%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW473^2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:14 AM UTC 2026
% Result : Theorem 30.90s 7.87s
% Output : Refutation 32.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 651
% Syntax : Number of formulae : 1304 ( 391 unt; 0 typ; 0 def)
% Number of atoms : 4834 (1082 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 9745 ( 342 ~; 90 |; 330 &;7561 @)
% ( 0 <=>;1422 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 2114 (2114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 93 ( 91 usr; 5 con; 0-3 aty)
% Number of variables : 3290 ( 162 ^;2998 !; 130 ?;3290 :)
% Comments :
%------------------------------------------------------------------------------
thf(x_a_type,type,
x_a: $tType ).
thf(com_type,type,
com: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(option_com_type,type,
option_com: $tType ).
thf(body_decl,type,
body: pname > option_com ).
thf(finite_card_a_o_decl,type,
finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
thf(finite_card_pname_o_decl,type,
finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
thf(finite_card_nat_o_decl,type,
finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
thf(finite_card_a_decl,type,
finite_card_a: ( x_a > $o ) > nat ).
thf(finite_card_pname_decl,type,
finite_card_pname: ( pname > $o ) > nat ).
thf(finite_card_nat_decl,type,
finite_card_nat: ( nat > $o ) > nat ).
thf(finite_finite_a_o_o_decl,type,
finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
thf(finite1066544169me_o_o_decl,type,
finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(finite1676163439at_o_o_decl,type,
finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
thf(finite_finite_a_o_decl,type,
finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
thf(finite297249702name_o_decl,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(finite_finite_nat_o_decl,type,
finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
thf(finite_finite_a_decl,type,
finite_finite_a: ( x_a > $o ) > $o ).
thf(finite_finite_pname_decl,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(finite_finite_nat_decl,type,
finite_finite_nat: ( nat > $o ) > $o ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > nat > nat ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > nat > nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(suc_decl,type,
suc: nat > nat ).
thf(nat_case_o_decl,type,
nat_case_o: $o > ( nat > $o ) > nat > $o ).
thf(the_com_decl,type,
the_com: option_com > com ).
thf(bot_bot_a_o_decl,type,
bot_bot_a_o: x_a > $o ).
thf(bot_bot_pname_o_decl,type,
bot_bot_pname_o: pname > $o ).
thf(bot_bot_nat_o_decl,type,
bot_bot_nat_o: nat > $o ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_eq_a_o_o_decl,type,
ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(ord_le1205211808me_o_o_decl,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(ord_less_eq_nat_o_o_decl,type,
ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(ord_less_eq_a_o_decl,type,
ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(ord_less_eq_pname_o_decl,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(ord_less_eq_nat_o_decl,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(ord_less_eq_o_decl,type,
ord_less_eq_o: $o > $o > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(collect_a_o_o_decl,type,
collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(collect_pname_o_o_decl,type,
collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(collect_nat_o_o_decl,type,
collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(collect_a_o_decl,type,
collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(collect_pname_o_decl,type,
collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(collect_nat_o_decl,type,
collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(collect_a_decl,type,
collect_a: ( x_a > $o ) > x_a > $o ).
thf(collect_pname_decl,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(collect_nat_decl,type,
collect_nat: ( nat > $o ) > nat > $o ).
thf(image_a_o_a_decl,type,
image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
thf(image_a_o_pname_decl,type,
image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
thf(image_a_o_nat_decl,type,
image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
thf(image_pname_o_a_decl,type,
image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
thf(image_pname_o_pname_decl,type,
image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(image_pname_o_nat_decl,type,
image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
thf(image_nat_o_a_decl,type,
image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
thf(image_nat_o_pname_decl,type,
image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
thf(image_nat_o_nat_decl,type,
image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $o ).
thf(image_a_a_o_decl,type,
image_a_a_o: ( x_a > x_a > $o ) > ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(image_a_pname_o_decl,type,
image_a_pname_o: ( x_a > pname > $o ) > ( x_a > $o ) > ( pname > $o ) > $o ).
thf(image_a_nat_o_decl,type,
image_a_nat_o: ( x_a > nat > $o ) > ( x_a > $o ) > ( nat > $o ) > $o ).
thf(image_a_a_decl,type,
image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
thf(image_a_pname_decl,type,
image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
thf(image_a_nat_decl,type,
image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
thf(image_pname_a_o_decl,type,
image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
thf(image_pname_pname_o_decl,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(image_pname_nat_o_decl,type,
image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
thf(image_pname_a_decl,type,
image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
thf(image_pname_pname_decl,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(image_pname_nat_decl,type,
image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
thf(image_nat_a_o_decl,type,
image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
thf(image_nat_pname_o_decl,type,
image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
thf(image_nat_nat_o_decl,type,
image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(image_nat_a_decl,type,
image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
thf(image_nat_pname_decl,type,
image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
thf(image_nat_nat_decl,type,
image_nat_nat: ( nat > nat ) > ( nat > $o ) > nat > $o ).
thf(insert_a_o_decl,type,
insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(insert_a_decl,type,
insert_a: x_a > ( x_a > $o ) > x_a > $o ).
thf(insert_pname_decl,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(insert_nat_decl,type,
insert_nat: nat > ( nat > $o ) > nat > $o ).
thf(fequal_a_decl,type,
fequal_a: x_a > x_a > $o ).
thf(fequal_pname_decl,type,
fequal_pname: pname > pname > $o ).
thf(member_a_o_decl,type,
member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(member_pname_o_decl,type,
member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(member_nat_o_decl,type,
member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(member_a_decl,type,
member_a: x_a > ( x_a > $o ) > $o ).
thf(member_pname_decl,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(member_nat_decl,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(g_decl,type,
g: x_a > $o ).
thf(p_decl,type,
p: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(u_decl,type,
u: pname > $o ).
thf(mgt_decl,type,
mgt: com > x_a ).
thf(mgt_call_decl,type,
mgt_call: pname > x_a ).
thf(na_decl,type,
na: nat ).
thf(pn_decl,type,
pn: pname ).
thf(wt_decl,type,
wt: com > $o ).
thf(434,axiom,
! [A: pname > nat > $o,B: pname > $o,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_nat_o_o @ C @ ( image_pname_nat_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_nat_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).
thf(2163,plain,
! [A: pname > nat > $o,B: pname > $o,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_nat_o_o @ C @ ( image_pname_nat_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_nat_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(642,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_subset__insertI2) ).
thf(2889,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(276,axiom,
! [A: nat,B: pname > nat,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_pname_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_rev__image__eqI) ).
