thf(the_in195660058tv_nat_type,type,
the_in195660058tv_nat: set_Pr1725653840tv_nat > ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat > produc194167194tv_nat ).
thf(the_in427240730lle_tv_type,type,
the_in427240730lle_tv: set_Pr2014382200lle_tv > ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
thf(plus_plus_nat_type,type,
plus_plus_nat: nat > nat > nat ).
thf(ord_less_nat_type,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_set_nat_type,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(ord_le727057319lle_tv_type,type,
ord_le727057319lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_set_nat_type,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(ord_le241064091lle_tv_type,type,
ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
thf(order_769474267at_nat_type,type,
order_769474267at_nat: ( nat > nat ) > $o ).
thf(top_top_nat_o_type,type,
top_top_nat_o: nat > $o ).
thf(top_to1299250770e_tv_o_type,type,
top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
thf(top_to632227436_nat_o_type,type,
top_to632227436_nat_o: product_prod_nat_nat > $o ).
thf(top_to1889334367e_tv_o_type,type,
top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
thf(top_to900819589_nat_o_type,type,
top_to900819589_nat_o: produc194167194tv_nat > $o ).
thf(top_top_o_type,type,
top_top_o: $o ).
thf(top_top_set_nat_type,type,
top_top_set_nat: set_nat ).
thf(top_to1057771083lle_tv_type,type,
top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
thf(top_to1555900337at_nat_type,type,
top_to1555900337at_nat: set_Pr1986765409at_nat ).
thf(top_to1411004326lle_tv_type,type,
top_to1411004326lle_tv: set_Pr13445366lle_tv ).
thf(top_to975729152tv_nat_type,type,
top_to975729152tv_nat: set_Pr1725653840tv_nat ).
thf(top_to1871154984lle_tv_type,type,
top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
thf(paraco1147068288nge_tv_type,type,
paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
thf(paraco793048302_Indet_type,type,
paraco793048302_Indet: nat > paraco1605129243lle_tv ).
thf(produc1320959600at_nat_type,type,
produc1320959600at_nat: ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(produc237097339lle_tv_type,type,
produc237097339lle_tv: ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
thf(produc1608943133tv_nat_type,type,
produc1608943133tv_nat: ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
thf(produc1804670661lle_tv_type,type,
produc1804670661lle_tv: ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc1647334210lle_tv ).
thf(produc2040316391tv_nat_type,type,
produc2040316391tv_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
thf(produc1408152463lle_tv_type,type,
produc1408152463lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
thf(produc505105722at_nat_type,type,
produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(produc2101297531lle_tv_type,type,
produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
thf(produc189459613tv_nat_type,type,
produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
thf(produc1975500101lle_tv_type,type,
produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
thf(produc386540311at_nat_type,type,
produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
thf(produc72207551lle_tv_type,type,
produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
thf(produc51277375tv_nat_type,type,
produc51277375tv_nat: ( paraco1605129243lle_tv > nat ) > ( paraco1605129243lle_tv > nat ) > produc1647334210lle_tv > product_prod_nat_nat ).
thf(produc1095080935lle_tv_type,type,
produc1095080935lle_tv: ( paraco1605129243lle_tv > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc270694976lle_tv ).
thf(produc42536895at_nat_type,type,
produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
thf(produc1521089895lle_tv_type,type,
produc1521089895lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc1647334210lle_tv ).
thf(produc1500159719tv_nat_type,type,
produc1500159719tv_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc1647334210lle_tv > produc194167194tv_nat ).
thf(produc1345917071lle_tv_type,type,
produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
thf(collect_nat_type,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(collec1111687558lle_tv_type,type,
collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(collec7649004at_nat_type,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(collec924990229lle_tv_type,type,
collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
thf(collec848462447tv_nat_type,type,
collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
thf(image_nat_nat_type,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(image_1151963140lle_tv_type,type,
image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
thf(image_376325286tv_nat_type,type,
image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
thf(image_335818702lle_tv_type,type,
image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(image_1397137548at_nat_type,type,
image_1397137548at_nat: ( product_prod_nat_nat > nat ) > set_Pr1986765409at_nat > set_nat ).
thf(image_1093035615lle_tv_type,type,
image_1093035615lle_tv: ( product_prod_nat_nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat > set_Pa1764573435lle_tv ).
thf(image_1597721174tv_nat_type,type,
image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
thf(image_1509856791tv_nat_type,type,
image_1509856791tv_nat: ( produc270694976lle_tv > nat ) > set_Pr13445366lle_tv > set_nat ).
thf(image_802013119lle_tv_type,type,
image_802013119lle_tv: ( produc270694976lle_tv > paraco1605129243lle_tv ) > set_Pr13445366lle_tv > set_Pa1764573435lle_tv ).
thf(image_149830562lle_tv_type,type,
image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
thf(image_53754658tv_nat_type,type,
image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
thf(image_988201162lle_tv_type,type,
image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
thf(image_1381266801at_nat_type,type,
image_1381266801at_nat: ( produc194167194tv_nat > nat ) > set_Pr1725653840tv_nat > set_nat ).
thf(image_2019567641lle_tv_type,type,
image_2019567641lle_tv: ( produc194167194tv_nat > paraco1605129243lle_tv ) > set_Pr1725653840tv_nat > set_Pa1764573435lle_tv ).
thf(image_1805124128at_nat_type,type,
image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
thf(image_1200372424lle_tv_type,type,
image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
thf(image_1104296520tv_nat_type,type,
image_1104296520tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > set_Pr1725653840tv_nat ).
thf(image_228488944lle_tv_type,type,
image_228488944lle_tv: ( produc194167194tv_nat > produc1647334210lle_tv ) > set_Pr1725653840tv_nat > set_Pr2014382200lle_tv ).
thf(image_901203832at_nat_type,type,
image_901203832at_nat: ( produc1647334210lle_tv > product_prod_nat_nat ) > set_Pr2014382200lle_tv > set_Pr1986765409at_nat ).
thf(image_1892891680lle_tv_type,type,
image_1892891680lle_tv: ( produc1647334210lle_tv > produc270694976lle_tv ) > set_Pr2014382200lle_tv > set_Pr13445366lle_tv ).
thf(image_1796815776tv_nat_type,type,
image_1796815776tv_nat: ( produc1647334210lle_tv > produc194167194tv_nat ) > set_Pr2014382200lle_tv > set_Pr1725653840tv_nat ).
thf(image_1221801032lle_tv_type,type,
image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).
thf(member_nat_type,type,
member_nat: nat > set_nat > $o ).
thf(member266900804lle_tv_type,type,
member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
thf(member701585322at_nat_type,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(member813679063lle_tv_type,type,
member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
thf(member737151281tv_nat_type,type,
member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
thf(member1531318361lle_tv_type,type,
member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
thf(f_type,type,
f: nat > nat ).
thf(84,axiom,
! [A: nat,B: set_Pa1764573435lle_tv > nat,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le727057319lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le727057319lle_tv @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_ord__eq__less__subst) ).
thf(629,plain,
! [A: nat,B: set_Pa1764573435lle_tv > nat,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le727057319lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le727057319lle_tv @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(307,axiom,
! [A: paraco1605129243lle_tv > nat,B: nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ? [C: paraco1605129243lle_tv] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_surjD) ).
thf(1469,plain,
! [A: paraco1605129243lle_tv > nat,B: nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ? [C: paraco1605129243lle_tv] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(46,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Collect__cong) ).
thf(479,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(138,axiom,
! [A: produc270694976lle_tv > produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
= ( ! [B: produc270694976lle_tv,C: produc270694976lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_inj__def) ).
thf(846,plain,
! [A: produc270694976lle_tv > produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
= ( ! [B: produc270694976lle_tv,C: produc270694976lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(230,axiom,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: produc270694976lle_tv,C: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_injD) ).
thf(1179,plain,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: produc270694976lle_tv,C: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(119,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_inj__eq) ).
thf(777,plain,
! [A: nat > nat,B: nat,C: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(87,axiom,
! [A: product_prod_nat_nat > product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ top_to1555900337at_nat )
= ( ! [B: product_prod_nat_nat,C: product_prod_nat_nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_inj__def) ).
thf(645,plain,
! [A: product_prod_nat_nat > product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ top_to1555900337at_nat )
= ( ! [B: product_prod_nat_nat,C: product_prod_nat_nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(152,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: nat,D: set_nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( ord_less_eq_set_nat @ D @ B )
=> ( ( member266900804lle_tv @ ( A @ C ) @ ( image_1151963140lle_tv @ A @ D ) )
= ( member_nat @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_inj__on__image__mem__iff) ).
thf(892,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: nat,D: set_nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( ord_less_eq_set_nat @ D @ B )
=> ( ( member266900804lle_tv @ ( A @ C ) @ ( image_1151963140lle_tv @ A @ D ) )
= ( member_nat @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(12,axiom,
! [A: set_Pr13445366lle_tv,B: produc270694976lle_tv > produc270694976lle_tv] :
( ! [C: produc270694976lle_tv,D: produc270694976lle_tv] :
( ( member813679063lle_tv @ C @ A )
=> ( ( member813679063lle_tv @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on1745913142lle_tv @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_inj__onI) ).
thf(365,plain,
! [A: set_Pr13445366lle_tv,B: produc270694976lle_tv > produc270694976lle_tv] :
( ! [C: produc270694976lle_tv,D: produc270694976lle_tv] :
( ( member813679063lle_tv @ C @ A )
=> ( ( member813679063lle_tv @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on1745913142lle_tv @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(278,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: nat > nat] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( ( image_nat_nat @ B @ top_top_set_nat )
= top_top_set_nat )
=> ( ( image_1104296520tv_nat @ ( produc42536895at_nat @ A @ B ) @ top_to975729152tv_nat )
= top_to975729152tv_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_map__prod__surj) ).
thf(1369,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: nat > nat] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( ( image_nat_nat @ B @ top_top_set_nat )
= top_top_set_nat )
=> ( ( image_1104296520tv_nat @ ( produc42536895at_nat @ A @ B ) @ top_to975729152tv_nat )
= top_to975729152tv_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(233,axiom,
! [A: produc270694976lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on394919723lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( member266900804lle_tv @ B @ ( image_802013119lle_tv @ A @ top_to1411004326lle_tv ) )
= ( ? [C: produc270694976lle_tv] :
( ( B
= ( A @ C ) )
& ! [D: produc270694976lle_tv] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_range__ex1__eq) ).
thf(1190,plain,
! [A: produc270694976lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on394919723lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( member266900804lle_tv @ B @ ( image_802013119lle_tv @ A @ top_to1411004326lle_tv ) )
= ( ? [C: produc270694976lle_tv] :
( ( B
= ( A @ C ) )
& ! [D: produc270694976lle_tv] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(202,axiom,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( member266900804lle_tv @ B @ ( image_1151963140lle_tv @ A @ top_top_set_nat ) )
= ( ? [C: nat] :
( ( B
= ( A @ C ) )
& ! [D: nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_range__ex1__eq) ).
thf(1083,plain,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( member266900804lle_tv @ B @ ( image_1151963140lle_tv @ A @ top_top_set_nat ) )
= ( ? [C: nat] :
( ( B
= ( A @ C ) )
& ! [D: nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(42,axiom,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv,C: produc270694976lle_tv,D: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ B )
=> ( ( member813679063lle_tv @ C @ B )
=> ( ( member813679063lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_inj__on__eq__iff) ).
thf(468,plain,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv,C: produc270694976lle_tv,D: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ B )
=> ( ( member813679063lle_tv @ C @ B )
=> ( ( member813679063lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(289,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_inj__eq) ).
thf(1406,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(198,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: produc194167194tv_nat,C: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_inj__eq) ).
thf(1068,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: produc194167194tv_nat,C: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(180,axiom,
! [A: produc194167194tv_nat > nat,B: nat] :
( ( inj_on808253149at_nat @ A @ top_to975729152tv_nat )
=> ( ( member_nat @ B @ ( image_1381266801at_nat @ A @ top_to975729152tv_nat ) )
= ( ? [C: produc194167194tv_nat] :
( ( B
= ( A @ C ) )
& ! [D: produc194167194tv_nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_range__ex1__eq) ).
thf(994,plain,
! [A: produc194167194tv_nat > nat,B: nat] :
( ( inj_on808253149at_nat @ A @ top_to975729152tv_nat )
=> ( ( member_nat @ B @ ( image_1381266801at_nat @ A @ top_to975729152tv_nat ) )
= ( ? [C: produc194167194tv_nat] :
( ( B
= ( A @ C ) )
& ! [D: produc194167194tv_nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(15,axiom,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat,D: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member701585322at_nat @ C @ B )
=> ( ( member701585322at_nat @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_inj__onD) ).
thf(379,plain,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat,D: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member701585322at_nat @ C @ B )
=> ( ( member701585322at_nat @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(260,axiom,
! [A: paraco1605129243lle_tv > nat,B: nat > nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( ( image_nat_nat @ B @ top_top_set_nat )
= top_top_set_nat )
=> ( ( image_1805124128at_nat @ ( produc386540311at_nat @ A @ B ) @ top_to975729152tv_nat )
= top_to1555900337at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_map__prod__surj) ).
thf(1305,plain,
! [A: paraco1605129243lle_tv > nat,B: nat > nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( ( image_nat_nat @ B @ top_top_set_nat )
= top_top_set_nat )
=> ( ( image_1805124128at_nat @ ( produc386540311at_nat @ A @ B ) @ top_to975729152tv_nat )
= top_to1555900337at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(76,axiom,
! [A: produc194167194tv_nat > paraco1605129243lle_tv,B: produc194167194tv_nat,C: set_Pr1725653840tv_nat] :
( ( inj_on1612474245lle_tv @ A @ top_to975729152tv_nat )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_2019567641lle_tv @ A @ C ) )
= ( member737151281tv_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_inj__image__mem__iff) ).
thf(597,plain,
! [A: produc194167194tv_nat > paraco1605129243lle_tv,B: produc194167194tv_nat,C: set_Pr1725653840tv_nat] :
( ( inj_on1612474245lle_tv @ A @ top_to975729152tv_nat )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_2019567641lle_tv @ A @ C ) )
= ( member737151281tv_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(17,axiom,
! [A: produc194167194tv_nat,B: product_prod_nat_nat > produc194167194tv_nat,C: set_Pr1986765409at_nat] :
( ( member737151281tv_nat @ A @ ( image_1597721174tv_nat @ B @ C ) )
= ( ? [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_image__iff) ).
thf(385,plain,
! [A: produc194167194tv_nat,B: product_prod_nat_nat > produc194167194tv_nat,C: set_Pr1986765409at_nat] :
( ( member737151281tv_nat @ A @ ( image_1597721174tv_nat @ B @ C ) )
= ( ? [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(60,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_ord__eq__less__subst) ).
thf(533,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(43,axiom,
! [A: produc270694976lle_tv] : ( member813679063lle_tv @ A @ top_to1411004326lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_UNIV__I) ).
thf(472,plain,
! [A: produc270694976lle_tv] : ( member813679063lle_tv @ A @ top_to1411004326lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(129,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: paraco1605129243lle_tv > $o] :
( ? [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1151963140lle_tv @ A @ B ) )
& ( C @ D ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_bex__imageD) ).
thf(814,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: paraco1605129243lle_tv > $o] :
( ? [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1151963140lle_tv @ A @ B ) )
& ( C @ D ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(247,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ? [C: paraco1605129243lle_tv] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_surjD) ).