thf(1633,plain,
! [A: nat,B: pname > nat,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_pname_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(504,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_less__Suc__eq__le) ).
thf(2412,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(552,axiom,
! [A: pname > x_a,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a @ ( image_pname_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
thf(2559,plain,
! [A: pname > x_a,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a @ ( image_pname_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(38,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_le0) ).
thf(777,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(185,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_insert__mono) ).
thf(1295,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(291,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_insertI2) ).
thf(1686,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(188,axiom,
! [A: nat,B: x_a > nat,C: x_a > $o] :
( ( member_nat @ A @ ( image_a_nat @ B @ C ) )
=> ~ ! [D: x_a] :
( ( A
= ( B @ D ) )
=> ~ ( member_a @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_imageE) ).
thf(1322,plain,
! [A: nat,B: x_a > nat,C: x_a > $o] :
( ( member_nat @ A @ ( image_a_nat @ B @ C ) )
=> ~ ! [D: x_a] :
( ( A
= ( B @ D ) )
=> ~ ( member_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(283,axiom,
( bot_bot_pname_o
= ( collect_pname
@ ^ [A: pname] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_empty__def) ).
thf(1665,plain,
( bot_bot_pname_o
= ( collect_pname
@ ^ [A: pname] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(624,axiom,
! [A: pname > x_a,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_a_o @ ( image_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_image__mono) ).
thf(2822,plain,
! [A: pname > x_a,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_a_o @ ( image_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(566,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ ( insert_a @ A @ B ) @ C )
= ( ( member_a @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__subset) ).
thf(2630,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ ( insert_a @ A @ B ) @ C )
= ( ( member_a @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(264,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ C @ B ) @ A )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_add__diff__assoc2) ).
thf(1586,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ C @ B ) @ A )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(515,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_diff__le__self) ).
thf(2452,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(50,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_diff__cancel2) ).
thf(809,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(347,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_ord__le__eq__trans) ).
thf(1879,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(192,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_empty__iff) ).
thf(1337,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(467,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_nat_Oinject) ).
thf(2295,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(35,axiom,
! [A: nat,B: nat > $o] :
( ( B = bot_bot_nat_o )
=> ~ ( member_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_equals0D) ).
thf(760,plain,
! [A: nat,B: nat > $o] :
( ( B = bot_bot_nat_o )
=> ~ ( member_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(614,axiom,
! [A: x_a > $o,B: com] :
( ( wt @ B )
=> ( ! [C: pname] :
( ( member_pname @ C @ u )
=> ( p @ A @ ( insert_a @ ( mgt_call @ C ) @ bot_bot_a_o ) ) )
=> ( p @ A @ ( insert_a @ ( mgt @ B ) @ bot_bot_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_assms_I3_J) ).
thf(2787,plain,
! [A: x_a > $o,B: com] :
( ( wt @ B )
=> ( ! [C: pname] :
( ( member_pname @ C @ u )
=> ( p @ A @ ( insert_a @ ( mgt_call @ C ) @ bot_bot_a_o ) ) )
=> ( p @ A @ ( insert_a @ ( mgt @ B ) @ bot_bot_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(337,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_subset__trans) ).
thf(1850,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(533,axiom,
! [A: pname > x_a,B: pname > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_pname_a @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_a @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_finite__subset__image) ).
thf(2499,plain,
! [A: pname > x_a,B: pname > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_pname_a @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_a @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(442,axiom,
! [A: x_a] :
~ ( member_a @ A @ bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_empty__iff) ).
thf(2210,plain,
! [A: x_a] :
~ ( member_a @ A @ bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(29,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_add__Suc__right) ).
thf(730,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(494,axiom,
! [A: pname,B: pname] :
( ( member_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_singletonE) ).
thf(2381,plain,
! [A: pname,B: pname] :
( ( member_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(577,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_order__eq__refl) ).
thf(2659,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(114,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_trans__less__add1) ).
thf(994,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(216,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( C = A )
| ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_insert__compr__raw) ).
thf(1401,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( C = A )
| ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(582,axiom,
! [A: x_a > $o] :
( ( ord_less_eq_a_o @ A @ bot_bot_a_o )
= ( A = bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_bot__unique) ).
thf(2676,plain,
! [A: x_a > $o] :
( ( ord_less_eq_a_o @ A @ bot_bot_a_o )
= ( A = bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(306,axiom,
! [A: nat,B: nat > $o,C: nat] :
( ( B @ C )
=> ( ! [D: nat] :
( ( B @ ( suc @ D ) )
=> ( B @ D ) )
=> ( B @ ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_zero__induct__lemma) ).
thf(1728,plain,
! [A: nat,B: nat > $o,C: nat] :
( ( B @ C )
=> ( ! [D: nat] :
( ( B @ ( suc @ D ) )
=> ( B @ D ) )
=> ( B @ ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(74,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_lessI) ).
thf(873,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(419,axiom,
! [A: $o,B: $o,C: $o] :
( ( ord_less_eq_o @ B @ C )
=> ( ( ord_less_eq_o @ C @ A )
=> ( ord_less_eq_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_order__trans) ).
thf(2099,plain,
! [A: $o,B: $o,C: $o] :
( ( ord_less_eq_o @ B @ C )
=> ( ( ord_less_eq_o @ C @ A )
=> ( ord_less_eq_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(628,axiom,
! [A: x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_pname_a
@ ^ [D: pname] : A
@ C )
= ( insert_a @ A @ bot_bot_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_image__constant) ).
thf(2837,plain,
! [A: x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_pname_a
@ ^ [D: pname] : A
@ C )
= ( insert_a @ A @ bot_bot_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(76,axiom,
! [A: nat] :
( ( finite_card_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_nat @ B @ A ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_card__Collect__less__nat) ).
thf(878,plain,
! [A: nat] :
( ( finite_card_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_nat @ B @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(294,axiom,
! [A: pname,B: pname > $o] :
( bot_bot_pname_o
!= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_empty__not__insert) ).
thf(1692,plain,
! [A: pname,B: pname > $o] :
( bot_bot_pname_o
!= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(339,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ! [D: nat] : ( ord_less_eq_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_o @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_lift__Suc__mono__le) ).
thf(1855,plain,
! [A: nat,B: nat,C: nat > $o] :
( ! [D: nat] : ( ord_less_eq_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_o @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(414,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_equalityD1) ).
thf(2077,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(267,axiom,
! [A: ( pname > $o ) > $o,B: nat > pname > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_nat_pname_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_finite__surj) ).
thf(1596,plain,
! [A: ( pname > $o ) > $o,B: nat > pname > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_nat_pname_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(218,axiom,
! [A: x_a > $o] :
( ( ! [B: x_a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_all__not__in__conv) ).
thf(1406,plain,
! [A: x_a > $o] :
( ( ! [B: x_a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(621,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_a_o @ A @ B )
=> ~ ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_equalityE) ).
thf(2808,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_a_o @ A @ B )
=> ~ ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(246,axiom,
! [A: pname > $o,B: x_a > pname,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_a_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_finite__surj) ).
thf(1522,plain,
! [A: pname > $o,B: x_a > pname,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_a_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(648,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ~ ( member_a @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ ( insert_a @ B @ A ) )
= ( ord_less_eq_a_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_subset__insert) ).
thf(2908,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ~ ( member_a @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ ( insert_a @ B @ A ) )
= ( ord_less_eq_a_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(409,axiom,
! [A: x_a > nat,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_nat @ ( image_a_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(2062,plain,
! [A: x_a > nat,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_nat @ ( image_a_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(378,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_nat_o @ A @ B )
=> ~ ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_equalityE) ).
thf(1971,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_nat_o @ A @ B )
=> ~ ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(320,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( member_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_set__rev__mp) ).
thf(1793,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( member_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(298,axiom,
! [A: nat > $o,B: ( pname > $o ) > nat,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_pname_o_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_finite__surj) ).
thf(1705,plain,
! [A: nat > $o,B: ( pname > $o ) > nat,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_pname_o_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(313,axiom,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_lift__Suc__mono__le) ).
thf(1756,plain,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(399,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ( minus_minus_nat @ C @ B )
= ( minus_minus_nat @ A @ B ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_eq__diff__iff) ).
thf(2035,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ( minus_minus_nat @ C @ B )
= ( minus_minus_nat @ A @ B ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(345,axiom,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_ex__in__conv) ).
thf(1872,plain,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(189,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( B = C )
=> ( ( ord_less_eq_nat_o @ A @ C )
=> ( ord_less_eq_nat_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_xt1_I3_J) ).
thf(1327,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( B = C )
=> ( ( ord_less_eq_nat_o @ A @ C )
=> ( ord_less_eq_nat_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_Suc__mono) ).
thf(945,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(402,axiom,
! [A: pname > $o,B: ( pname > $o ) > pname,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_pname_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_finite__surj) ).
thf(2042,plain,
! [A: pname > $o,B: ( pname > $o ) > pname,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_pname_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(243,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_less__diff__iff) ).
thf(1507,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(160,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
=> ( ( A != B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_insertE) ).
thf(1164,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
=> ( ( A != B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(46,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_diff__0__eq__0) ).
thf(797,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(361,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_subset__insertI2) ).
thf(1919,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(383,axiom,
! [A: nat > pname > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite297249702name_o @ ( image_nat_pname_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(1988,plain,
! [A: nat > pname > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite297249702name_o @ ( image_nat_pname_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(518,axiom,
! [A: pname > $o,B: ( nat > $o ) > pname,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_nat_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_finite__surj) ).
thf(2459,plain,
! [A: pname > $o,B: ( nat > $o ) > pname,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_nat_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(9,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_Suc__not__Zero) ).
thf(670,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(558,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_card__mono) ).
thf(2575,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_add__Suc) ).
thf(898,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(331,axiom,
! [A: nat > $o,B: ( nat > $o ) > nat,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_nat_o_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_finite__surj) ).
thf(1835,plain,
! [A: nat > $o,B: ( nat > $o ) > nat,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_nat_o_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(444,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ C )
= ( ( member_pname @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_insert__subset) ).
thf(2216,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ C )
= ( ( member_pname @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(484,axiom,
! [A: ( pname > $o ) > nat,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite_finite_nat @ ( image_pname_o_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(2348,plain,
! [A: ( pname > $o ) > nat,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite_finite_nat @ ( image_pname_o_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(404,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_xt1_I6_J) ).
thf(2046,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(606,axiom,
! [A: pname > x_a,B: x_a > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_a @ ( A @ D ) @ B ) )
=> ( ord_less_eq_a_o @ ( image_pname_a @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_image__subsetI) ).
thf(2763,plain,
! [A: pname > x_a,B: x_a > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_a @ ( A @ D ) @ B ) )
=> ( ord_less_eq_a_o @ ( image_pname_a @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(212,axiom,
! [A: pname > $o,B: pname] :
( ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( ( A = bot_bot_pname_o )
| ( A
= ( insert_pname @ B @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_subset__singletonD) ).
thf(1391,plain,
! [A: pname > $o,B: pname] :
( ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( ( A = bot_bot_pname_o )
| ( A
= ( insert_pname @ B @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(40,axiom,
! [A: nat,B: nat] : ( ord_less_nat @ A @ ( suc @ ( plus_plus_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_less__add__Suc2) ).
thf(782,plain,
! [A: nat,B: nat] : ( ord_less_nat @ A @ ( suc @ ( plus_plus_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(394,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_add__diff__assoc) ).
thf(2020,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(240,axiom,
! [A: x_a > pname,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_a_pname @ A @ C ) )
= ( image_a_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_insert__image) ).
thf(1475,plain,
! [A: x_a > pname,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_a_pname @ A @ C ) )
= ( image_a_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(436,axiom,
! [A: nat > x_a > $o,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_a_o @ ( image_nat_a_o @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_pigeonhole__infinite) ).
thf(2173,plain,
! [A: nat > x_a > $o,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_a_o @ ( image_nat_a_o @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(324,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_le__funE) ).
thf(1803,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(350,axiom,
! [A: x_a > $o] :
( ( ( collect_a @ A )
= bot_bot_a_o )
= ( ! [B: x_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Collect__empty__eq) ).
thf(1887,plain,
! [A: x_a > $o] :
( ( ( collect_a @ A )
= bot_bot_a_o )
= ( ! [B: x_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(510,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ C @ B ) ) @ A )
= ( minus_minus_nat @ ( suc @ C ) @ ( plus_plus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_diff__Suc__diff__eq2) ).
thf(2432,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ C @ B ) ) @ A )
= ( minus_minus_nat @ ( suc @ C ) @ ( plus_plus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(359,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_equalityI) ).
thf(1914,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(279,axiom,
! [A: nat > nat,B: nat > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_nat_nat @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_finite__subset__image) ).
thf(1650,plain,
! [A: nat > nat,B: nat > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_nat_nat @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(362,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Suc__n__not__n) ).
thf(1921,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(269,axiom,
! [A: nat > x_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_a @ ( A @ B ) @ ( image_nat_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_imageI) ).
thf(1601,plain,
! [A: nat > x_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_a @ ( A @ B ) @ ( image_nat_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(210,axiom,
! [A: pname > nat,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_card__image__le) ).