thf(1260,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ? [C: paraco1605129243lle_tv] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(113,axiom,
! [A: set_nat,B: nat > nat] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_nat_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_inj__onI) ).
thf(747,plain,
! [A: set_nat,B: nat > nat] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_nat_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(167,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec1111687558lle_tv @ A )
= ( collec1111687558lle_tv @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Collect__cong) ).
thf(945,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec1111687558lle_tv @ A )
= ( collec1111687558lle_tv @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(133,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: produc1647334210lle_tv,C: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_injD) ).
thf(829,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: produc1647334210lle_tv,C: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(154,axiom,
! [A: nat > nat,B: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ B @ A ) @ ( image_nat_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_inj__on__the__inv__into) ).
thf(898,plain,
! [A: nat > nat,B: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ B @ A ) @ ( image_nat_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(213,axiom,
! [A: nat > nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_surj__def) ).
thf(1127,plain,
! [A: nat > nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(285,axiom,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv > nat] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ( ( ( image_376325286tv_nat @ B @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ A @ B ) @ top_to1411004326lle_tv )
= top_to975729152tv_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_map__prod__surj) ).
thf(1391,plain,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv > nat] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ( ( ( image_376325286tv_nat @ B @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ A @ B ) @ top_to1411004326lle_tv )
= top_to975729152tv_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(67,axiom,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: product_prod_nat_nat,C: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ top_to1555900337at_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_inj__eq) ).
thf(565,plain,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: product_prod_nat_nat,C: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ top_to1555900337at_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(319,axiom,
? [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_UNIV__witness) ).
thf(1518,plain,
? [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(310,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_injI) ).
thf(1482,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(258,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ ( image_335818702lle_tv @ A @ B ) )
=> ( ( ord_le241064091lle_tv @ B @ D )
=> ( member266900804lle_tv @ ( the_in452116896lle_tv @ B @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_the__inv__into__into) ).
thf(1298,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ ( image_335818702lle_tv @ A @ B ) )
=> ( ( ord_le241064091lle_tv @ B @ D )
=> ( member266900804lle_tv @ ( the_in452116896lle_tv @ B @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(248,axiom,
! [A: nat > nat,B: nat] :
( ( paraco1147068288nge_tv @ A @ ( paraco793048302_Indet @ B ) )
= ( paraco793048302_Indet @ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_change__tv_Osimps_I2_J) ).
thf(1264,plain,
! [A: nat > nat,B: nat] :
( ( paraco1147068288nge_tv @ A @ ( paraco793048302_Indet @ B ) )
= ( paraco793048302_Indet @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(266,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ord_le727057319lle_tv @ C @ B )
=> ( ord_le727057319lle_tv @ ( image_335818702lle_tv @ A @ C ) @ ( image_335818702lle_tv @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_inj__on__strict__subset) ).
thf(1323,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ord_le727057319lle_tv @ C @ B )
=> ( ord_le727057319lle_tv @ ( image_335818702lle_tv @ A @ C ) @ ( image_335818702lle_tv @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(302,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_the__inv__f__f) ).
thf(1455,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(39,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat,C: produc194167194tv_nat,D: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ B )
=> ( ( C != D )
=> ( ( member737151281tv_nat @ C @ B )
=> ( ( member737151281tv_nat @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_inj__on__contraD) ).
thf(460,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat,C: produc194167194tv_nat,D: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ B )
=> ( ( C != D )
=> ( ( member737151281tv_nat @ C @ B )
=> ( ( member737151281tv_nat @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(262,axiom,
inj_on_nat_nat @ f @ top_top_set_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_assms) ).
thf(1313,plain,
inj_on_nat_nat @ f @ top_top_set_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(252,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( ( image_335818702lle_tv @ B @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ A @ B ) @ top_to1871154984lle_tv )
= top_to1871154984lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_map__prod__surj) ).
thf(1279,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( ( image_335818702lle_tv @ B @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ A @ B ) @ top_to1871154984lle_tv )
= top_to1871154984lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(130,axiom,
! [A: nat > nat,B: set_nat,C: nat > $o] :
( ! [D: nat] :
( ( member_nat @ D @ ( image_nat_nat @ A @ B ) )
=> ( C @ D ) )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_ball__imageD) ).
thf(817,plain,
! [A: nat > nat,B: set_nat,C: nat > $o] :
( ! [D: nat] :
( ( member_nat @ D @ ( image_nat_nat @ A @ B ) )
=> ( C @ D ) )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(203,axiom,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: produc270694976lle_tv,C: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_inj__eq) ).
thf(1087,plain,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: produc270694976lle_tv,C: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(219,axiom,
( top_top_nat_o
= ( ^ [A: nat] : ( member_nat @ A @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_top__empty__eq) ).
thf(1147,plain,
( top_top_nat_o
= ( ^ [A: nat] : ( member_nat @ A @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(243,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_mem__Collect__eq) ).
thf(1247,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(146,axiom,
! [A: paraco1605129243lle_tv] : ( top_to1299250770e_tv_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_top1I) ).
thf(870,plain,
! [A: paraco1605129243lle_tv] : ( top_to1299250770e_tv_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(273,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( ( member266900804lle_tv @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on772319074lle_tv @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_inj__onI) ).
thf(1347,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( ( member266900804lle_tv @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on772319074lle_tv @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(25,axiom,
( inj_on1745913142lle_tv
= ( ^ [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv] :
! [C: produc270694976lle_tv] :
( ( member813679063lle_tv @ C @ B )
=> ! [D: produc270694976lle_tv] :
( ( member813679063lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_inj__on__def) ).
thf(416,plain,
( inj_on1745913142lle_tv
= ( ^ [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv] :
! [C: produc270694976lle_tv] :
( ( member813679063lle_tv @ C @ B )
=> ! [D: produc270694976lle_tv] :
( ( member813679063lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(210,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_subsetD) ).
thf(1115,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(276,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( inj_on772319074lle_tv @ B @ top_to1057771083lle_tv )
=> ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ A @ B ) @ top_to1871154984lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_prod_Oinj__map) ).
thf(1362,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( inj_on772319074lle_tv @ B @ top_to1057771083lle_tv )
=> ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ A @ B ) @ top_to1871154984lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(207,axiom,
! [A: set_nat,B: nat > nat,C: nat > nat] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_nat_nat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_inj__on__inverseI) ).
thf(1100,plain,
! [A: set_nat,B: nat > nat,C: nat > nat] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_nat_nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(74,axiom,
! [A: set_nat] :
~ ( ord_less_set_nat @ top_top_set_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_top_Oextremum__strict) ).
thf(591,plain,
! [A: set_nat] :
~ ( ord_less_set_nat @ top_top_set_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(279,axiom,
! [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_iso__tuple__UNIV__I) ).
thf(1373,plain,
! [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(292,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ B @ A ) @ ( image_335818702lle_tv @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_inj__on__the__inv__into) ).
thf(1418,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ B @ A ) @ ( image_335818702lle_tv @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(216,axiom,
! [A: produc270694976lle_tv > nat,B: nat] :
( ( inj_on936843139tv_nat @ A @ top_to1411004326lle_tv )
=> ( ( member_nat @ B @ ( image_1509856791tv_nat @ A @ top_to1411004326lle_tv ) )
= ( ? [C: produc270694976lle_tv] :
( ( B
= ( A @ C ) )
& ! [D: produc270694976lle_tv] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_range__ex1__eq) ).
thf(1136,plain,
! [A: produc270694976lle_tv > nat,B: nat] :
( ( inj_on936843139tv_nat @ A @ top_to1411004326lle_tv )
=> ( ( member_nat @ B @ ( image_1509856791tv_nat @ A @ top_to1411004326lle_tv ) )
= ( ? [C: produc270694976lle_tv] :
( ( B
= ( A @ C ) )
& ! [D: produc270694976lle_tv] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(55,axiom,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_subset__iff) ).
thf(514,plain,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(156,axiom,
! [A: nat > nat,B: set_nat] :
( ( order_769474267at_nat @ A )
=> ( inj_on_nat_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_strict__mono__imp__inj__on) ).
thf(905,plain,
! [A: nat > nat,B: set_nat] :
( ( order_769474267at_nat @ A )
=> ( inj_on_nat_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(231,axiom,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_surjD) ).
thf(1183,plain,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(253,axiom,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_top__greatest) ).
thf(1283,plain,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(177,axiom,
! [A: nat > nat,B: nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( member_nat @ ( A @ B ) @ ( image_nat_nat @ A @ C ) )
= ( member_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_inj__image__mem__iff) ).
thf(981,plain,
! [A: nat > nat,B: nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( member_nat @ ( A @ B ) @ ( image_nat_nat @ A @ C ) )
= ( member_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(21,axiom,
! [A: set_Pr1725653840tv_nat,B: produc194167194tv_nat > produc194167194tv_nat] :
( ! [C: produc194167194tv_nat,D: produc194167194tv_nat] :
( ( member737151281tv_nat @ C @ A )
=> ( ( member737151281tv_nat @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on552895452tv_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_inj__onI) ).
thf(397,plain,
! [A: set_Pr1725653840tv_nat,B: produc194167194tv_nat > produc194167194tv_nat] :
( ! [C: produc194167194tv_nat,D: produc194167194tv_nat] :
( ( member737151281tv_nat @ C @ A )
=> ( ( member737151281tv_nat @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on552895452tv_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(239,axiom,
! [A: nat,B: set_nat] : ( inj_on_nat_nat @ ( plus_plus_nat @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_inj__on__add) ).
thf(1215,plain,
! [A: nat,B: set_nat] : ( inj_on_nat_nat @ ( plus_plus_nat @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(98,axiom,
! [A: produc270694976lle_tv > paraco1605129243lle_tv,B: produc270694976lle_tv,C: set_Pr13445366lle_tv] :
( ( inj_on394919723lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_802013119lle_tv @ A @ C ) )
= ( member813679063lle_tv @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_inj__image__mem__iff) ).
thf(692,plain,
! [A: produc270694976lle_tv > paraco1605129243lle_tv,B: produc270694976lle_tv,C: set_Pr13445366lle_tv] :
( ( inj_on394919723lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_802013119lle_tv @ A @ C ) )
= ( member813679063lle_tv @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(171,axiom,
! [A: nat > nat,B: set_nat,C: nat,D: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( ord_less_eq_set_nat @ D @ B )
=> ( ( member_nat @ ( A @ C ) @ ( image_nat_nat @ A @ D ) )
= ( member_nat @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_inj__on__image__mem__iff) ).
thf(956,plain,
! [A: nat > nat,B: set_nat,C: nat,D: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( ord_less_eq_set_nat @ D @ B )
=> ( ( member_nat @ ( A @ C ) @ ( image_nat_nat @ A @ D ) )
= ( member_nat @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(199,axiom,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_inj__onD) ).
thf(1072,plain,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(181,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: produc1647334210lle_tv,C: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_inj__eq) ).
thf(998,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: produc1647334210lle_tv,C: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(30,axiom,
( inj_on552895452tv_nat
= ( ^ [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat] :
! [C: produc194167194tv_nat] :
( ( member737151281tv_nat @ C @ B )
=> ! [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_inj__on__def) ).
thf(428,plain,
( inj_on552895452tv_nat
= ( ^ [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat] :
! [C: produc194167194tv_nat] :
( ( member737151281tv_nat @ C @ B )
=> ! [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(236,axiom,
! [A: product_prod_nat_nat > produc194167194tv_nat,B: set_Pr1986765409at_nat] :
( ( inj_on1764151786tv_nat @ A @ B )
=> ( ( image_1805124128at_nat @ ( the_in667485224tv_nat @ B @ A ) @ ( image_1597721174tv_nat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_the__inv__into__onto) ).
thf(1201,plain,
! [A: product_prod_nat_nat > produc194167194tv_nat,B: set_Pr1986765409at_nat] :
( ( inj_on1764151786tv_nat @ A @ B )
=> ( ( image_1805124128at_nat @ ( the_in667485224tv_nat @ B @ A ) @ ( image_1597721174tv_nat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(208,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_image__subsetI) ).
thf(1104,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(139,axiom,
! [A: set_Pr2014382200lle_tv,B: produc1647334210lle_tv > produc1647334210lle_tv,C: produc1647334210lle_tv > produc1647334210lle_tv] :
( ! [D: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on2112487900lle_tv @ B @ A )
= ( inj_on2112487900lle_tv @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_inj__on__cong) ).
thf(849,plain,
! [A: set_Pr2014382200lle_tv,B: produc1647334210lle_tv > produc1647334210lle_tv,C: produc1647334210lle_tv > produc1647334210lle_tv] :
( ! [D: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on2112487900lle_tv @ B @ A )
= ( inj_on2112487900lle_tv @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(92,axiom,
( top_top_nat_o
= ( ^ [A: nat] : top_top_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_top__apply) ).
thf(661,plain,
( top_top_nat_o
= ( ^ [A: nat] : top_top_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(162,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > nat,C: set_nat] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member_nat @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_nat @ ( image_376325286tv_nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_image__subsetI) ).
thf(925,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > nat,C: set_nat] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member_nat @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_nat @ ( image_376325286tv_nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(128,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv,C: produc1647334210lle_tv,D: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member1531318361lle_tv @ C @ B )
=> ( ( member1531318361lle_tv @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_inj__onD) ).
thf(810,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv,C: produc1647334210lle_tv,D: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member1531318361lle_tv @ C @ B )
=> ( ( member1531318361lle_tv @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(204,axiom,
! [A: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv,C: nat,D: set_Pa1764573435lle_tv] :
( ( inj_on1179712058tv_nat @ A @ B )
=> ( ( member_nat @ C @ ( image_376325286tv_nat @ A @ B ) )
=> ( ( ord_le241064091lle_tv @ B @ D )
=> ( member266900804lle_tv @ ( the_in1509933432tv_nat @ B @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_the__inv__into__into) ).
thf(1091,plain,
! [A: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv,C: nat,D: set_Pa1764573435lle_tv] :
( ( inj_on1179712058tv_nat @ A @ B )
=> ( ( member_nat @ C @ ( image_376325286tv_nat @ A @ B ) )
=> ( ( ord_le241064091lle_tv @ B @ D )
=> ( member266900804lle_tv @ ( the_in1509933432tv_nat @ B @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(192,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_335818702lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_imageI) ).
thf(1042,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_335818702lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(274,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ B @ A ) @ ( image_335818702lle_tv @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_the__inv__into__onto) ).
thf(1355,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ B @ A ) @ ( image_335818702lle_tv @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(228,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
= ( ! [B: produc194167194tv_nat,C: produc194167194tv_nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_inj__def) ).
thf(1174,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
= ( ! [B: produc194167194tv_nat,C: produc194167194tv_nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(240,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv,C: produc1647334210lle_tv,D: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ B )
=> ( ( C != D )
=> ( ( member1531318361lle_tv @ C @ B )
=> ( ( member1531318361lle_tv @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_inj__on__contraD) ).
thf(1217,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv,C: produc1647334210lle_tv,D: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ B )
=> ( ( C != D )
=> ( ( member1531318361lle_tv @ C @ B )
=> ( ( member1531318361lle_tv @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(131,axiom,
! [A: product_prod_nat_nat > nat,B: nat] :
( ( inj_on642995232at_nat @ A @ top_to1555900337at_nat )
=> ( ( member_nat @ B @ ( image_1397137548at_nat @ A @ top_to1555900337at_nat ) )
= ( ? [C: product_prod_nat_nat] :
( ( B
= ( A @ C ) )
& ! [D: product_prod_nat_nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_range__ex1__eq) ).