thf(1386,plain,
! [A: pname > nat,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(500,axiom,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( member_pname @ C @ B )
=> ( member_pname @ C @ A ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_subsetI) ).
thf(2400,plain,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( member_pname @ C @ B )
=> ( member_pname @ C @ A ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(411,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_insert__compr) ).
thf(2067,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(249,axiom,
! [A: nat,B: nat] :
( ( member_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_singletonE) ).
thf(1529,plain,
! [A: nat,B: nat] :
( ( member_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(575,axiom,
! [A: x_a,B: x_a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_a_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_singleton__iff) ).
thf(2654,plain,
! [A: x_a,B: x_a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_a_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(219,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a
@ ( collect_a
@ ^ [C: x_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a @ ( collect_a @ A ) )
& ( finite_finite_a @ ( collect_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_finite__Collect__disjI) ).
thf(1409,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a
@ ( collect_a
@ ^ [C: x_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a @ ( collect_a @ A ) )
& ( finite_finite_a @ ( collect_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(183,axiom,
! [A: x_a,B: nat > x_a,C: nat > $o] :
( ( member_a @ A @ ( image_nat_a @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( B @ D ) )
=> ~ ( member_nat @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_imageE) ).
thf(1287,plain,
! [A: x_a,B: nat > x_a,C: nat > $o] :
( ( member_a @ A @ ( image_nat_a @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( B @ D ) )
=> ~ ( member_nat @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(597,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( member_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_set__rev__mp) ).
thf(2735,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( member_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(481,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_insert__absorb) ).
thf(2339,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(460,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_diff__less__mono) ).
thf(2274,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(328,axiom,
! [A: pname > x_a > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_a_o @ ( image_pname_a_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_pigeonhole__infinite) ).
thf(1826,plain,
! [A: pname > x_a > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_a_o @ ( image_pname_a_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(330,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( suc @ B ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_diff__Suc__eq__diff__pred) ).
thf(1832,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( suc @ B ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(423,axiom,
! [A: x_a > x_a > $o,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_a_o @ ( image_a_a_o @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_pigeonhole__infinite) ).
thf(2126,plain,
! [A: x_a > x_a > $o,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_a_o @ ( image_a_a_o @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(153,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( A @ C )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( ( A @ ( suc @ D ) )
=> ( A @ D ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_inc__induct) ).
thf(1132,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( A @ C )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( ( A @ ( suc @ D ) )
=> ( A @ D ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(590,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
= ( ! [C: x_a] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_le__fun__def) ).
thf(2703,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
= ( ! [C: x_a] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(580,axiom,
! [A: nat > $o,B: x_a > nat,C: x_a > $o] :
( ( ord_less_eq_nat_o @ A @ ( image_a_nat @ B @ C ) )
= ( ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ C )
& ( A
= ( image_a_nat @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_subset__image__iff) ).
thf(2667,plain,
! [A: nat > $o,B: x_a > nat,C: x_a > $o] :
( ( ord_less_eq_nat_o @ A @ ( image_a_nat @ B @ C ) )
= ( ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ C )
& ( A
= ( image_a_nat @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(25,axiom,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ A @ one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_Suc__eq__plus1) ).
thf(719,plain,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ A @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(99,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_le__0__eq) ).
thf(949,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(599,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_xt1_I6_J) ).
thf(2745,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(556,axiom,
member_pname @ pn @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(2571,plain,
member_pname @ pn @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(549,axiom,
! [A: x_a,B: x_a,C: x_a,D: x_a] :
( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_a_o ) )
= ( insert_a @ C @ ( insert_a @ D @ bot_bot_a_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_doubleton__eq__iff) ).
thf(2552,plain,
! [A: x_a,B: x_a,C: x_a,D: x_a] :
( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_a_o ) )
= ( insert_a @ C @ ( insert_a @ D @ bot_bot_a_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(351,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_card__insert__disjoint) ).
thf(1890,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(607,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( p @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(2767,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( p @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_le__eq__less__or__eq) ).
thf(881,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(258,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_order__antisym__conv) ).
thf(1568,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(432,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_nat_o @ ( insert_nat @ A @ B ) @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_insert__mono) ).
thf(2158,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_nat_o @ ( insert_nat @ A @ B ) @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(346,axiom,
! [A: pname > nat,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_nat @ ( image_pname_nat @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_pigeonhole__infinite) ).
thf(1875,plain,
! [A: pname > nat,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_nat @ ( image_pname_nat @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(142,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_termination__basic__simps_I5_J) ).
thf(1100,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(336,axiom,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_all__not__in__conv) ).
thf(1847,plain,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_add__le__mono) ).
thf(817,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(586,axiom,
! [A: nat > x_a,B: x_a > $o,C: nat > $o] :
( ! [D: nat] :
( ( member_nat @ D @ C )
=> ( member_a @ ( A @ D ) @ B ) )
=> ( ord_less_eq_a_o @ ( image_nat_a @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_image__subsetI) ).
thf(2691,plain,
! [A: nat > x_a,B: x_a > $o,C: nat > $o] :
( ! [D: nat] :
( ( member_nat @ D @ C )
=> ( member_a @ ( A @ D ) @ B ) )
=> ( ord_less_eq_a_o @ ( image_nat_a @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(435,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_order__eq__refl) ).
thf(2169,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(138,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_Zero__neq__Suc) ).
thf(1087,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(105,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_diff__self__eq__0) ).
thf(969,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(492,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_empty__subsetI) ).
thf(2373,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(147,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_nat_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_doubleton__eq__iff) ).
thf(1115,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_nat_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(568,axiom,
! [A: x_a > $o,B: ( pname > $o ) > x_a,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_pname_o_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_finite__surj) ).
thf(2635,plain,
! [A: x_a > $o,B: ( pname > $o ) > x_a,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_pname_o_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(200,axiom,
! [A: pname,B: pname,C: pname,D: pname] :
( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
= ( insert_pname @ C @ ( insert_pname @ D @ bot_bot_pname_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_doubleton__eq__iff) ).
thf(1362,plain,
! [A: pname,B: pname,C: pname,D: pname] :
( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
= ( insert_pname @ C @ ( insert_pname @ D @ bot_bot_pname_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(375,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_mem__def) ).
thf(1963,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(242,axiom,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_o_pname @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_pname_o_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_finite__subset__image) ).
thf(1489,plain,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_o_pname @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_pname_o_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_nat__less__le) ).
thf(924,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(616,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > x_a,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_a_o_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_finite__surj) ).