thf(820,plain,
! [A: product_prod_nat_nat > nat,B: nat] :
( ( inj_on642995232at_nat @ A @ top_to1555900337at_nat )
=> ( ( member_nat @ B @ ( image_1397137548at_nat @ A @ top_to1555900337at_nat ) )
= ( ? [C: product_prod_nat_nat] :
( ( B
= ( A @ C ) )
& ! [D: product_prod_nat_nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(311,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( image_335818702lle_tv @ A @ B )
= ( image_335818702lle_tv @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_inj__image__eq__iff) ).
thf(1487,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( image_335818702lle_tv @ A @ B )
= ( image_335818702lle_tv @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(107,axiom,
! [A: nat] : ( inj_on_nat_nat @ ( plus_plus_nat @ A ) @ top_top_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_inj__add__left) ).
thf(729,plain,
! [A: nat] : ( inj_on_nat_nat @ ( plus_plus_nat @ A ) @ top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(143,axiom,
! [A: set_nat,B: nat > nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ ( image_nat_nat @ B @ C ) )
= ( ? [D: set_nat] :
( ( ord_less_eq_set_nat @ D @ C )
& ( inj_on_nat_nat @ B @ D )
& ( A
= ( image_nat_nat @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_subset__image__inj) ).
thf(862,plain,
! [A: set_nat,B: nat > nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ ( image_nat_nat @ B @ C ) )
= ( ? [D: set_nat] :
( ( ord_less_eq_set_nat @ D @ C )
& ( inj_on_nat_nat @ B @ D )
& ( A
= ( image_nat_nat @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(8,axiom,
! [A: set_Pr1986765409at_nat,B: product_prod_nat_nat > product_prod_nat_nat,C: product_prod_nat_nat > product_prod_nat_nat] :
( ! [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on26176689at_nat @ B @ A )
= ( inj_on26176689at_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_inj__on__cong) ).
thf(349,plain,
! [A: set_Pr1986765409at_nat,B: product_prod_nat_nat > product_prod_nat_nat,C: product_prod_nat_nat > product_prod_nat_nat] :
( ! [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on26176689at_nat @ B @ A )
= ( inj_on26176689at_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(48,axiom,
( inj_on1955349912lle_tv
= ( ^ [A: nat > paraco1605129243lle_tv,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ B )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_inj__on__def) ).
thf(484,plain,
( inj_on1955349912lle_tv
= ( ^ [A: nat > paraco1605129243lle_tv,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ B )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(189,axiom,
( inj_on2112487900lle_tv
= ( ^ [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv] :
! [C: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ C @ B )
=> ! [D: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_inj__on__def) ).
thf(1032,plain,
( inj_on2112487900lle_tv
= ( ^ [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv] :
! [C: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ C @ B )
=> ! [D: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(277,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ A @ B ) @ ( image_335818702lle_tv @ A @ C ) )
= ( ord_le241064091lle_tv @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_inj__image__subset__iff) ).
thf(1365,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ A @ B ) @ ( image_335818702lle_tv @ A @ C ) )
= ( ord_le241064091lle_tv @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(82,axiom,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_subset__eq) ).
thf(625,plain,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(149,axiom,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ord_less_eq_set_nat @ ( image_nat_nat @ A @ B ) @ ( image_nat_nat @ A @ C ) )
= ( ord_less_eq_set_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_inj__image__subset__iff) ).
thf(879,plain,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ord_less_eq_set_nat @ ( image_nat_nat @ A @ B ) @ ( image_nat_nat @ A @ C ) )
= ( ord_less_eq_set_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(32,axiom,
? [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ top_to1555900337at_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_UNIV__witness) ).
thf(435,plain,
? [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ top_to1555900337at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(102,axiom,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_subsetD) ).
thf(710,plain,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(175,axiom,
! [A: nat > nat,B: set_nat,C: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( the_inv_into_nat_nat @ B @ A @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_the__inv__into__f__f) ).
thf(974,plain,
! [A: nat > nat,B: set_nat,C: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( the_inv_into_nat_nat @ B @ A @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(73,axiom,
! [A: set_nat,B: set_Pa1764573435lle_tv > set_nat,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le727057319lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le727057319lle_tv @ E @ F )
=> ( ord_less_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ord__eq__less__subst) ).
thf(583,plain,
! [A: set_nat,B: set_Pa1764573435lle_tv > set_nat,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le727057319lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le727057319lle_tv @ E @ F )
=> ( ord_less_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(57,axiom,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: product_prod_nat_nat,C: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ top_to1555900337at_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_injD) ).
thf(522,plain,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: product_prod_nat_nat,C: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ top_to1555900337at_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(250,axiom,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_subset__UNIV) ).
thf(1270,plain,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(168,axiom,
! [A: nat > nat,B: nat] : ( member_nat @ ( A @ B ) @ ( image_nat_nat @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_rangeI) ).
thf(948,plain,
! [A: nat > nat,B: nat] : ( member_nat @ ( A @ B ) @ ( image_nat_nat @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(280,axiom,
! [A: nat > paraco1605129243lle_tv] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_surj__def) ).
thf(1375,plain,
! [A: nat > paraco1605129243lle_tv] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(106,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv,C: set_Pr2014382200lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
=> ( ( ( image_1221801032lle_tv @ A @ B )
= ( image_1221801032lle_tv @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_inj__image__eq__iff) ).
thf(725,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv,C: set_Pr2014382200lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
=> ( ( ( image_1221801032lle_tv @ A @ B )
= ( image_1221801032lle_tv @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(183,axiom,
! [A: nat > nat,B: set_nat,C: set_nat,D: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ B )
=> ( ( ord_less_eq_set_nat @ D @ B )
=> ( ( ( image_nat_nat @ A @ C )
= ( image_nat_nat @ A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_inj__on__image__eq__iff) ).
thf(1006,plain,
! [A: nat > nat,B: set_nat,C: set_nat,D: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ B )
=> ( ( ord_less_eq_set_nat @ D @ B )
=> ( ( ( image_nat_nat @ A @ C )
= ( image_nat_nat @ A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(18,axiom,
! [A: set_Pr13445366lle_tv] :
( ! [B: produc270694976lle_tv] : ( member813679063lle_tv @ B @ A )
=> ( top_to1411004326lle_tv = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_UNIV__eq__I) ).
thf(388,plain,
! [A: set_Pr13445366lle_tv] :
( ! [B: produc270694976lle_tv] : ( member813679063lle_tv @ B @ A )
=> ( top_to1411004326lle_tv = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(79,axiom,
! [A: set_Pa1764573435lle_tv,B: set_nat > set_Pa1764573435lle_tv,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_set_nat @ E @ F )
=> ( ord_le727057319lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le727057319lle_tv @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_ord__eq__less__subst) ).
thf(610,plain,
! [A: set_Pa1764573435lle_tv,B: set_nat > set_Pa1764573435lle_tv,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_set_nat @ E @ F )
=> ( ord_le727057319lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le727057319lle_tv @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(179,axiom,
! [A: nat,B: paraco1605129243lle_tv > nat,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member_nat @ A @ ( image_376325286tv_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_image__eqI) ).
thf(989,plain,
! [A: nat,B: paraco1605129243lle_tv > nat,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member_nat @ A @ ( image_376325286tv_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(148,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat] :
( ! [B: produc194167194tv_nat,C: produc194167194tv_nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_injI) ).
thf(874,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat] :
( ! [B: produc194167194tv_nat,C: produc194167194tv_nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(218,axiom,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( the_in1388677748lle_tv @ top_to1411004326lle_tv @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_the__inv__f__f) ).
thf(1143,plain,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( the_in1388677748lle_tv @ top_to1411004326lle_tv @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(27,axiom,
! [A: set_Pr1725653840tv_nat] :
( ! [B: produc194167194tv_nat] : ( member737151281tv_nat @ B @ A )
=> ( top_to975729152tv_nat = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_UNIV__eq__I) ).
thf(420,plain,
! [A: set_Pr1725653840tv_nat] :
( ! [B: produc194167194tv_nat] : ( member737151281tv_nat @ B @ A )
=> ( top_to975729152tv_nat = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(211,axiom,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv,C: set_Pr13445366lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( ( image_149830562lle_tv @ A @ B )
= ( image_149830562lle_tv @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_inj__image__eq__iff) ).
thf(1118,plain,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv,C: set_Pr13445366lle_tv] :
( ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv )
=> ( ( ( image_149830562lle_tv @ A @ B )
= ( image_149830562lle_tv @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(256,axiom,
( top_to1299250770e_tv_o
= ( ^ [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_top__empty__eq) ).
thf(1292,plain,
( top_to1299250770e_tv_o
= ( ^ [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(65,axiom,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_set_nat @ E @ F )
=> ( ord_less_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_ord__eq__less__subst) ).
thf(554,plain,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_set_nat @ E @ F )
=> ( ord_less_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(304,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ ( image_335818702lle_tv @ B @ C ) )
= ( ? [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
& ( inj_on772319074lle_tv @ B @ D )
& ( A
= ( image_335818702lle_tv @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_subset__image__inj) ).
thf(1461,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ ( image_335818702lle_tv @ B @ C ) )
= ( ? [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
& ( inj_on772319074lle_tv @ B @ D )
& ( A
= ( image_335818702lle_tv @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(45,axiom,
! [A: product_prod_nat_nat > produc194167194tv_nat,B: set_Pr1986765409at_nat,C: produc194167194tv_nat > $o] :
( ! [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ ( image_1597721174tv_nat @ A @ B ) )
=> ( C @ D ) )
=> ! [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ball__imageD) ).
thf(476,plain,
! [A: product_prod_nat_nat > produc194167194tv_nat,B: set_Pr1986765409at_nat,C: produc194167194tv_nat > $o] :
( ! [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ ( image_1597721174tv_nat @ A @ B ) )
=> ( C @ D ) )
=> ! [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(294,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ C @ B )
=> ( inj_on772319074lle_tv @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_inj__on__subset) ).
thf(1424,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ C @ B )
=> ( inj_on772319074lle_tv @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(85,axiom,
! [A: nat > paraco1605129243lle_tv,B: nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( the_in138087638lle_tv @ top_top_set_nat @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_the__inv__f__f) ).
thf(637,plain,
! [A: nat > paraco1605129243lle_tv,B: nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( the_in138087638lle_tv @ top_top_set_nat @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(191,axiom,
! [A: nat > nat] :
( ( inj_on552895452tv_nat @ ( produc237097339lle_tv @ A ) @ top_to975729152tv_nat )
= ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_inj__apsnd) ).
thf(1039,plain,
! [A: nat > nat] :
( ( inj_on552895452tv_nat @ ( produc237097339lle_tv @ A ) @ top_to975729152tv_nat )
= ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(291,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv > nat] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( ( image_376325286tv_nat @ B @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( image_1796815776tv_nat @ ( produc1500159719tv_nat @ A @ B ) @ top_to1871154984lle_tv )
= top_to975729152tv_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_map__prod__surj) ).
thf(1414,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv > nat] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( ( image_376325286tv_nat @ B @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( image_1796815776tv_nat @ ( produc1500159719tv_nat @ A @ B ) @ top_to1871154984lle_tv )
= top_to975729152tv_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(58,axiom,
! [A: product_prod_nat_nat > paraco1605129243lle_tv,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( inj_on520021963lle_tv @ A @ top_to1555900337at_nat )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_1093035615lle_tv @ A @ C ) )
= ( member701585322at_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_inj__image__mem__iff) ).
thf(526,plain,
! [A: product_prod_nat_nat > paraco1605129243lle_tv,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( inj_on520021963lle_tv @ A @ top_to1555900337at_nat )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_1093035615lle_tv @ A @ C ) )
= ( member701585322at_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(135,axiom,
! [A: nat] : ( member_nat @ A @ top_top_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_iso__tuple__UNIV__I) ).
thf(837,plain,
! [A: nat] : ( member_nat @ A @ top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(178,axiom,
! [A: nat > nat,B: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( member_nat @ B @ ( image_nat_nat @ A @ top_top_set_nat ) )
= ( ? [C: nat] :
( ( B
= ( A @ C ) )
& ! [D: nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_range__ex1__eq) ).
thf(985,plain,
! [A: nat > nat,B: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( member_nat @ B @ ( image_nat_nat @ A @ top_top_set_nat ) )
= ( ? [C: nat] :
( ( B
= ( A @ C ) )
& ! [D: nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(309,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( ord_le241064091lle_tv @ D @ B )
=> ( ( member266900804lle_tv @ ( A @ C ) @ ( image_335818702lle_tv @ A @ D ) )
= ( member266900804lle_tv @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_inj__on__image__mem__iff) ).
thf(1478,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( ord_le241064091lle_tv @ D @ B )
=> ( ( member266900804lle_tv @ ( A @ C ) @ ( image_335818702lle_tv @ A @ D ) )
= ( member266900804lle_tv @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(301,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( the_in452116896lle_tv @ B @ A @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_the__inv__into__f__f) ).
thf(1451,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( the_in452116896lle_tv @ B @ A @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(90,axiom,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ B )
=> ( inj_on_nat_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_subset__inj__on) ).
thf(654,plain,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ B )
=> ( inj_on_nat_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(194,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: produc194167194tv_nat,C: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_injD) ).
thf(1050,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: produc194167194tv_nat,C: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(105,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: nat,D: nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( C != D )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_inj__on__contraD) ).
thf(721,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: nat,D: nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( C != D )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(182,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
=> ( ( the_in195660058tv_nat @ top_to975729152tv_nat @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_the__inv__f__f) ).
thf(1002,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
=> ( ( the_in195660058tv_nat @ top_to975729152tv_nat @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(68,axiom,
! [A: nat > paraco1605129243lle_tv,B: nat,C: nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_injD) ).
thf(569,plain,
! [A: nat > paraco1605129243lle_tv,B: nat,C: nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(123,axiom,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_inj__on__eq__iff) ).
thf(792,plain,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(61,axiom,
! [A: nat] : ( top_top_nat_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_top1I) ).
thf(541,plain,
! [A: nat] : ( top_top_nat_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(91,axiom,
! [A: set_nat,B: paraco1605129243lle_tv > nat,C: nat > paraco1605129243lle_tv] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on1955349912lle_tv @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_inj__on__inverseI) ).
thf(657,plain,
! [A: set_nat,B: paraco1605129243lle_tv > nat,C: nat > paraco1605129243lle_tv] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on1955349912lle_tv @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(195,axiom,
! [A: set_nat,B: set_nat,C: nat > nat,D: nat > nat] :
( ( A = B )
=> ( ! [E: nat] :
( ( member_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_nat_nat @ C @ A )
= ( image_nat_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_image__cong) ).
thf(1054,plain,
! [A: set_nat,B: set_nat,C: nat > nat,D: nat > nat] :
( ( A = B )
=> ( ! [E: nat] :
( ( member_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_nat_nat @ C @ A )
= ( image_nat_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(306,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on1745913142lle_tv @ ( produc2040316391tv_nat @ A ) @ top_to1411004326lle_tv )
= ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_inj__apsnd) ).
thf(1466,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on1745913142lle_tv @ ( produc2040316391tv_nat @ A ) @ top_to1411004326lle_tv )
= ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(232,axiom,
! [A: set_nat,B: nat > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1151963140lle_tv @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_image__subsetI) ).
thf(1187,plain,
! [A: set_nat,B: nat > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1151963140lle_tv @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(318,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ C @ B )
=> ( inj_on772319074lle_tv @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_subset__inj__on) ).
thf(1515,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ C @ B )
=> ( inj_on772319074lle_tv @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(59,axiom,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( strict2146030304at_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( A @ C ) @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_strict__mono__onD) ).
thf(530,plain,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( strict2146030304at_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( A @ C ) @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(170,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv] :
( ( inj_on2112487900lle_tv @ A @ B )
=> ( ( image_1221801032lle_tv @ ( the_in427240730lle_tv @ B @ A ) @ ( image_1221801032lle_tv @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_the__inv__into__onto) ).
thf(953,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv] :
( ( inj_on2112487900lle_tv @ A @ B )
=> ( ( image_1221801032lle_tv @ ( the_in427240730lle_tv @ B @ A ) @ ( image_1221801032lle_tv @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(104,axiom,
! [A: nat > paraco1605129243lle_tv] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
= ( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_inj__def) ).
thf(718,plain,
! [A: nat > paraco1605129243lle_tv] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
= ( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(6,axiom,
! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ top_to1555900337at_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_iso__tuple__UNIV__I) ).
thf(343,plain,
! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ top_to1555900337at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(264,axiom,
( inj_on772319074lle_tv
= ( ^ [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ B )
=> ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_inj__on__def) ).
thf(1318,plain,
( inj_on772319074lle_tv
= ( ^ [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ B )
=> ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(187,axiom,
! [A: nat > nat] :
( ( inj_on26176689at_nat @ ( produc1320959600at_nat @ A ) @ top_to1555900337at_nat )
= ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_inj__apsnd) ).
thf(1026,plain,
! [A: nat > nat] :
( ( inj_on26176689at_nat @ ( produc1320959600at_nat @ A ) @ top_to1555900337at_nat )
= ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(226,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv,C: produc1647334210lle_tv,D: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ B )
=> ( ( member1531318361lle_tv @ C @ B )
=> ( ( member1531318361lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_inj__on__eq__iff) ).
thf(1167,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: set_Pr2014382200lle_tv,C: produc1647334210lle_tv,D: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ B )
=> ( ( member1531318361lle_tv @ C @ B )
=> ( ( member1531318361lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(317,axiom,
! [A: nat,B: paraco1605129243lle_tv > nat,C: paraco1605129243lle_tv] :
( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_376325286tv_nat @ B @ top_to1057771083lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_range__eqI) ).
thf(1510,plain,
! [A: nat,B: paraco1605129243lle_tv > nat,C: paraco1605129243lle_tv] :
( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_376325286tv_nat @ B @ top_to1057771083lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(80,axiom,
! [A: set_nat,B: set_nat] :
( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) )
=> ( ord_less_eq_set_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_subsetI) ).
thf(618,plain,
! [A: set_nat,B: set_nat] :
( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) )
=> ( ord_less_eq_set_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(31,axiom,
! [A: set_Pr1725653840tv_nat,B: produc194167194tv_nat > produc194167194tv_nat,C: produc194167194tv_nat > produc194167194tv_nat] :
( ! [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on552895452tv_nat @ B @ A )
= ( inj_on552895452tv_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_inj__on__cong) ).
thf(430,plain,
! [A: set_Pr1725653840tv_nat,B: produc194167194tv_nat > produc194167194tv_nat,C: produc194167194tv_nat > produc194167194tv_nat] :
( ! [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on552895452tv_nat @ B @ A )
= ( inj_on552895452tv_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(132,axiom,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member_nat @ C @ B )
=> ( ( the_inv_into_nat_nat @ B @ A @ D )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_the__inv__into__f__eq) ).
thf(824,plain,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member_nat @ C @ B )
=> ( ( the_inv_into_nat_nat @ B @ A @ D )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(141,axiom,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_subset__iff) ).
thf(856,plain,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(259,axiom,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_surjE) ).
thf(1301,plain,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(69,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: paraco1605129243lle_tv,D: set_nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ ( image_1151963140lle_tv @ A @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ D )
=> ( member_nat @ ( the_in138087638lle_tv @ B @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_the__inv__into__into) ).
thf(573,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: paraco1605129243lle_tv,D: set_nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ ( image_1151963140lle_tv @ A @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ D )
=> ( member_nat @ ( the_in138087638lle_tv @ B @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(77,axiom,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_psubsetD) ).
thf(601,plain,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(14,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat,C: produc194167194tv_nat,D: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member737151281tv_nat @ C @ B )
=> ( ( member737151281tv_nat @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_inj__onD) ).
thf(375,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat,C: produc194167194tv_nat,D: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member737151281tv_nat @ C @ B )
=> ( ( member737151281tv_nat @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(109,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
= ( ! [B: produc1647334210lle_tv,C: produc1647334210lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_inj__def) ).
thf(733,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
= ( ! [B: produc1647334210lle_tv,C: produc1647334210lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(222,axiom,
! [A: nat > nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
= ( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_inj__def) ).
thf(1154,plain,
! [A: nat > nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
= ( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(66,axiom,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_in__mono) ).
thf(562,plain,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(28,axiom,
! [A: set_Pr1986765409at_nat] :
( ! [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A )
=> ( top_to1555900337at_nat = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_UNIV__eq__I) ).
thf(423,plain,
! [A: set_Pr1986765409at_nat] :
( ! [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A )
=> ( top_to1555900337at_nat = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(137,axiom,
! [A: set_nat] :
( ! [B: nat] : ( member_nat @ B @ A )
=> ( top_top_set_nat = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_UNIV__eq__I) ).
thf(843,plain,
! [A: set_nat] :
( ! [B: nat] : ( member_nat @ B @ A )
=> ( top_top_set_nat = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(118,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: nat,D: paraco1605129243lle_tv > nat] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_nat @ C @ ( image_376325286tv_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_rev__image__eqI) ).
thf(772,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: nat,D: paraco1605129243lle_tv > nat] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_nat @ C @ ( image_376325286tv_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(284,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on2112487900lle_tv @ ( produc1408152463lle_tv @ A ) @ top_to1871154984lle_tv )
= ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_inj__apsnd) ).
thf(1388,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on2112487900lle_tv @ ( produc1408152463lle_tv @ A ) @ top_to1871154984lle_tv )
= ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(71,axiom,
( strict1310998166et_nat
= ( ^ [A: nat > set_nat,B: set_nat] :
! [C: nat,D: nat] :
( ( ( member_nat @ C @ B )
& ( member_nat @ D @ B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_less_set_nat @ ( A @ C ) @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_strict__mono__on__def) ).
thf(579,plain,
( strict1310998166et_nat
= ( ^ [A: nat > set_nat,B: set_nat] :
! [C: nat,D: nat] :
( ( ( member_nat @ C @ B )
& ( member_nat @ D @ B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_less_set_nat @ ( A @ C ) @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(288,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv] :
? [C: paraco1605129243lle_tv] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_surj__def) ).
thf(1403,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv] :
? [C: paraco1605129243lle_tv] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(320,axiom,
! [A: paraco1605129243lle_tv > nat,B: nat > paraco1605129243lle_tv] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( ( image_1151963140lle_tv @ B @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ A @ B ) @ top_to975729152tv_nat )
= top_to1411004326lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_map__prod__surj) ).
thf(1520,plain,
! [A: paraco1605129243lle_tv > nat,B: nat > paraco1605129243lle_tv] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( ( image_1151963140lle_tv @ B @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ A @ B ) @ top_to975729152tv_nat )
= top_to1411004326lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(246,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( C != D )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( member266900804lle_tv @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_inj__on__contraD) ).
thf(1256,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( C != D )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( member266900804lle_tv @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(63,axiom,
! [A: nat > set_nat,B: set_nat,C: nat,D: nat] :
( ( strict1310998166et_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_set_nat @ ( A @ C ) @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_strict__mono__onD) ).
thf(545,plain,
! [A: nat > set_nat,B: set_nat,C: nat,D: nat] :
( ( strict1310998166et_nat @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_set_nat @ ( A @ C ) @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(86,axiom,
! [A: nat > paraco1605129243lle_tv,B: nat,C: nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_inj__eq) ).
thf(641,plain,
! [A: nat > paraco1605129243lle_tv,B: nat,C: nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(122,axiom,
! [A: nat,B: set_nat,C: nat,D: nat > nat] :
( ( member_nat @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_nat @ C @ ( image_nat_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_rev__image__eqI) ).
thf(787,plain,
! [A: nat,B: set_nat,C: nat,D: nat > nat] :
( ( member_nat @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_nat @ C @ ( image_nat_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(209,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le727057319lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le727057319lle_tv @ E @ F )
=> ( ord_le727057319lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le727057319lle_tv @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_ord__eq__less__subst) ).
thf(1107,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le727057319lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le727057319lle_tv @ E @ F )
=> ( ord_le727057319lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le727057319lle_tv @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(41,axiom,
( top_to900819589_nat_o
= ( ^ [A: produc194167194tv_nat] : ( member737151281tv_nat @ A @ top_to975729152tv_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_top__empty__eq) ).
thf(466,plain,
( top_to900819589_nat_o
= ( ^ [A: produc194167194tv_nat] : ( member737151281tv_nat @ A @ top_to975729152tv_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(5,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat > produc194167194tv_nat,D: product_prod_nat_nat > produc194167194tv_nat] :
( ( A = B )
=> ( ! [E: product_prod_nat_nat] :
( ( member701585322at_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_1597721174tv_nat @ C @ A )
= ( image_1597721174tv_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_image__cong) ).
thf(335,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat > produc194167194tv_nat,D: product_prod_nat_nat > produc194167194tv_nat] :
( ( A = B )
=> ( ! [E: product_prod_nat_nat] :
( ( member701585322at_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_1597721174tv_nat @ C @ A )
= ( image_1597721174tv_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(100,axiom,
! [A: set_nat] :
( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
= ( A = top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_top_Oextremum__unique) ).
thf(704,plain,
! [A: set_nat] :
( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
= ( A = top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(305,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] : ( member266900804lle_tv @ ( A @ B ) @ ( image_335818702lle_tv @ A @ top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_rangeI) ).
thf(1464,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] : ( member266900804lle_tv @ ( A @ B ) @ ( image_335818702lle_tv @ A @ top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(95,axiom,
! [A: set_nat,B: nat > paraco1605129243lle_tv] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on1955349912lle_tv @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_inj__onI) ).
thf(672,plain,
! [A: set_nat,B: nat > paraco1605129243lle_tv] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on1955349912lle_tv @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(19,axiom,
! [A: set_Pr1986765409at_nat,B: product_prod_nat_nat > product_prod_nat_nat,C: product_prod_nat_nat > product_prod_nat_nat] :
( ! [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on26176689at_nat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_inj__on__inverseI) ).
thf(391,plain,
! [A: set_Pr1986765409at_nat,B: product_prod_nat_nat > product_prod_nat_nat,C: product_prod_nat_nat > product_prod_nat_nat] :
( ! [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on26176689at_nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(315,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: nat > nat] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( inj_on_nat_nat @ B @ top_top_set_nat )
=> ( inj_on552895452tv_nat @ ( produc42536895at_nat @ A @ B ) @ top_to975729152tv_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_prod_Oinj__map) ).
thf(1503,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: nat > nat] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( inj_on_nat_nat @ B @ top_top_set_nat )
=> ( inj_on552895452tv_nat @ ( produc42536895at_nat @ A @ B ) @ top_to975729152tv_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(103,axiom,
! [A: set_nat,B: nat > paraco1605129243lle_tv,C: nat > paraco1605129243lle_tv] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on1955349912lle_tv @ B @ A )
= ( inj_on1955349912lle_tv @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_inj__on__cong) ).
thf(713,plain,
! [A: set_nat,B: nat > paraco1605129243lle_tv,C: nat > paraco1605129243lle_tv] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on1955349912lle_tv @ B @ A )
= ( inj_on1955349912lle_tv @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(52,axiom,
! [A: produc270694976lle_tv > nat,B: produc270694976lle_tv,C: set_Pr13445366lle_tv] :
( ( inj_on936843139tv_nat @ A @ top_to1411004326lle_tv )
=> ( ( member_nat @ ( A @ B ) @ ( image_1509856791tv_nat @ A @ C ) )
= ( member813679063lle_tv @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_inj__image__mem__iff) ).
thf(498,plain,
! [A: produc270694976lle_tv > nat,B: produc270694976lle_tv,C: set_Pr13445366lle_tv] :
( ( inj_on936843139tv_nat @ A @ top_to1411004326lle_tv )
=> ( ( member_nat @ ( A @ B ) @ ( image_1509856791tv_nat @ A @ C ) )
= ( member813679063lle_tv @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(160,axiom,
! [A: nat > nat,B: nat > nat] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_surjI) ).
thf(919,plain,
! [A: nat > nat,B: nat > nat] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(126,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > nat] :
( ( member266900804lle_tv @ A @ B )
=> ( member_nat @ ( C @ A ) @ ( image_376325286tv_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_imageI) ).
thf(804,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > nat] :
( ( member266900804lle_tv @ A @ B )
=> ( member_nat @ ( C @ A ) @ ( image_376325286tv_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(78,axiom,
! [A: set_nat,B: nat > nat] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( B @ C ) @ ( B @ D ) ) ) ) )
=> ( strict2146030304at_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_strict__mono__onI) ).
thf(604,plain,
! [A: set_nat,B: nat > nat] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( B @ C ) @ ( B @ D ) ) ) ) )
=> ( strict2146030304at_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(234,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) )
=> ( ord_le241064091lle_tv @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_subsetI) ).
thf(1194,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) )
=> ( ord_le241064091lle_tv @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(155,axiom,
! [A: nat > nat] :
( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_injI) ).
thf(900,plain,
! [A: nat > nat] :
( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(121,axiom,
! [A: nat > paraco1605129243lle_tv] :
( ( inj_on967082628lle_tv @ ( produc1804670661lle_tv @ A ) @ top_to975729152tv_nat )
= ( inj_on1955349912lle_tv @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_inj__apsnd) ).
thf(784,plain,
! [A: nat > paraco1605129243lle_tv] :
( ( inj_on967082628lle_tv @ ( produc1804670661lle_tv @ A ) @ top_to975729152tv_nat )
= ( inj_on1955349912lle_tv @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(321,axiom,
! [A: nat > nat,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( inj_on772319074lle_tv @ B @ top_to1057771083lle_tv )
=> ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ A @ B ) @ top_to1411004326lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_prod_Oinj__map) ).
thf(1524,plain,
! [A: nat > nat,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( inj_on772319074lle_tv @ B @ top_to1057771083lle_tv )
=> ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ A @ B ) @ top_to1411004326lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(110,axiom,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ top_to1555900337at_nat )
=> ( ( the_in2068894451at_nat @ top_to1555900337at_nat @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_the__inv__f__f) ).
thf(736,plain,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ top_to1555900337at_nat )
=> ( ( the_in2068894451at_nat @ top_to1555900337at_nat @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(212,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_335818702lle_tv @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_image__eqI) ).
thf(1122,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_335818702lle_tv @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(11,axiom,
! [A: product_prod_nat_nat > produc194167194tv_nat,B: set_Pr1986765409at_nat,C: produc194167194tv_nat > $o] :
( ? [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ ( image_1597721174tv_nat @ A @ B ) )
& ( C @ D ) )
=> ? [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_bex__imageD) ).
thf(362,plain,
! [A: product_prod_nat_nat > produc194167194tv_nat,B: set_Pr1986765409at_nat,C: produc194167194tv_nat > $o] :
( ? [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ ( image_1597721174tv_nat @ A @ B ) )
& ( C @ D ) )
=> ? [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(36,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat,C: produc194167194tv_nat,D: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ B )
=> ( ( member737151281tv_nat @ C @ B )
=> ( ( member737151281tv_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_inj__on__eq__iff) ).