thf(2794,plain,
! [A: x_a > $o,B: ( x_a > $o ) > x_a,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_a_o_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(302,axiom,
! [A: ( nat > $o ) > pname,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( finite_finite_pname @ ( image_nat_o_pname @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(1714,plain,
! [A: ( nat > $o ) > pname,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( finite_finite_pname @ ( image_nat_o_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(204,axiom,
! [A: nat > $o,B: nat] :
( ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( ( A = bot_bot_nat_o )
| ( A
= ( insert_nat @ B @ bot_bot_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_subset__singletonD) ).
thf(1373,plain,
! [A: nat > $o,B: nat] :
( ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( ( A = bot_bot_nat_o )
| ( A
= ( insert_nat @ B @ bot_bot_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(191,axiom,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_diff__Suc__1) ).
thf(1334,plain,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(545,axiom,
! [A: pname > $o,B: x_a > pname,C: x_a > $o] :
( ( ord_less_eq_pname_o @ A @ ( image_a_pname @ B @ C ) )
= ( ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ C )
& ( A
= ( image_a_pname @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_subset__image__iff) ).
thf(2540,plain,
! [A: pname > $o,B: x_a > pname,C: x_a > $o] :
( ( ord_less_eq_pname_o @ A @ ( image_a_pname @ B @ C ) )
= ( ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ C )
& ( A
= ( image_a_pname @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(611,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_set__mp) ).
thf(2777,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(129,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_add__leD1) ).
thf(1051,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(517,axiom,
! [A: $o] : ( ord_less_eq_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_order__refl) ).
thf(2456,plain,
! [A: $o] : ( ord_less_eq_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(389,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_le__funE) ).
thf(2007,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(358,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( insert_nat @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_insert__absorb) ).
thf(1911,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( insert_nat @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(613,axiom,
! [A: x_a,B: pname > x_a,C: pname > $o] :
( ( member_a @ A @ ( image_pname_a @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_imageE) ).
thf(2782,plain,
! [A: x_a,B: pname > x_a,C: pname > $o] :
( ( member_a @ A @ ( image_pname_a @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(145,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ( finite297249702name_o @ ( collect_pname_o @ B ) )
| ( finite297249702name_o @ ( collect_pname_o @ A ) ) )
=> ( finite297249702name_o
@ ( collect_pname_o
@ ^ [C: pname > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_finite__Collect__conjI) ).
thf(1109,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ( finite297249702name_o @ ( collect_pname_o @ B ) )
| ( finite297249702name_o @ ( collect_pname_o @ A ) ) )
=> ( finite297249702name_o
@ ( collect_pname_o
@ ^ [C: pname > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(521,axiom,
! [A: pname > pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_card__image__le) ).
thf(2469,plain,
! [A: pname > pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(221,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_le__diff__conv2) ).
thf(1418,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(451,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ A ) @ ( finite_card_a_o @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_card__mono) ).
thf(2236,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ A ) @ ( finite_card_a_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(550,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ ( insert_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_card__insert__le) ).
thf(2555,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ ( insert_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(49,axiom,
! [A: nat > $o] :
( ( ? [B: nat] : ( member_nat @ B @ A ) )
= ( A != bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_ex__in__conv) ).
thf(806,plain,
! [A: nat > $o] :
( ( ? [B: nat] : ( member_nat @ B @ A ) )
= ( A != bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(480,axiom,
! [A: x_a > nat,B: nat > $o,C: x_a > $o] :
( ! [D: x_a] :
( ( member_a @ D @ C )
=> ( member_nat @ ( A @ D ) @ B ) )
=> ( ord_less_eq_nat_o @ ( image_a_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_image__subsetI) ).
thf(2335,plain,
! [A: x_a > nat,B: nat > $o,C: x_a > $o] :
( ! [D: x_a] :
( ( member_a @ D @ C )
=> ( member_nat @ ( A @ D ) @ B ) )
=> ( ord_less_eq_nat_o @ ( image_a_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(104,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_less__SucE) ).
thf(966,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(164,axiom,
! [A: ( x_a > $o ) > x_a,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_card__image__le) ).
thf(1183,plain,
! [A: ( x_a > $o ) > x_a,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(413,axiom,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_equals0D) ).
thf(2073,plain,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(535,axiom,
! [A: nat > x_a,B: nat > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_nat_a @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_a @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_finite__subset__image) ).
thf(2508,plain,
! [A: nat > x_a,B: nat > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_nat_a @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_a @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(15,axiom,
! [A: pname,B: pname] :
( ~ ( fequal_pname @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
thf(687,plain,
! [A: pname,B: pname] :
( ~ ( fequal_pname @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(490,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Suc__diff__le) ).
thf(2367,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(463,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_linorder__le__cases) ).
thf(2281,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(71,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_trans__less__add2) ).
thf(866,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(213,axiom,
! [A: ( x_a > $o ) > $o,B: nat > x_a > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_a_o_o @ A @ ( image_nat_a_o @ B @ C ) )
=> ( finite_finite_a_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_finite__surj) ).
thf(1394,plain,
! [A: ( x_a > $o ) > $o,B: nat > x_a > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_a_o_o @ A @ ( image_nat_a_o @ B @ C ) )
=> ( finite_finite_a_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(426,axiom,
! [A: x_a > x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_card__image__le) ).
thf(2137,plain,
! [A: x_a > x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(5,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ B )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C = A )
| ( member_a_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_insert__compr) ).
thf(660,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ B )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C = A )
| ( member_a_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(387,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_xt1_I5_J) ).
thf(2002,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(225,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_diff__commute) ).
thf(1433,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(230,axiom,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
=> ( finite297249702name_o
@ ( collect_pname_o
@ ^ [B: pname > $o] : ( ord_less_eq_pname_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
thf(1447,plain,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
=> ( finite297249702name_o
@ ( collect_pname_o
@ ^ [B: pname > $o] : ( ord_less_eq_pname_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(527,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ! [C: x_a] :
( ( member_a @ C @ B )
=> ( member_a @ C @ A ) )
=> ( ord_less_eq_a_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_subsetI) ).
thf(2483,plain,
! [A: x_a > $o,B: x_a > $o] :
( ! [C: x_a] :
( ( member_a @ C @ B )
=> ( member_a @ C @ A ) )
=> ( ord_less_eq_a_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(101,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_diff__add__0) ).
thf(956,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(272,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_diff__is__0__eq_H) ).
thf(1622,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(509,axiom,
! [A: pname > $o,B: pname] :
( ( ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_pname @ B @ bot_bot_pname_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_Collect__conv__if) ).
thf(2424,plain,
! [A: pname > $o,B: pname] :
( ( ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_pname @ B @ bot_bot_pname_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(195,axiom,
! [A: nat > $o,B: x_a,C: nat > x_a,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member_a @ B @ ( image_nat_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_image__eqI) ).