thf(451,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat,C: produc194167194tv_nat,D: produc194167194tv_nat] :
( ( inj_on552895452tv_nat @ A @ B )
=> ( ( member737151281tv_nat @ C @ B )
=> ( ( member737151281tv_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(3,axiom,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv,C: produc270694976lle_tv,D: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member813679063lle_tv @ C @ B )
=> ( ( member813679063lle_tv @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_inj__onD) ).
thf(323,plain,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv,C: produc270694976lle_tv,D: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member813679063lle_tv @ C @ B )
=> ( ( member813679063lle_tv @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(75,axiom,
! [A: nat > set_Pa1764573435lle_tv,B: set_nat,C: nat,D: nat] :
( ( strict1658340843lle_tv @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_le727057319lle_tv @ ( A @ C ) @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_strict__mono__onD) ).
thf(594,plain,
! [A: nat > set_Pa1764573435lle_tv,B: set_nat,C: nat,D: nat] :
( ( strict1658340843lle_tv @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_le727057319lle_tv @ ( A @ C ) @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(81,axiom,
! [A: produc194167194tv_nat > nat,B: produc194167194tv_nat,C: set_Pr1725653840tv_nat] :
( ( inj_on808253149at_nat @ A @ top_to975729152tv_nat )
=> ( ( member_nat @ ( A @ B ) @ ( image_1381266801at_nat @ A @ C ) )
= ( member737151281tv_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_inj__image__mem__iff) ).
thf(621,plain,
! [A: produc194167194tv_nat > nat,B: produc194167194tv_nat,C: set_Pr1725653840tv_nat] :
( ( inj_on808253149at_nat @ A @ top_to975729152tv_nat )
=> ( ( member_nat @ ( A @ B ) @ ( image_1381266801at_nat @ A @ C ) )
= ( member737151281tv_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(188,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( image_376325286tv_nat @ ( the_in138087638lle_tv @ B @ A ) @ ( image_1151963140lle_tv @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_the__inv__into__onto) ).
thf(1029,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( image_376325286tv_nat @ ( the_in138087638lle_tv @ B @ A ) @ ( image_1151963140lle_tv @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(220,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_mem__Collect__eq) ).
thf(1149,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(159,axiom,
! [A: nat > nat,B: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( the_inv_into_nat_nat @ top_top_set_nat @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_the__inv__f__f) ).
thf(915,plain,
! [A: nat > nat,B: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( the_inv_into_nat_nat @ top_top_set_nat @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(272,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_inj__def) ).
thf(1344,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(164,axiom,
! [A: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv] :
( ( inj_on1179712058tv_nat @ A @ B )
=> ( ( image_1151963140lle_tv @ ( the_in1509933432tv_nat @ B @ A ) @ ( image_376325286tv_nat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_the__inv__into__onto) ).
thf(932,plain,
! [A: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv] :
( ( inj_on1179712058tv_nat @ A @ B )
=> ( ( image_1151963140lle_tv @ ( the_in1509933432tv_nat @ B @ A ) @ ( image_376325286tv_nat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(51,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: nat,D: nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_inj__onD) ).
thf(494,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: nat,D: nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(201,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_in__mono) ).
thf(1080,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(115,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv] :
( ! [B: produc1647334210lle_tv,C: produc1647334210lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_injI) ).
thf(758,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv] :
( ! [B: produc1647334210lle_tv,C: produc1647334210lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(270,axiom,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv] : ( member_nat @ ( A @ B ) @ ( image_376325286tv_nat @ A @ top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_rangeI) ).
thf(1339,plain,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv] : ( member_nat @ ( A @ B ) @ ( image_376325286tv_nat @ A @ top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(7,axiom,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat,D: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ B )
=> ( ( C != D )
=> ( ( member701585322at_nat @ C @ B )
=> ( ( member701585322at_nat @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_inj__on__contraD) ).
thf(345,plain,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat,D: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ B )
=> ( ( C != D )
=> ( ( member701585322at_nat @ C @ B )
=> ( ( member701585322at_nat @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(142,axiom,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_surjE) ).
thf(858,plain,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(229,axiom,
( inj_on_nat_nat
= ( ^ [A: nat > nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ B )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_inj__on__def) ).
thf(1177,plain,
( inj_on_nat_nat
= ( ^ [A: nat > nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ B )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(282,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ~ ! [C: paraco1605129243lle_tv] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_surjE) ).
thf(1381,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ~ ! [C: paraco1605129243lle_tv] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(117,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_injD) ).
thf(768,plain,
! [A: nat > nat,B: nat,C: nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(145,axiom,
( top_to1299250770e_tv_o
= ( ^ [A: paraco1605129243lle_tv] : top_top_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_top__apply) ).
thf(868,plain,
( top_to1299250770e_tv_o
= ( ^ [A: paraco1605129243lle_tv] : top_top_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(185,axiom,
! [A: set_nat,B: set_nat,C: nat > paraco1605129243lle_tv,D: nat > paraco1605129243lle_tv] :
( ( A = B )
=> ( ! [E: nat] :
( ( member_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_1151963140lle_tv @ C @ A )
= ( image_1151963140lle_tv @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_image__cong) ).
thf(1015,plain,
! [A: set_nat,B: set_nat,C: nat > paraco1605129243lle_tv,D: nat > paraco1605129243lle_tv] :
( ( A = B )
=> ( ! [E: nat] :
( ( member_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_1151963140lle_tv @ C @ A )
= ( image_1151963140lle_tv @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(244,axiom,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_top__set__def) ).
thf(1250,plain,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(158,axiom,
! [A: nat,B: set_nat,C: nat > nat] :
( ( member_nat @ A @ B )
=> ( member_nat @ ( C @ A ) @ ( image_nat_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_imageI) ).
thf(912,plain,
! [A: nat,B: set_nat,C: nat > nat] :
( ( member_nat @ A @ B )
=> ( member_nat @ ( C @ A ) @ ( image_nat_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(227,axiom,
! [A: nat > nat,B: set_nat,C: nat > $o] :
( ? [D: nat] :
( ( member_nat @ D @ ( image_nat_nat @ A @ B ) )
& ( C @ D ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_bex__imageD) ).
thf(1171,plain,
! [A: nat > nat,B: set_nat,C: nat > $o] :
( ? [D: nat] :
( ( member_nat @ D @ ( image_nat_nat @ A @ B ) )
& ( C @ D ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(37,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat > produc194167194tv_nat] :
( ( member701585322at_nat @ A @ B )
=> ( member737151281tv_nat @ ( C @ A ) @ ( image_1597721174tv_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_imageI) ).
thf(455,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat > produc194167194tv_nat] :
( ( member701585322at_nat @ A @ B )
=> ( member737151281tv_nat @ ( C @ A ) @ ( image_1597721174tv_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(150,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: set_nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( ( image_1151963140lle_tv @ A @ B )
= ( image_1151963140lle_tv @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_inj__image__eq__iff) ).
thf(883,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: set_nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( ( image_1151963140lle_tv @ A @ B )
= ( image_1151963140lle_tv @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(200,axiom,
! [A: produc194167194tv_nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on1612474245lle_tv @ A @ top_to975729152tv_nat )
=> ( ( member266900804lle_tv @ B @ ( image_2019567641lle_tv @ A @ top_to975729152tv_nat ) )
= ( ? [C: produc194167194tv_nat] :
( ( B
= ( A @ C ) )
& ! [D: produc194167194tv_nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_range__ex1__eq) ).
thf(1076,plain,
! [A: produc194167194tv_nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on1612474245lle_tv @ A @ top_to975729152tv_nat )
=> ( ( member266900804lle_tv @ B @ ( image_2019567641lle_tv @ A @ top_to975729152tv_nat ) )
= ( ? [C: produc194167194tv_nat] :
( ( B
= ( A @ C ) )
& ! [D: produc194167194tv_nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(190,axiom,
! [A: nat,B: set_nat,C: paraco1605129243lle_tv,D: nat > paraco1605129243lle_tv] :
( ( member_nat @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_1151963140lle_tv @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_rev__image__eqI) ).
thf(1034,plain,
! [A: nat,B: set_nat,C: paraco1605129243lle_tv,D: nat > paraco1605129243lle_tv] :
( ( member_nat @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_1151963140lle_tv @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(29,axiom,
! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ top_to1555900337at_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_UNIV__I) ).
thf(426,plain,
! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ top_to1555900337at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(96,axiom,
! [A: nat > paraco1605129243lle_tv] :
( ! [B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( A @ B )
!= ( A @ C ) ) )
=> ( inj_on1955349912lle_tv @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_linorder__injI) ).
thf(680,plain,
! [A: nat > paraco1605129243lle_tv] :
( ! [B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( A @ B )
!= ( A @ C ) ) )
=> ( inj_on1955349912lle_tv @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(293,axiom,
! [A: paraco1605129243lle_tv > nat,B: nat] :
( ( inj_on1179712058tv_nat @ A @ top_to1057771083lle_tv )
=> ( ( member_nat @ B @ ( image_376325286tv_nat @ A @ top_to1057771083lle_tv ) )
= ( ? [C: paraco1605129243lle_tv] :
( ( B
= ( A @ C ) )
& ! [D: paraco1605129243lle_tv] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_range__ex1__eq) ).
thf(1420,plain,
! [A: paraco1605129243lle_tv > nat,B: nat] :
( ( inj_on1179712058tv_nat @ A @ top_to1057771083lle_tv )
=> ( ( member_nat @ B @ ( image_376325286tv_nat @ A @ top_to1057771083lle_tv ) )
= ( ? [C: paraco1605129243lle_tv] :
( ( B
= ( A @ C ) )
& ! [D: paraco1605129243lle_tv] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(88,axiom,
! [A: product_prod_nat_nat > produc194167194tv_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inj_on1764151786tv_nat @ A @ top_to1555900337at_nat )
=> ( ( ( image_1597721174tv_nat @ A @ B )
= ( image_1597721174tv_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_inj__image__eq__iff) ).
thf(648,plain,
! [A: product_prod_nat_nat > produc194167194tv_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inj_on1764151786tv_nat @ A @ top_to1555900337at_nat )
=> ( ( ( image_1597721174tv_nat @ A @ B )
= ( image_1597721174tv_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(56,axiom,
! [A: set_nat,B: nat > set_nat] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_set_nat @ ( B @ C ) @ ( B @ D ) ) ) ) )
=> ( strict1310998166et_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_strict__mono__onI) ).
thf(516,plain,
! [A: set_nat,B: nat > set_nat] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_set_nat @ ( B @ C ) @ ( B @ D ) ) ) ) )
=> ( strict1310998166et_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(38,axiom,
! [A: produc194167194tv_nat] : ( member737151281tv_nat @ A @ top_to975729152tv_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_UNIV__I) ).
thf(458,plain,
! [A: produc194167194tv_nat] : ( member737151281tv_nat @ A @ top_to975729152tv_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(93,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: nat,D: nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_inj__on__eq__iff) ).
thf(663,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: nat,D: nat] :
( ( inj_on1955349912lle_tv @ A @ B )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(64,axiom,
! [A: set_nat,B: nat > set_Pa1764573435lle_tv] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_le727057319lle_tv @ ( B @ C ) @ ( B @ D ) ) ) ) )
=> ( strict1658340843lle_tv @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_strict__mono__onI) ).
thf(548,plain,
! [A: set_nat,B: nat > set_Pa1764573435lle_tv] :
( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_le727057319lle_tv @ ( B @ C ) @ ( B @ D ) ) ) ) )
=> ( strict1658340843lle_tv @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(147,axiom,
! [A: nat] : ( member_nat @ A @ top_top_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_UNIV__I) ).
thf(872,plain,
! [A: nat] : ( member_nat @ A @ top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(151,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_335818702lle_tv @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_rev__image__eqI) ).
thf(887,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_335818702lle_tv @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(24,axiom,
( top_to1889334367e_tv_o
= ( ^ [A: produc270694976lle_tv] : ( member813679063lle_tv @ A @ top_to1411004326lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_top__empty__eq) ).
thf(414,plain,
( top_to1889334367e_tv_o
= ( ^ [A: produc270694976lle_tv] : ( member813679063lle_tv @ A @ top_to1411004326lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
! [A: set_Pr1986765409at_nat,B: product_prod_nat_nat > product_prod_nat_nat] :
( ! [C: product_prod_nat_nat,D: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ A )
=> ( ( member701585322at_nat @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on26176689at_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_inj__onI) ).
thf(327,plain,
! [A: set_Pr1986765409at_nat,B: product_prod_nat_nat > product_prod_nat_nat] :
( ! [C: product_prod_nat_nat,D: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ A )
=> ( ( member701585322at_nat @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on26176689at_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(245,axiom,
! [A: paraco1605129243lle_tv > nat,B: nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ~ ! [C: paraco1605129243lle_tv] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_surjE) ).
thf(1252,plain,
! [A: paraco1605129243lle_tv > nat,B: nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ~ ! [C: paraco1605129243lle_tv] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(249,axiom,
! [A: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
=> ( A = top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_top_Oextremum__uniqueI) ).
thf(1267,plain,
! [A: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
=> ( A = top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(23,axiom,
! [A: set_Pr13445366lle_tv,B: produc270694976lle_tv > produc270694976lle_tv,C: produc270694976lle_tv > produc270694976lle_tv] :
( ! [D: produc270694976lle_tv] :
( ( member813679063lle_tv @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on1745913142lle_tv @ B @ A )
= ( inj_on1745913142lle_tv @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_inj__on__cong) ).
thf(409,plain,
! [A: set_Pr13445366lle_tv,B: produc270694976lle_tv > produc270694976lle_tv,C: produc270694976lle_tv > produc270694976lle_tv] :
( ! [D: produc270694976lle_tv] :
( ( member813679063lle_tv @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on1745913142lle_tv @ B @ A )
= ( inj_on1745913142lle_tv @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(206,axiom,
( top_to1555900337at_nat
= ( collec7649004at_nat @ top_to632227436_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_top__set__def) ).
thf(1098,plain,
( top_to1555900337at_nat
= ( collec7649004at_nat @ top_to632227436_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(242,axiom,
! [A: set_nat,B: nat > nat] :
( ! [C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( B @ C )
!= ( B @ D ) ) ) ) )
=> ( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ C @ D )
| ( ord_less_eq_nat @ D @ C ) ) ) )
=> ( inj_on_nat_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_linorder__inj__onI) ).
thf(1225,plain,
! [A: set_nat,B: nat > nat] :
( ! [C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( B @ C )
!= ( B @ D ) ) ) ) )
=> ( ! [C: nat,D: nat] :
( ( member_nat @ C @ A )
=> ( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ C @ D )
| ( ord_less_eq_nat @ D @ C ) ) ) )
=> ( inj_on_nat_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(101,axiom,
! [A: set_nat] :
( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
=> ( A = top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_top_Oextremum__uniqueI) ).
thf(707,plain,
! [A: set_nat] :
( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
=> ( A = top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(314,axiom,
! [A: paraco1605129243lle_tv > nat,B: nat > paraco1605129243lle_tv] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_surjI) ).
thf(1499,plain,
! [A: paraco1605129243lle_tv > nat,B: nat > paraco1605129243lle_tv] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(296,axiom,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on1179712058tv_nat @ A @ top_to1057771083lle_tv )
=> ( ( member_nat @ ( A @ B ) @ ( image_376325286tv_nat @ A @ C ) )
= ( member266900804lle_tv @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_inj__image__mem__iff) ).