thf(1345,plain,
! [A: nat > $o,B: x_a,C: nat > x_a,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member_a @ B @ ( image_nat_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(112,axiom,
! [A: nat] :
( ( collect_nat
@ ^ [B: nat] : ( B = A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_singleton__conv) ).
thf(988,plain,
! [A: nat] :
( ( collect_nat
@ ^ [B: nat] : ( B = A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(618,axiom,
! [A: x_a,B: pname > x_a,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_a @ A @ ( image_pname_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_rev__image__eqI) ).
thf(2799,plain,
! [A: x_a,B: pname > x_a,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_a @ A @ ( image_pname_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(571,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_xt1_I4_J) ).
thf(2639,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(295,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ ( insert_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_card__insert__le) ).
thf(1696,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ ( insert_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(560,axiom,
! [A: ( pname > $o ) > x_a,B: ( pname > $o ) > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_pname_o_a @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_pname_o_a @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_finite__subset__image) ).
thf(2586,plain,
! [A: ( pname > $o ) > x_a,B: ( pname > $o ) > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_pname_o_a @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_pname_o_a @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(96,axiom,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
= ( A = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_bot__unique) ).
thf(942,plain,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
= ( A = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(12,axiom,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_less__mono__imp__le__mono) ).
thf(678,plain,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_less__imp__le__nat) ).
thf(793,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(238,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_Suc__leI) ).
thf(1470,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(598,axiom,
! [A: x_a > $o,B: x_a] :
( ( ( A @ B )
=> ( ( collect_a
@ ^ [C: x_a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_a @ B @ bot_bot_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_a
@ ^ [C: x_a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_Collect__conv__if2) ).
thf(2737,plain,
! [A: x_a > $o,B: x_a] :
( ( ( A @ B )
=> ( ( collect_a
@ ^ [C: x_a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_a @ B @ bot_bot_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_a
@ ^ [C: x_a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(449,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_insertI2) ).
thf(2232,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(386,axiom,
( bot_bot_a_o
= ( collect_a
@ ^ [A: x_a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_empty__def) ).
thf(2000,plain,
( bot_bot_a_o
= ( collect_a
@ ^ [A: x_a] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(168,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_equalityE) ).
thf(1199,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(489,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_emptyE) ).
thf(2364,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(416,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le__trans) ).
thf(2083,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(134,axiom,
! [A: ( nat > $o ) > nat,B: ( nat > $o ) > $o] :
( ~ ( finite_finite_nat_o @ B )
=> ( ( finite_finite_nat @ ( image_nat_o_nat @ A @ B ) )
=> ? [C: nat > $o] :
( ( member_nat_o @ C @ B )
& ~ ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [D: nat > $o] :
( ( member_nat_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_pigeonhole__infinite) ).
thf(1067,plain,
! [A: ( nat > $o ) > nat,B: ( nat > $o ) > $o] :
( ~ ( finite_finite_nat_o @ B )
=> ( ( finite_finite_nat @ ( image_nat_o_nat @ A @ B ) )
=> ? [C: nat > $o] :
( ( member_nat_o @ C @ B )
& ~ ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [D: nat > $o] :
( ( member_nat_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(178,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_subset__refl) ).
thf(1274,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(139,axiom,
! [A: nat > $o] :
( ( bot_bot_nat_o
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_empty__Collect__eq) ).
thf(1091,plain,
! [A: nat > $o] :
( ( bot_bot_nat_o
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(176,axiom,
! [A: $o,B: $o,C: $o] :
( ( ord_less_eq_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_xt1_I4_J) ).
thf(1255,plain,
! [A: $o,B: $o,C: $o] :
( ( ord_less_eq_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(150,axiom,
! [A: ( pname > $o ) > nat,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_o_nat @ A @ B ) ) @ ( finite_card_pname_o @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_card__image__le) ).
thf(1123,plain,
! [A: ( pname > $o ) > nat,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_o_nat @ A @ B ) ) @ ( finite_card_pname_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(327,axiom,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_pname @ ( image_a_o_pname @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(1824,plain,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_pname @ ( image_a_o_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(541,axiom,
finite_finite_pname @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2528,plain,
finite_finite_pname @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(499,axiom,
! [A: nat > $o,B: pname,C: nat > pname,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member_pname @ B @ ( image_nat_pname @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_image__eqI) ).
thf(2396,plain,
! [A: nat > $o,B: pname,C: nat > pname,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member_pname @ B @ ( image_nat_pname @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(348,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_subset__trans) ).
thf(1883,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(354,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_le__Suc__eq) ).
thf(1900,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_add__less__mono1) ).
thf(910,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(56,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_add__less__mono) ).
thf(825,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(194,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_le__SucI) ).
thf(1343,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(620,axiom,
! [A: x_a,B: x_a] :
( ( ( insert_a @ A @ bot_bot_a_o )
= ( insert_a @ B @ bot_bot_a_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_singleton__inject) ).
thf(2805,plain,
! [A: x_a,B: x_a] :
( ( ( insert_a @ A @ bot_bot_a_o )
= ( insert_a @ B @ bot_bot_a_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(454,axiom,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
= ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_subset__empty) ).
thf(2249,plain,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
= ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(121,axiom,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_Collect__conv__if) ).
thf(1021,plain,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(126,axiom,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [C: nat > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat_o @ ( collect_nat_o @ A ) )
& ( finite_finite_nat_o @ ( collect_nat_o @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_finite__Collect__disjI) ).
thf(1042,plain,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [C: nat > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat_o @ ( collect_nat_o @ A ) )
& ( finite_finite_nat_o @ ( collect_nat_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(100,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_nat_Osimps_I3_J) ).
thf(952,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(287,axiom,
! [A: x_a > pname,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_card__image__le) ).
thf(1676,plain,
! [A: x_a > pname,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(425,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( ( finite_finite_a_o @ ( collect_a_o @ B ) )
| ( finite_finite_a_o @ ( collect_a_o @ A ) ) )
=> ( finite_finite_a_o
@ ( collect_a_o
@ ^ [C: x_a > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_finite__Collect__conjI) ).
thf(2133,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( ( finite_finite_a_o @ ( collect_a_o @ B ) )
| ( finite_finite_a_o @ ( collect_a_o @ A ) ) )
=> ( finite_finite_a_o
@ ( collect_a_o
@ ^ [C: x_a > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(398,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
= ( ( ord_less_eq_nat_o @ A @ B )
& ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_set__eq__subset) ).
thf(2032,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
= ( ( ord_less_eq_nat_o @ A @ B )
& ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_less__imp__diff__less) ).