thf(1432,plain,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on1179712058tv_nat @ A @ top_to1057771083lle_tv )
=> ( ( member_nat @ ( A @ B ) @ ( image_376325286tv_nat @ A @ C ) )
= ( member266900804lle_tv @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(53,axiom,
! [A: product_prod_nat_nat > nat,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( inj_on642995232at_nat @ A @ top_to1555900337at_nat )
=> ( ( member_nat @ ( A @ B ) @ ( image_1397137548at_nat @ A @ C ) )
= ( member701585322at_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_inj__image__mem__iff) ).
thf(502,plain,
! [A: product_prod_nat_nat > nat,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( inj_on642995232at_nat @ A @ top_to1555900337at_nat )
=> ( ( member_nat @ ( A @ B ) @ ( image_1397137548at_nat @ A @ C ) )
= ( member701585322at_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(70,axiom,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ B )
=> ( inj_on_nat_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_inj__on__subset) ).
thf(576,plain,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ B )
=> ( inj_on_nat_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(214,axiom,
! [A: set_nat,B: nat > nat,C: set_nat] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( member_nat @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_nat @ ( image_nat_nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_image__subsetI) ).
thf(1130,plain,
! [A: set_nat,B: nat > nat,C: set_nat] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( member_nat @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_nat @ ( image_nat_nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(254,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_335818702lle_tv @ A @ C ) )
= ( member266900804lle_tv @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_inj__image__mem__iff) ).
thf(1285,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_335818702lle_tv @ A @ C ) )
= ( member266900804lle_tv @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(275,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( member266900804lle_tv @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_inj__onD) ).
thf(1358,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( member266900804lle_tv @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(112,axiom,
! [A: produc194167194tv_nat > product_prod_nat_nat,B: set_Pr1725653840tv_nat] :
( ( inj_on1971554740at_nat @ A @ B )
=> ( ( image_1597721174tv_nat @ ( the_in874888178at_nat @ B @ A ) @ ( image_1805124128at_nat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_the__inv__into__onto) ).
thf(744,plain,
! [A: produc194167194tv_nat > product_prod_nat_nat,B: set_Pr1725653840tv_nat] :
( ( inj_on1971554740at_nat @ A @ B )
=> ( ( image_1597721174tv_nat @ ( the_in874888178at_nat @ B @ A ) @ ( image_1805124128at_nat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(186,axiom,
! [A: nat,B: set_nat,C: nat > paraco1605129243lle_tv] :
( ( member_nat @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_1151963140lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_imageI) ).
thf(1023,plain,
! [A: nat,B: set_nat,C: nat > paraco1605129243lle_tv] :
( ( member_nat @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_1151963140lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(241,axiom,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( image_nat_nat @ A @ B )
= ( image_nat_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_inj__image__eq__iff) ).
thf(1221,plain,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( ( image_nat_nat @ A @ B )
= ( image_nat_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(316,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on772319074lle_tv @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_inj__on__inverseI) ).
thf(1506,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on772319074lle_tv @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(295,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( A
= ( B @ C ) )
=> ( member266900804lle_tv @ A @ ( image_335818702lle_tv @ B @ top_to1057771083lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_range__eqI) ).
thf(1427,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( A
= ( B @ C ) )
=> ( member266900804lle_tv @ A @ ( image_335818702lle_tv @ B @ top_to1057771083lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(35,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: produc194167194tv_nat,D: product_prod_nat_nat > produc194167194tv_nat] :
( ( member701585322at_nat @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member737151281tv_nat @ C @ ( image_1597721174tv_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_rev__image__eqI) ).
thf(446,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: produc194167194tv_nat,D: product_prod_nat_nat > produc194167194tv_nat] :
( ( member701585322at_nat @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member737151281tv_nat @ C @ ( image_1597721174tv_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(251,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ! [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on772319074lle_tv @ C @ A )
=> ( ( inj_on772319074lle_tv @ B @ ( image_335818702lle_tv @ C @ A ) )
= ( inj_on772319074lle_tv @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_inj__on__image__iff) ).
thf(1272,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ! [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on772319074lle_tv @ C @ A )
=> ( ( inj_on772319074lle_tv @ B @ ( image_335818702lle_tv @ C @ A ) )
= ( inj_on772319074lle_tv @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(205,axiom,
! [A: nat > nat] :
( ! [B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( A @ B )
!= ( A @ C ) ) )
=> ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_linorder__injI) ).
thf(1094,plain,
! [A: nat > nat] :
( ! [B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( A @ B )
!= ( A @ C ) ) )
=> ( inj_on_nat_nat @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(176,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le727057319lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_psubsetD) ).
thf(978,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le727057319lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(217,axiom,
! [A: paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: set_nat] :
( ( member266900804lle_tv @ A @ ( image_1151963140lle_tv @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_image__iff) ).
thf(1140,plain,
! [A: paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: set_nat] :
( ( member266900804lle_tv @ A @ ( image_1151963140lle_tv @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(83,axiom,
( strict2146030304at_nat
= ( ^ [A: nat > nat,B: set_nat] :
! [C: nat,D: nat] :
( ( ( member_nat @ C @ B )
& ( member_nat @ D @ B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_less_nat @ ( A @ C ) @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_strict__mono__on__def) ).
thf(627,plain,
( strict2146030304at_nat
= ( ^ [A: nat > nat,B: set_nat] :
! [C: nat,D: nat] :
( ( ( member_nat @ C @ B )
& ( member_nat @ D @ B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_less_nat @ ( A @ C ) @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(303,axiom,
! [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_UNIV__I) ).
thf(1459,plain,
! [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(47,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_subset__UNIV) ).
thf(482,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(223,axiom,
! [A: product_prod_nat_nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on520021963lle_tv @ A @ top_to1555900337at_nat )
=> ( ( member266900804lle_tv @ B @ ( image_1093035615lle_tv @ A @ top_to1555900337at_nat ) )
= ( ? [C: product_prod_nat_nat] :
( ( B
= ( A @ C ) )
& ! [D: product_prod_nat_nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_range__ex1__eq) ).
thf(1157,plain,
! [A: product_prod_nat_nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on520021963lle_tv @ A @ top_to1555900337at_nat )
=> ( ( member266900804lle_tv @ B @ ( image_1093035615lle_tv @ A @ top_to1555900337at_nat ) )
= ( ? [C: product_prod_nat_nat] :
( ( B
= ( A @ C ) )
& ! [D: product_prod_nat_nat] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(72,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_top__greatest) ).
thf(581,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(300,axiom,
! [A: set_Pa1764573435lle_tv] :
( ! [B: paraco1605129243lle_tv] : ( member266900804lle_tv @ B @ A )
=> ( top_to1057771083lle_tv = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_UNIV__eq__I) ).
thf(1448,plain,
! [A: set_Pa1764573435lle_tv] :
( ! [B: paraco1605129243lle_tv] : ( member266900804lle_tv @ B @ A )
=> ( top_to1057771083lle_tv = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(184,axiom,
! [A: set_nat,B: nat > nat,C: nat > nat] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_nat_nat @ B @ A )
= ( inj_on_nat_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_inj__on__cong) ).
thf(1010,plain,
! [A: set_nat,B: nat > nat,C: nat > nat] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_nat_nat @ B @ A )
= ( inj_on_nat_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(255,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ f @ A )
= ( paraco1147068288nge_tv @ f @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060And_062tv2_Atv1_O_Achange__tv_Af_Atv1_A_061_Achange__tv_Af_Atv2_A_092_060Longrightarrow_062_Atv1_A_061_Atv2_092_060close_062) ).
thf(1289,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( paraco1147068288nge_tv @ f @ A )
= ( paraco1147068288nge_tv @ f @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(267,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on772319074lle_tv @ B @ A )
= ( inj_on772319074lle_tv @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_inj__on__cong) ).
thf(1326,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on772319074lle_tv @ B @ A )
= ( inj_on772319074lle_tv @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(283,axiom,
! [A: set_Pa1764573435lle_tv] :
( ( A != top_to1057771083lle_tv )
= ( ord_le727057319lle_tv @ A @ top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_top_Onot__eq__extremum) ).
thf(1385,plain,
! [A: set_Pa1764573435lle_tv] :
( ( A != top_to1057771083lle_tv )
= ( ord_le727057319lle_tv @ A @ top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(173,axiom,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( C != D )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_inj__on__contraD) ).
thf(963,plain,
! [A: nat > nat,B: set_nat,C: nat,D: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( C != D )
=> ( ( member_nat @ C @ B )
=> ( ( member_nat @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(196,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat] :
( ( inj_on552895452tv_nat @ A @ B )
=> ( ( image_1104296520tv_nat @ ( the_in195660058tv_nat @ B @ A ) @ ( image_1104296520tv_nat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_the__inv__into__onto) ).
thf(1062,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat] :
( ( inj_on552895452tv_nat @ A @ B )
=> ( ( image_1104296520tv_nat @ ( the_in195660058tv_nat @ B @ A ) @ ( image_1104296520tv_nat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(89,axiom,
( top_top_set_nat
= ( collect_nat @ top_top_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_top__set__def) ).
thf(652,plain,
( top_top_set_nat
= ( collect_nat @ top_top_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(120,axiom,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ord_less_set_nat @ C @ B )
=> ( ord_less_set_nat @ ( image_nat_nat @ A @ C ) @ ( image_nat_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_inj__on__strict__subset) ).
thf(781,plain,
! [A: nat > nat,B: set_nat,C: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( ord_less_set_nat @ C @ B )
=> ( ord_less_set_nat @ ( image_nat_nat @ A @ C ) @ ( image_nat_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(271,axiom,
! [A: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
= ( A = top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_top_Oextremum__unique) ).
thf(1341,plain,
! [A: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
= ( A = top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(153,axiom,
? [A: nat] : ( member_nat @ A @ top_top_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_UNIV__witness) ).
thf(896,plain,
? [A: nat] : ( member_nat @ A @ top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(108,axiom,
! [A: nat > nat,B: set_nat] :
( ( strict2146030304at_nat @ A @ B )
=> ( inj_on_nat_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_strict__mono__on__imp__inj__on) ).
thf(731,plain,
! [A: nat > nat,B: set_nat] :
( ( strict2146030304at_nat @ A @ B )
=> ( inj_on_nat_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(26,axiom,
! [A: produc194167194tv_nat] : ( member737151281tv_nat @ A @ top_to975729152tv_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_iso__tuple__UNIV__I) ).
thf(418,plain,
! [A: produc194167194tv_nat] : ( member737151281tv_nat @ A @ top_to975729152tv_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(312,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ ( image_335818702lle_tv @ A @ B ) )
=> ( ( A @ ( the_in452116896lle_tv @ B @ A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_f__the__inv__into__f) ).
thf(1491,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ ( image_335818702lle_tv @ A @ B ) )
=> ( ( A @ ( the_in452116896lle_tv @ B @ A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(298,axiom,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv] :
( ( inj_on1179712058tv_nat @ A @ top_to1057771083lle_tv )
=> ( ( the_in1509933432tv_nat @ top_to1057771083lle_tv @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_the__inv__f__f) ).
thf(1440,plain,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv] :
( ( inj_on1179712058tv_nat @ A @ top_to1057771083lle_tv )
=> ( ( the_in1509933432tv_nat @ top_to1057771083lle_tv @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(238,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: paraco1605129243lle_tv > $o] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1151963140lle_tv @ A @ B ) )
=> ( C @ D ) )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_ball__imageD) ).
thf(1212,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: paraco1605129243lle_tv > $o] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1151963140lle_tv @ A @ B ) )
=> ( C @ D ) )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(116,axiom,
! [A: paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_1151963140lle_tv @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_image__eqI) ).
thf(763,plain,
! [A: paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_1151963140lle_tv @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(16,axiom,
? [A: produc270694976lle_tv] : ( member813679063lle_tv @ A @ top_to1411004326lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_UNIV__witness) ).
thf(383,plain,
? [A: produc270694976lle_tv] : ( member813679063lle_tv @ A @ top_to1411004326lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(97,axiom,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_ord__eq__less__subst) ).
thf(684,plain,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(261,axiom,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_surjD) ).
thf(1309,plain,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(299,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( member266900804lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_inj__on__eq__iff) ).
thf(1444,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( member266900804lle_tv @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(193,axiom,
! [A: nat,B: nat > nat,C: nat] :
( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_nat_nat @ B @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_range__eqI) ).
thf(1045,plain,
! [A: nat,B: nat > nat,C: nat] :
( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_nat_nat @ B @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(224,axiom,
! [A: nat > nat,B: set_nat,C: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ ( image_nat_nat @ A @ B ) )
=> ( ( A @ ( the_inv_into_nat_nat @ B @ A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_f__the__inv__into__f) ).
thf(1161,plain,
! [A: nat > nat,B: set_nat,C: nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ ( image_nat_nat @ A @ B ) )
=> ( ( A @ ( the_inv_into_nat_nat @ B @ A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(94,axiom,
! [A: product_prod_nat_nat > product_prod_nat_nat] :
( ! [B: product_prod_nat_nat,C: product_prod_nat_nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on26176689at_nat @ A @ top_to1555900337at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_injI) ).
thf(667,plain,
! [A: product_prod_nat_nat > product_prod_nat_nat] :
( ! [B: product_prod_nat_nat,C: product_prod_nat_nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on26176689at_nat @ A @ top_to1555900337at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(257,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ C @ B )
=> ( ( ord_le241064091lle_tv @ D @ B )
=> ( ( ( image_335818702lle_tv @ A @ C )
= ( image_335818702lle_tv @ A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_inj__on__image__eq__iff) ).
thf(1294,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ C @ B )
=> ( ( ord_le241064091lle_tv @ D @ B )
=> ( ( ( image_335818702lle_tv @ A @ C )
= ( image_335818702lle_tv @ A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(215,axiom,
! [A: nat > paraco1605129243lle_tv] :
( ( inj_on1840679568lle_tv @ ( produc1608943133tv_nat @ A ) @ top_to1555900337at_nat )
= ( inj_on1955349912lle_tv @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_inj__apsnd) ).
thf(1133,plain,
! [A: nat > paraco1605129243lle_tv] :
( ( inj_on1840679568lle_tv @ ( produc1608943133tv_nat @ A ) @ top_to1555900337at_nat )
= ( inj_on1955349912lle_tv @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( ( paraco793048302_Indet @ A )
= ( paraco793048302_Indet @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_tv_Oinject_I2_J) ).
thf(950,plain,
! [A: nat,B: nat] :
( ( ( paraco793048302_Indet @ A )
= ( paraco793048302_Indet @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(286,axiom,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ( ( ( image_335818702lle_tv @ B @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ A @ B ) @ top_to1411004326lle_tv )
= top_to1871154984lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_map__prod__surj) ).
thf(1395,plain,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ( ( ( image_335818702lle_tv @ B @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ A @ B ) @ top_to1411004326lle_tv )
= top_to1871154984lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(22,axiom,
! [A: set_Pr13445366lle_tv,B: produc270694976lle_tv > produc270694976lle_tv,C: produc270694976lle_tv > produc270694976lle_tv] :
( ! [D: produc270694976lle_tv] :
( ( member813679063lle_tv @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on1745913142lle_tv @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_inj__on__inverseI) ).
thf(405,plain,
! [A: set_Pr13445366lle_tv,B: produc270694976lle_tv > produc270694976lle_tv,C: produc270694976lle_tv > produc270694976lle_tv] :
( ! [D: produc270694976lle_tv] :
( ( member813679063lle_tv @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on1745913142lle_tv @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(140,axiom,
( top_to975729152tv_nat
= ( collec848462447tv_nat @ top_to900819589_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_top__set__def) ).
thf(854,plain,
( top_to975729152tv_nat
= ( collec848462447tv_nat @ top_to900819589_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(144,axiom,
! [A: nat > nat,B: set_nat,C: nat,D: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ ( image_nat_nat @ A @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ D )
=> ( member_nat @ ( the_inv_into_nat_nat @ B @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_the__inv__into__into) ).
thf(865,plain,
! [A: nat > nat,B: set_nat,C: nat,D: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( member_nat @ C @ ( image_nat_nat @ A @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ D )
=> ( member_nat @ ( the_inv_into_nat_nat @ B @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(13,axiom,
? [A: produc194167194tv_nat] : ( member737151281tv_nat @ A @ top_to975729152tv_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_UNIV__witness) ).
thf(373,plain,
? [A: produc194167194tv_nat] : ( member737151281tv_nat @ A @ top_to975729152tv_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(134,axiom,
! [A: set_Pr2014382200lle_tv,B: produc1647334210lle_tv > produc1647334210lle_tv,C: produc1647334210lle_tv > produc1647334210lle_tv] :
( ! [D: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on2112487900lle_tv @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_inj__on__inverseI) ).
thf(833,plain,
! [A: set_Pr2014382200lle_tv,B: produc1647334210lle_tv > produc1647334210lle_tv,C: produc1647334210lle_tv > produc1647334210lle_tv] :
( ! [D: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on2112487900lle_tv @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(174,axiom,
! [A: set_nat,B: nat > nat,C: nat > nat] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on_nat_nat @ C @ A )
=> ( ( inj_on_nat_nat @ B @ ( image_nat_nat @ C @ A ) )
= ( inj_on_nat_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_inj__on__image__iff) ).
thf(967,plain,
! [A: set_nat,B: nat > nat,C: nat > nat] :
( ! [D: nat] :
( ( member_nat @ D @ A )
=> ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on_nat_nat @ C @ A )
=> ( ( inj_on_nat_nat @ B @ ( image_nat_nat @ C @ A ) )
= ( inj_on_nat_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(297,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( member266900804lle_tv @ B @ ( image_335818702lle_tv @ A @ top_to1057771083lle_tv ) )
= ( ? [C: paraco1605129243lle_tv] :
( ( B
= ( A @ C ) )
& ! [D: paraco1605129243lle_tv] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_range__ex1__eq) ).
thf(1436,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( member266900804lle_tv @ B @ ( image_335818702lle_tv @ A @ top_to1057771083lle_tv ) )
= ( ? [C: paraco1605129243lle_tv] :
( ( B
= ( A @ C ) )
& ! [D: paraco1605129243lle_tv] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(125,axiom,
! [A: nat > nat,B: nat > nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( inj_on_nat_nat @ B @ top_top_set_nat )
=> ( inj_on26176689at_nat @ ( produc505105722at_nat @ A @ B ) @ top_to1555900337at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_prod_Oinj__map) ).
thf(801,plain,
! [A: nat > nat,B: nat > nat] :
( ( inj_on_nat_nat @ A @ top_top_set_nat )
=> ( ( inj_on_nat_nat @ B @ top_top_set_nat )
=> ( inj_on26176689at_nat @ ( produc505105722at_nat @ A @ B ) @ top_to1555900337at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(263,axiom,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv > nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( ( image_376325286tv_nat @ B @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( image_901203832at_nat @ ( produc51277375tv_nat @ A @ B ) @ top_to1871154984lle_tv )
= top_to1555900337at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_map__prod__surj) ).
thf(1314,plain,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv > nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( ( image_376325286tv_nat @ B @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( image_901203832at_nat @ ( produc51277375tv_nat @ A @ B ) @ top_to1871154984lle_tv )
= top_to1555900337at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(313,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_injD) ).
thf(1495,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv,C: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ top_to1057771083lle_tv )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(54,axiom,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_set_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_ord__eq__less__subst) ).
thf(506,plain,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_set_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(235,axiom,
! [A: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( inj_on1179712058tv_nat @ A @ B )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( ord_le241064091lle_tv @ D @ B )
=> ( ( member_nat @ ( A @ C ) @ ( image_376325286tv_nat @ A @ D ) )
= ( member266900804lle_tv @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_inj__on__image__mem__iff) ).
thf(1197,plain,
! [A: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( inj_on1179712058tv_nat @ A @ B )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( ord_le241064091lle_tv @ D @ B )
=> ( ( member_nat @ ( A @ C ) @ ( image_376325286tv_nat @ A @ D ) )
= ( member266900804lle_tv @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(197,axiom,
! [A: set_Pa1764573435lle_tv] :
( ( collec1111687558lle_tv
@ ^ [B: paraco1605129243lle_tv] : ( member266900804lle_tv @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Collect__mem__eq) ).
thf(1065,plain,
! [A: set_Pa1764573435lle_tv] :
( ( collec1111687558lle_tv
@ ^ [B: paraco1605129243lle_tv] : ( member266900804lle_tv @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(99,axiom,
! [A: set_Pa1764573435lle_tv,B: nat > set_Pa1764573435lle_tv,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_le727057319lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le727057319lle_tv @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_ord__eq__less__subst) ).
thf(696,plain,
! [A: set_Pa1764573435lle_tv,B: nat > set_Pa1764573435lle_tv,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_le727057319lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le727057319lle_tv @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(225,axiom,
( top_to1411004326lle_tv
= ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_top__set__def) ).
thf(1165,plain,
( top_to1411004326lle_tv
= ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(124,axiom,
! [A: nat,B: nat > nat,C: nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( member_nat @ A @ ( image_nat_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_image__eqI) ).
thf(796,plain,
! [A: nat,B: nat > nat,C: nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( member_nat @ A @ ( image_nat_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(163,axiom,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
=> ( ( the_in427240730lle_tv @ top_to1871154984lle_tv @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_the__inv__f__f) ).
thf(928,plain,
! [A: produc1647334210lle_tv > produc1647334210lle_tv,B: produc1647334210lle_tv] :
( ( inj_on2112487900lle_tv @ A @ top_to1871154984lle_tv )
=> ( ( the_in427240730lle_tv @ top_to1871154984lle_tv @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(10,axiom,
! [A: set_Pr1725653840tv_nat,B: produc194167194tv_nat > produc194167194tv_nat,C: produc194167194tv_nat > produc194167194tv_nat] :
( ! [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on552895452tv_nat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_inj__on__inverseI) ).
thf(358,plain,
! [A: set_Pr1725653840tv_nat,B: produc194167194tv_nat > produc194167194tv_nat,C: produc194167194tv_nat > produc194167194tv_nat] :
( ! [D: produc194167194tv_nat] :
( ( member737151281tv_nat @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on552895452tv_nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(127,axiom,
! [A: nat > nat,B: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( image_nat_nat @ ( the_inv_into_nat_nat @ B @ A ) @ ( image_nat_nat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_the__inv__into__onto) ).
thf(807,plain,
! [A: nat > nat,B: set_nat] :
( ( inj_on_nat_nat @ A @ B )
=> ( ( image_nat_nat @ ( the_inv_into_nat_nat @ B @ A ) @ ( image_nat_nat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(33,axiom,
! [A: produc194167194tv_nat,B: product_prod_nat_nat > produc194167194tv_nat,C: product_prod_nat_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( B @ C ) )
=> ( ( member701585322at_nat @ C @ D )
=> ( member737151281tv_nat @ A @ ( image_1597721174tv_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_image__eqI) ).
thf(437,plain,
! [A: produc194167194tv_nat,B: product_prod_nat_nat > produc194167194tv_nat,C: product_prod_nat_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( B @ C ) )
=> ( ( member701585322at_nat @ C @ D )
=> ( member737151281tv_nat @ A @ ( image_1597721174tv_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(269,axiom,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( ( image_335818702lle_tv @ B @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( image_1892891680lle_tv @ ( produc1095080935lle_tv @ A @ B ) @ top_to1871154984lle_tv )
= top_to1411004326lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_map__prod__surj) ).
thf(1335,plain,
! [A: paraco1605129243lle_tv > nat,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
=> ( ( ( image_335818702lle_tv @ B @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( image_1892891680lle_tv @ ( produc1095080935lle_tv @ A @ B ) @ top_to1871154984lle_tv )
= top_to1411004326lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(44,axiom,
( inj_on26176689at_nat
= ( ^ [A: product_prod_nat_nat > product_prod_nat_nat,B: set_Pr1986765409at_nat] :
! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ B )
=> ! [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_inj__on__def) ).
thf(474,plain,
( inj_on26176689at_nat
= ( ^ [A: product_prod_nat_nat > product_prod_nat_nat,B: set_Pr1986765409at_nat] :
! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ B )
=> ! [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(290,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( ( image_1151963140lle_tv @ B @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ( ( image_228488944lle_tv @ ( produc1521089895lle_tv @ A @ B ) @ top_to975729152tv_nat )
= top_to1871154984lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_map__prod__surj) ).
thf(1410,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv] :
( ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv )
=> ( ( ( image_1151963140lle_tv @ B @ top_top_set_nat )
= top_to1057771083lle_tv )
=> ( ( image_228488944lle_tv @ ( produc1521089895lle_tv @ A @ B ) @ top_to975729152tv_nat )
= top_to1871154984lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(172,axiom,
! [A: nat,B: nat > nat,C: set_nat] :
( ( member_nat @ A @ ( image_nat_nat @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_image__iff) ).
thf(960,plain,
! [A: nat,B: nat > nat,C: set_nat] :
( ( member_nat @ A @ ( image_nat_nat @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(308,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( the_in452116896lle_tv @ B @ A @ D )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_the__inv__into__f__eq) ).
thf(1473,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv] :
( ( inj_on772319074lle_tv @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member266900804lle_tv @ C @ B )
=> ( ( the_in452116896lle_tv @ B @ A @ D )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(111,axiom,
! [A: nat > paraco1605129243lle_tv,B: nat,C: set_nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_1151963140lle_tv @ A @ C ) )
= ( member_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_inj__image__mem__iff) ).
thf(740,plain,
! [A: nat > paraco1605129243lle_tv,B: nat,C: set_nat] :
( ( inj_on1955349912lle_tv @ A @ top_top_set_nat )
=> ( ( member266900804lle_tv @ ( A @ B ) @ ( image_1151963140lle_tv @ A @ C ) )
= ( member_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(40,axiom,
! [A: produc270694976lle_tv] : ( member813679063lle_tv @ A @ top_to1411004326lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_iso__tuple__UNIV__I) ).
thf(464,plain,
! [A: produc270694976lle_tv] : ( member813679063lle_tv @ A @ top_to1411004326lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(221,axiom,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_subset__eq) ).
thf(1152,plain,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(281,axiom,
! [A: set_Pa1764573435lle_tv] :
~ ( ord_le727057319lle_tv @ top_to1057771083lle_tv @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_top_Oextremum__strict) ).
thf(1378,plain,
! [A: set_Pa1764573435lle_tv] :
~ ( ord_le727057319lle_tv @ top_to1057771083lle_tv @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(157,axiom,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat,C: set_Pr1725653840tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
=> ( ( ( image_1104296520tv_nat @ A @ B )
= ( image_1104296520tv_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_inj__image__eq__iff) ).
thf(908,plain,
! [A: produc194167194tv_nat > produc194167194tv_nat,B: set_Pr1725653840tv_nat,C: set_Pr1725653840tv_nat] :
( ( inj_on552895452tv_nat @ A @ top_to975729152tv_nat )
=> ( ( ( image_1104296520tv_nat @ A @ B )
= ( image_1104296520tv_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(34,axiom,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat,D: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ B )
=> ( ( member701585322at_nat @ C @ B )
=> ( ( member701585322at_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_inj__on__eq__iff) ).
thf(442,plain,
! [A: product_prod_nat_nat > product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat,D: product_prod_nat_nat] :
( ( inj_on26176689at_nat @ A @ B )
=> ( ( member701585322at_nat @ C @ B )
=> ( ( member701585322at_nat @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(287,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_surjI) ).
thf(1399,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_335818702lle_tv @ A @ top_to1057771083lle_tv )
= top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(20,axiom,
( top_to632227436_nat_o
= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ top_to1555900337at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_top__empty__eq) ).
thf(395,plain,
( top_to632227436_nat_o
= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ top_to1555900337at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(136,axiom,
! [A: nat > nat,B: nat > nat] :
( ( order_769474267at_nat @ A )
=> ( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ( ! [C: nat] :
( ( B @ ( A @ C ) )
= C )
=> ( order_769474267at_nat @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_strict__mono__inv) ).
thf(839,plain,
! [A: nat > nat,B: nat > nat] :
( ( order_769474267at_nat @ A )
=> ( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ( ! [C: nat] :
( ( B @ ( A @ C ) )
= C )
=> ( order_769474267at_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(268,axiom,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv > nat] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_surjI) ).
thf(1331,plain,
! [A: nat > paraco1605129243lle_tv,B: paraco1605129243lle_tv > nat] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1151963140lle_tv @ A @ top_top_set_nat )
= top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1,conjecture,
inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(322,plain,
~ ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ f ) @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,axiom,
! [A: nat > paraco1605129243lle_tv] :
( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on1955349912lle_tv @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_injI) ).
thf(486,plain,
! [A: nat > paraco1605129243lle_tv] :
( ! [B: nat,C: nat] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on1955349912lle_tv @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(265,axiom,
! [A: paraco1605129243lle_tv > nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: paraco1605129243lle_tv] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_surj__def) ).
thf(1320,plain,
! [A: paraco1605129243lle_tv > nat] :
( ( ( image_376325286tv_nat @ A @ top_to1057771083lle_tv )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: paraco1605129243lle_tv] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(166,axiom,
! [A: paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: nat] :
( ( A
= ( B @ C ) )
=> ( member266900804lle_tv @ A @ ( image_1151963140lle_tv @ B @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_range__eqI) ).
thf(940,plain,
! [A: paraco1605129243lle_tv,B: nat > paraco1605129243lle_tv,C: nat] :
( ( A
= ( B @ C ) )
=> ( member266900804lle_tv @ A @ ( image_1151963140lle_tv @ B @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(9,axiom,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv,C: produc270694976lle_tv,D: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ B )
=> ( ( C != D )
=> ( ( member813679063lle_tv @ C @ B )
=> ( ( member813679063lle_tv @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_inj__on__contraD) ).
thf(354,plain,
! [A: produc270694976lle_tv > produc270694976lle_tv,B: set_Pr13445366lle_tv,C: produc270694976lle_tv,D: produc270694976lle_tv] :
( ( inj_on1745913142lle_tv @ A @ B )
=> ( ( C != D )
=> ( ( member813679063lle_tv @ C @ B )
=> ( ( member813679063lle_tv @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(165,axiom,
! [A: produc270694976lle_tv > produc270694976lle_tv] :
( ! [B: produc270694976lle_tv,C: produc270694976lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_injI) ).
thf(935,plain,
! [A: produc270694976lle_tv > produc270694976lle_tv] :
( ! [B: produc270694976lle_tv,C: produc270694976lle_tv] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on1745913142lle_tv @ A @ top_to1411004326lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(161,axiom,
! [A: nat > paraco1605129243lle_tv,B: nat] : ( member266900804lle_tv @ ( A @ B ) @ ( image_1151963140lle_tv @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_rangeI) ).