thf(815,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(88,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ? [C: nat] :
( B
= ( suc @ ( plus_plus_nat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_less__iff__Suc__add) ).
thf(916,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ? [C: nat] :
( B
= ( suc @ ( plus_plus_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(524,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_order__trans) ).
thf(2477,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(162,axiom,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_nat @ ( image_a_o_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(1178,plain,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_nat @ ( image_a_o_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(372,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_equalityD2) ).
thf(1951,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(7,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ B ) @ ( finite_card_a_o @ ( insert_a_o @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_card__insert__le) ).
thf(665,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ B ) @ ( finite_card_a_o @ ( insert_a_o @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(58,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_Suc__less__SucD) ).
thf(830,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(159,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Suc__inject) ).
thf(1159,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(483,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( C = A )
| ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_insert__compr) ).
thf(2345,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( C = A )
| ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(13,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_add__leD2) ).
thf(682,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_le__iff__add) ).
thf(710,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(608,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_finite__subset) ).
thf(2769,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_Suc__lessI) ).
thf(1106,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(520,axiom,
! [A: nat,B: pname > nat,C: pname > $o] :
( ( member_nat @ A @ ( image_pname_nat @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_imageE) ).
thf(2464,plain,
! [A: nat,B: pname > nat,C: pname > $o] :
( ( member_nat @ A @ ( image_pname_nat @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(64,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o
@ ( collect_pname_o
@ ^ [C: pname > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite297249702name_o @ ( collect_pname_o @ A ) )
& ( finite297249702name_o @ ( collect_pname_o @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_finite__Collect__disjI) ).
thf(847,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o
@ ( collect_pname_o
@ ^ [C: pname > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite297249702name_o @ ( collect_pname_o @ A ) )
& ( finite297249702name_o @ ( collect_pname_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(123,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_Suc__lessE) ).
thf(1032,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(332,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_finite__subset) ).
thf(1837,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(201,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( finite_finite_a_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_rev__finite__subset) ).
thf(1365,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( finite_finite_a_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(581,axiom,
! [A: x_a > x_a,B: x_a > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_a_a @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_a @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_finite__subset__image) ).
thf(2670,plain,
! [A: x_a > x_a,B: x_a > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_a_a @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_a @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(66,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_nat__add__left__cancel__less) ).
thf(852,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(578,axiom,
! [A: x_a,B: x_a > $o] : ( member_a @ A @ ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_insertI1) ).
thf(2663,plain,
! [A: x_a,B: x_a > $o] : ( member_a @ A @ ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(479,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( finite_card_nat @ ( insert_nat @ A @ B ) )
= ( suc @ ( finite_card_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_card__insert__disjoint) ).
thf(2332,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( finite_card_nat @ ( insert_nat @ A @ B ) )
= ( suc @ ( finite_card_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(623,axiom,
! [A: x_a > $o,B: x_a > x_a,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_a_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_finite__surj) ).
thf(2820,plain,
! [A: x_a > $o,B: x_a > x_a,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_a_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(318,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( ord_less_eq_nat_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_subset__insert) ).
thf(1787,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( ord_less_eq_nat_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(438,axiom,
! [A: nat > $o,B: nat] : ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_subset__insertI) ).
thf(2181,plain,
! [A: nat > $o,B: nat] : ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(170,axiom,
! [A: $o,B: $o,C: $o] :
( ( ord_less_eq_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_ord__le__eq__trans) ).
thf(1210,plain,
! [A: $o,B: $o,C: $o] :
( ( ord_less_eq_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(280,axiom,
! [A: nat > $o,B: x_a > nat,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_a_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_finite__surj) ).
thf(1656,plain,
! [A: nat > $o,B: x_a > nat,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_a_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(135,axiom,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_emptyE) ).
thf(1079,plain,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(443,axiom,
! [A: nat,B: nat] :
( ( A = B )
= ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_order__eq__iff) ).
thf(2213,plain,
! [A: nat,B: nat] :
( ( A = B )
= ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(547,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_le__funE) ).
thf(2547,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(152,axiom,
! [A: pname > pname,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( image_pname_pname @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_pigeonhole__infinite) ).
thf(1128,plain,
! [A: pname > pname,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( image_pname_pname @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(530,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_subset__refl) ).
thf(2492,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(308,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ ( insert_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite_OinsertI) ).
thf(1740,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ ( insert_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(62,axiom,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_zero__less__Suc) ).
thf(842,plain,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(32,axiom,
( bot_bot_nat_o
= ( collect_nat
@ ^ [A: nat] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_empty__def) ).
thf(742,plain,
( bot_bot_nat_o
= ( collect_nat
@ ^ [A: nat] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(629,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_card__seteq) ).
thf(2840,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(584,axiom,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) )
= ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_insert__image) ).
thf(2685,plain,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) )
= ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(644,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_insert__compr__raw) ).
thf(2895,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(559,axiom,
! [A: x_a,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_pname_a
@ ^ [C: pname] : A
@ B )
= bot_bot_a_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_pname_a
@ ^ [C: pname] : A
@ B )
= ( insert_a @ A @ bot_bot_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_image__constant__conv) ).
thf(2577,plain,
! [A: x_a,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_pname_a
@ ^ [C: pname] : A
@ B )
= bot_bot_a_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_pname_a
@ ^ [C: pname] : A
@ B )
= ( insert_a @ A @ bot_bot_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(27,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_One__nat__def) ).
thf(725,plain,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(109,axiom,
! [A: nat,B: nat] : ( ord_less_nat @ A @ ( suc @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_less__add__Suc1) ).
thf(980,plain,
! [A: nat,B: nat] : ( ord_less_nat @ A @ ( suc @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(223,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ( member_nat @ A @ B )
=> ( ( finite_card_nat @ ( insert_nat @ A @ B ) )
= ( finite_card_nat @ B ) ) )
& ( ~ ( member_nat @ A @ B )
=> ( ( finite_card_nat @ ( insert_nat @ A @ B ) )
= ( suc @ ( finite_card_nat @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_card__insert__if) ).
thf(1425,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ( member_nat @ A @ B )
=> ( ( finite_card_nat @ ( insert_nat @ A @ B ) )
= ( finite_card_nat @ B ) ) )
& ( ~ ( member_nat @ A @ B )
=> ( ( finite_card_nat @ ( insert_nat @ A @ B ) )
= ( suc @ ( finite_card_nat @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(286,axiom,
! [A: nat > pname > $o,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite297249702name_o @ ( image_nat_pname_o @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_pigeonhole__infinite) ).