thf(923,plain,
! [A: nat > paraco1605129243lle_tv,B: nat] : ( member266900804lle_tv @ ( A @ B ) @ ( image_1151963140lle_tv @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(62,axiom,
( strict1658340843lle_tv
= ( ^ [A: nat > set_Pa1764573435lle_tv,B: set_nat] :
! [C: nat,D: nat] :
( ( ( member_nat @ C @ B )
& ( member_nat @ D @ B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_le727057319lle_tv @ ( A @ C ) @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_strict__mono__on__def) ).
thf(543,plain,
( strict1658340843lle_tv
= ( ^ [A: nat > set_Pa1764573435lle_tv,B: set_nat] :
! [C: nat,D: nat] :
( ( ( member_nat @ C @ B )
& ( member_nat @ D @ B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_le727057319lle_tv @ ( A @ C ) @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(114,axiom,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_Collect__mem__eq) ).
thf(755,plain,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(50,axiom,
! [A: set_nat] :
( ( A != top_top_set_nat )
= ( ord_less_set_nat @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_top_Onot__eq__extremum) ).
thf(491,plain,
! [A: set_nat] :
( ( A != top_top_set_nat )
= ( ord_less_set_nat @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(237,axiom,
! [A: set_Pr2014382200lle_tv,B: produc1647334210lle_tv > produc1647334210lle_tv] :
( ! [C: produc1647334210lle_tv,D: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ C @ A )
=> ( ( member1531318361lle_tv @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on2112487900lle_tv @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_inj__onI) ).
thf(1204,plain,
! [A: set_Pr2014382200lle_tv,B: produc1647334210lle_tv > produc1647334210lle_tv] :
( ! [C: produc1647334210lle_tv,D: produc1647334210lle_tv] :
( ( member1531318361lle_tv @ C @ A )
=> ( ( member1531318361lle_tv @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on2112487900lle_tv @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1528,plain,
$false,
inference(e,[status(thm)],[629,1469,479,846,1179,777,645,892,365,1369,1190,1083,468,1406,1068,994,379,1305,597,385,533,472,814,1260,747,945,829,898,1127,1391,565,1518,1482,1298,1264,1323,1455,460,1313,1279,817,1087,1147,1247,870,1347,416,1115,1362,1100,591,1373,1418,1136,514,905,1183,1283,981,397,1215,692,956,1072,998,428,1201,1104,849,661,925,810,1091,1042,1355,1174,1217,820,1487,729,862,349,484,1032,1365,625,879,435,710,974,583,522,1270,948,1375,725,1006,388,610,989,874,1143,420,1118,1292,554,1461,476,1424,637,1039,1414,526,837,985,1478,1451,654,1050,721,1002,569,792,541,657,1054,1466,1187,1515,530,953,718,343,1318,1026,1167,1510,618,430,824,856,1301,573,601,375,733,1154,562,423,843,772,1388,579,1403,1520,1256,545,641,787,1107,466,335,704,1464,672,391,1503,713,498,919,804,604,1194,900,784,1524,736,1122,362,451,323,594,621,1029,1149,915,1344,932,494,1080,758,1339,345,858,1177,1381,768,868,1015,1250,912,1171,455,883,1076,1034,426,680,1420,648,516,458,663,548,872,887,414,327,1252,1267,409,1098,1225,707,1499,1432,502,576,1130,1285,1358,744,1023,1221,1506,1427,446,1272,1094,978,1140,627,1459,482,1157,581,1448,1010,1289,1326,1385,963,1062,652,781,1341,896,731,418,1491,1440,1212,763,383,684,1309,1444,1045,1161,667,1294,1133,950,1395,405,854,865,373,833,967,1436,801,1314,1495,506,1197,1065,696,1165,796,928,358,807,437,1335,474,1410,960,1473,740,464,1152,1378,908,442,1399,395,839,1331,322,486,1320,940,354,935,923,543,755,491,1204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP139^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:34:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.93/1.09 % [INFO] Parsing done (243ms).
% 1.93/1.10 % [INFO] Running in sequential loop mode.
% 2.67/1.30 % [INFO] eprover registered as external prover.
% 2.67/1.31 % [INFO] cvc4 registered as external prover.
% 2.67/1.31 % [INFO] Scanning for conjecture ...
% 2.84/1.40 % [INFO] Found a conjecture and 355 axioms. Running axiom selection ...
% 3.32/1.51 % [INFO] Axiom selection finished. Selected 319 axioms (removed 36 axioms).
% 3.90/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 3.90/1.70 % [INFO] Type checking passed.
% 3.90/1.70 % [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 ...
% 16.65/5.10 % External prover 'e' found a proof!
% 16.65/5.10 % [INFO] Killing All external provers ...
% 16.65/5.10 % Time passed: 4584ms (effective reasoning time: 4004ms)
% 16.65/5.10 % 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)>
% 16.65/5.11 % Axioms used in derivation (319): fact_125_inj__apsnd, fact_336_inj__on__image__mem__iff, fact_139_inj__image__mem__iff, fact_165_image__eqI, fact_212_rev__image__eqI, fact_136_inj__image__mem__iff, fact_303_the__inv__into__into, fact_19_injD, fact_250_mem__Collect__eq, fact_200_image__cong, fact_128_inj__apsnd, fact_294_the__inv__into__f__f, fact_254_Collect__cong, fact_259_inj__on__the__inv__into, fact_296_the__inv__into__f__eq, fact_148_inj__image__eq__iff, fact_308_subsetI, fact_149_range__ex1__eq, fact_311_image__subsetI, fact_113_the__inv__f__f, fact_4_UNIV__I, fact_232_strict__mono__on__def, fact_114_the__inv__f__f, fact_321_subset__UNIV, fact_42_inj__onD, fact_258_inj__on__the__inv__into, fact_103_inj__on__contraD, fact_224_strict__mono__onI, fact_184_imageI, fact_59_inj__on__def, fact_328_subsetD, fact_183_imageI, fact_123_change__tv_Osimps_I2_J, fact_31_inj__eq, fact_262_strict__mono__inv, fact_216_strict__mono__onD, fact_98_inj__on__inverseI, fact_68_inj__on__cong, fact_326_in__mono, fact_38_inj__def, fact_268_surjE, fact_159_strict__mono__imp__inj__on, fact_205_ball__imageD, fact_155_range__ex1__eq, fact_64_inj__on__cong, fact_35_inj__def, fact_14_injD, fact_333_subset__iff, fact_314_top_Oextremum__uniqueI, fact_225_strict__mono__onI, fact_7_iso__tuple__UNIV__I, fact_288_inj__on__image__iff, fact_69_inj__on__eq__iff, fact_192_bex__imageD, fact_27_inj__eq, fact_309_subsetI, fact_54_inj__onI, fact_104_inj__on__contraD, fact_83_UNIV__witness, fact_186_imageI, fact_152_range__ex1__eq, fact_140_inj__image__eq__iff, fact_305_prod_Oinj__map, fact_201_image__cong, fact_81_top__set__def, fact_55_inj__on__def, fact_298_psubsetD, fact_297_the__inv__into__f__eq, fact_124_inj__apsnd, fact_25_injI, fact_141_inj__image__eq__iff, fact_168_top1I, fact_90_UNIV__eq__I, fact_8_iso__tuple__UNIV__I, fact_292_top_Onot__eq__extremum, fact_147_inj__image__eq__iff, fact_102_inj__on__contraD, fact_36_inj__def, fact_63_inj__on__cong, fact_109_top__empty__eq, fact_213_rev__image__eqI, fact_281_surj__def, fact_137_inj__image__mem__iff, fact_325_inj__on__subset, fact_129_inj__apsnd, fact_331_subset__eq, fact_71_inj__on__eq__iff, fact_306_prod_Oinj__map, fact_243_ord__eq__less__subst, fact_207_rev__image__eqI, fact_151_range__ex1__eq, fact_252_Collect__mem__eq, fact_293_inj__on__add, fact_257_inj__on__strict__subset, fact_163_image__eqI, fact_180_imageI, fact_70_inj__on__eq__iff, fact_115_the__inv__f__f, fact_251_mem__Collect__eq, fact_88_UNIV__eq__I, fact_119_strict__mono__on__imp__inj__on, fact_178_the__inv__into__onto, fact_79_top__set__def, fact_135_inj__image__mem__iff, fact_247_ord__eq__less__subst, fact_283_range__eqI, fact_97_inj__on__inverseI, fact_286_range__eqI, fact_301_the__inv__into__into, fact_253_Collect__mem__eq, fact_46_inj__onD, fact_28_inj__eq, fact_112_the__inv__f__f, fact_37_inj__def, fact_93_inj__on__inverseI, fact_78_top__set__def, fact_48_inj__onI, fact_126_inj__apsnd, fact_11_top__apply, fact_56_inj__on__def, fact_341_inj__image__subset__iff, fact_320_subset__UNIV, fact_346_map__prod__surj, fact_300_the__inv__into__into, fact_150_range__ex1__eq, fact_329_subsetD, fact_92_inj__on__inverseI, fact_13_injD, fact_266_surjD, fact_340_inj__on__image__eq__iff, fact_100_inj__on__contraD, fact_53_inj__onI, fact_299_psubsetD, fact_291_top_Onot__eq__extremum, fact_270_surjE, fact_339_inj__on__image__eq__iff, fact_122_inj__add__left, fact_279_surj__def, fact_287_inj__on__image__iff, fact_153_range__ex1__eq, fact_130_inj__image__mem__iff, fact_111_the__inv__f__f, fact_133_inj__image__mem__iff, fact_86_UNIV__witness, fact_255_Collect__cong, fact_179_the__inv__into__onto, fact_156_range__ex1__eq, fact_89_UNIV__eq__I, fact_350_map__prod__surj, fact_74_inj__on__eq__iff, fact_197_image__cong, fact_142_inj__image__eq__iff, fact_202_ball__imageD, fact_338_inj__on__image__mem__iff, fact_30_inj__eq, fact_334_linorder__inj__onI, fact_108_top__empty__eq, fact_195_bex__imageD, fact_110_top__empty__eq, fact_249_ord__eq__less__subst, fact_174_the__inv__into__onto, fact_116_the__inv__f__f, fact_138_inj__image__mem__iff, fact_327_in__mono, fact_173_the__inv__into__onto, fact_96_inj__on__inverseI, fact_215_strict__mono__onD, fact_18_injD, fact_332_subset__iff, fact_310_image__subsetI, fact_265_surjD, fact_263_surjD, fact_289_top_Oextremum__strict, fact_105_inj__on__contraD, fact_41_inj__onD, fact_20_injI, fact_23_injI, fact_234_strict__mono__on__def, fact_15_injD, fact_244_ord__eq__less__subst, fact_269_surjE, fact_241_ord__eq__less__subst, fact_10_iso__tuple__UNIV__I, fact_101_inj__on__contraD, fact_47_inj__onD, fact_29_inj__eq, fact_264_surjD, fact_352_map__prod__surj, fact_77_top__set__def, fact_0__092_060open_062_092_060And_062tv2_Atv1_O_Achange__tv_Af_Atv1_A_061_Achange__tv_Af_Atv2_A_092_060Longrightarrow_062_Atv1_A_061_Atv2_092_060close_062, fact_76_assms, fact_295_the__inv__into__f__f, fact_171_the__inv__into__onto, fact_315_top_Oextremum__uniqueI, fact_323_subset__inj__on, fact_167_tv_Oinject_I2_J, fact_65_inj__on__cong, fact_118_the__inv__f__f, fact_347_map__prod__surj, fact_260_f__the__inv__into__f, fact_285_range__eqI, fact_117_the__inv__f__f, fact_57_inj__on__def, fact_345_map__prod__surj, fact_6_iso__tuple__UNIV__I, fact_172_the__inv__into__onto, fact_277_rangeI, fact_302_the__inv__into__into, fact_273_surjI, fact_120_linorder__injI, fact_330_subset__eq, fact_272_surjI, fact_307_prod_Oinj__map, fact_185_imageI, fact_33_inj__eq, fact_52_inj__onI, fact_284_range__eqI, fact_107_top__empty__eq, fact_157_range__ex1__eq, fact_85_UNIV__witness, fact_316_top_Oextremum__unique, fact_290_top_Oextremum__strict, fact_166_image__eqI, fact_51_inj__onI, fact_84_UNIV__witness, fact_342_inj__image__subset__iff, fact_61_inj__on__def, fact_58_inj__on__def, fact_50_inj__onI, fact_154_range__ex1__eq, fact_131_inj__image__mem__iff, fact_43_inj__onD, fact_144_inj__image__eq__iff, fact_82_UNIV__witness, fact_245_ord__eq__less__subst, fact_317_top_Oextremum__unique, fact_17_injD, fact_324_inj__on__subset, fact_196_bex__imageD, fact_1_UNIV__I, fact_248_ord__eq__less__subst, fact_312_image__subsetI, fact_160_image__eqI, fact_206_ball__imageD, fact_223_strict__mono__onI, fact_343_map__prod__surj, fact_132_inj__image__mem__iff, fact_267_surjE, fact_5_UNIV__I, fact_164_image__eqI, fact_353_subset__image__inj, fact_3_UNIV__I, fact_39_inj__def, fact_246_ord__eq__less__subst, fact_75_inj__on__eq__iff, fact_214_strict__mono__onD, fact_191_image__iff, fact_80_top__set__def, fact_95_inj__on__inverseI, fact_313_image__subsetI, fact_319_top__greatest, fact_24_injI, fact_16_injD, fact_143_inj__image__eq__iff, fact_45_inj__onD, fact_106_top__empty__eq, fact_344_map__prod__surj, fact_349_map__prod__surj, fact_187_image__iff, fact_134_inj__image__mem__iff, fact_176_the__inv__into__onto, fact_335_inj__on__image__mem__iff, fact_190_image__iff, fact_280_surj__def, fact_99_inj__on__contraD, fact_40_inj__def, fact_73_inj__on__eq__iff, fact_354_subset__image__inj, fact_337_inj__on__image__mem__iff, fact_275_rangeI, fact_21_injI, fact_210_rev__image__eqI, fact_304_prod_Oinj__map, fact_9_iso__tuple__UNIV__I, fact_322_subset__inj__on, fact_276_rangeI, fact_94_inj__on__inverseI, fact_44_inj__onD, fact_121_linorder__injI, fact_12_top__apply, fact_158_range__ex1__eq, fact_62_inj__on__cong, fact_2_UNIV__I, fact_169_top1I, fact_67_inj__on__cong, fact_91_UNIV__eq__I, fact_170_the__inv__into__onto, fact_261_f__the__inv__into__f, fact_318_top__greatest, fact_282_surj__def, fact_211_rev__image__eqI, fact_87_UNIV__eq__I, fact_278_rangeI, fact_127_inj__apsnd, fact_66_inj__on__cong, fact_26_injI, fact_274_surjI, fact_348_map__prod__surj, fact_22_injI, fact_351_map__prod__surj, fact_32_inj__eq, fact_60_inj__on__def, fact_72_inj__on__eq__iff, fact_233_strict__mono__on__def, fact_49_inj__onI, fact_271_surjI, fact_256_inj__on__strict__subset, fact_34_inj__def, fact_242_ord__eq__less__subst
% 16.65/5.11 % No. of inferences in proof: 642
% 16.65/5.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4584 ms resp. 4004 ms w/o parsing
% 17.67/5.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.83/5.29 % [INFO] Killing All external provers ...
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