thf(1672,plain,
! [A: nat > pname > $o,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite297249702name_o @ ( image_nat_pname_o @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(304,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_order__eq__iff) ).
thf(1719,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(68,axiom,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_empty__iff) ).
thf(857,plain,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(199,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_order__trans) ).
thf(1360,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(367,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_ord__eq__le__trans) ).
thf(1936,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_less__not__refl2) ).
thf(697,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(173,axiom,
! [A: $o,B: $o,C: $o] :
( ( C = B )
=> ( ( ord_less_eq_o @ A @ B )
=> ( ord_less_eq_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_xt1_I3_J) ).
thf(1234,plain,
! [A: $o,B: $o,C: $o] :
( ( C = B )
=> ( ( ord_less_eq_o @ A @ B )
=> ( ord_less_eq_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(592,axiom,
! [A: x_a > x_a > $o,B: x_a > $o,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_a_o_o @ C @ ( image_a_a_o @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_a_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_finite__subset__image) ).
thf(2709,plain,
! [A: x_a > x_a > $o,B: x_a > $o,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_a_o_o @ C @ ( image_a_a_o @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_a_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(171,axiom,
! [A: ( x_a > $o ) > $o] :
( ( collect_a_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Collect__def) ).
thf(1227,plain,
! [A: ( x_a > $o ) > $o] :
( ( collect_a_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(570,axiom,
ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(2638,plain,
ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(148,axiom,
! [A: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_bot__least) ).
thf(1118,plain,
! [A: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(290,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ ( insert_pname @ A @ B ) )
= ( finite_finite_pname @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_finite__insert) ).
thf(1683,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ ( insert_pname @ A @ B ) )
= ( finite_finite_pname @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_nat__add__commute) ).
thf(884,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(369,axiom,
! [A: x_a,B: x_a] :
( ~ ( fequal_a @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).
thf(1942,plain,
! [A: x_a,B: x_a] :
( ~ ( fequal_a @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(476,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_diff__le__mono2) ).
thf(2323,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(184,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
= ( ! [C: nat] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_le__fun__def) ).
thf(1292,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
= ( ! [C: nat] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(553,axiom,
! [A: x_a] :
( ( collect_a
@ ^ [B: x_a] : ( B = A ) )
= ( insert_a @ A @ bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_singleton__conv) ).
thf(2561,plain,
! [A: x_a] :
( ( collect_a
@ ^ [B: x_a] : ( B = A ) )
= ( insert_a @ A @ bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(473,axiom,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_a_o_pname @ A @ B ) )
=> ? [D: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ D @ B )
& ( finite_finite_a_o @ D )
& ( C
= ( image_a_o_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_finite__subset__image) ).
thf(2312,plain,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_a_o_pname @ A @ B ) )
=> ? [D: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ D @ B )
& ( finite_finite_a_o @ D )
& ( C
= ( image_a_o_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(263,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ! [D: nat] : ( ord_less_eq_nat_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat_o @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_lift__Suc__mono__le) ).
thf(1584,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ! [D: nat] : ( ord_less_eq_nat_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat_o @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(310,axiom,
! [A: nat,B: x_a > nat,C: x_a,D: x_a > $o] :
( ( member_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_a_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_rev__image__eqI) ).
thf(1744,plain,
! [A: nat,B: x_a > nat,C: x_a,D: x_a > $o] :
( ( member_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_a_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(136,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_minus__nat_Odiff__0) ).
thf(1082,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(395,axiom,
! [A: pname] :
( ( collect_pname @ ( fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_singleton__conv2) ).
thf(2023,plain,
! [A: pname] :
( ( collect_pname @ ( fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(83,axiom,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_finite__Collect__less__nat) ).
thf(901,plain,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(507,axiom,
! [A: x_a > $o] :
( ( ? [B: x_a] : ( member_a @ B @ A ) )
= ( A != bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_ex__in__conv) ).
thf(2419,plain,
! [A: x_a > $o] :
( ( ? [B: x_a] : ( member_a @ B @ A ) )
= ( A != bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(453,axiom,
! [A: $o,B: $o] :
( ( B = A )
=> ( ord_less_eq_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_order__eq__refl) ).
thf(2240,plain,
! [A: $o,B: $o] :
( ( B = A )
=> ( ord_less_eq_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(334,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_le__less__Suc__eq) ).
thf(1842,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(400,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_xt1_I6_J) ).
thf(2038,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(229,axiom,
finite_finite_a @ bot_bot_a_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_finite_OemptyI) ).
thf(1446,plain,
finite_finite_a @ bot_bot_a_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_diff__diff__cancel) ).
thf(1207,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(417,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_insert__absorb2) ).
thf(2085,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(573,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( insert_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_insert__commute) ).
thf(2649,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( insert_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(125,axiom,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
= ( A = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_subset__empty) ).
thf(1039,plain,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
= ( A = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(315,axiom,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
=> ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_le__bot) ).
thf(1776,plain,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
=> ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(111,axiom,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_nat_o )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Collect__empty__eq) ).
thf(985,plain,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_nat_o )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(20,axiom,
! [A: ( nat > $o ) > $o] :
( ( collect_nat_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_Collect__def) ).
thf(701,plain,
! [A: ( nat > $o ) > $o] :
( ( collect_nat_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(241,axiom,
! [A: $o,B: $o] :
( ( B = A )
= ( ( ord_less_eq_o @ B @ A )
& ( ord_less_eq_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_order__eq__iff) ).
thf(1478,plain,
! [A: $o,B: $o] :
( ( B = A )
= ( ( ord_less_eq_o @ B @ A )
& ( ord_less_eq_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(186,axiom,
! [A: x_a] :
~ ( member_a @ A @ bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_emptyE) ).
thf(1297,plain,
! [A: x_a] :
~ ( member_a @ A @ bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(470,axiom,
! [A: nat,B: nat > $o] :
( ! [C: nat] :
( ( member_nat @ C @ B )
=> ( ord_less_nat @ C @ A ) )
=> ( finite_finite_nat @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_bounded__nat__set__is__finite) ).
thf(2304,plain,
! [A: nat,B: nat > $o] :
( ! [C: nat] :
( ( member_nat @ C @ B )
=> ( ord_less_nat @ C @ A ) )
=> ( finite_finite_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(496,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_order__antisym__conv) ).
thf(2387,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(3,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ ( collect_a_o @ B ) )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_insert__Collect) ).
thf(654,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ ( collect_a_o @ B ) )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(534,axiom,
! [A: x_a,B: x_a > $o,C: x_a] :
( ( insert_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_insert__code) ).
thf(2505,plain,
! [A: x_a,B: x_a > $o,C: x_a] :
( ( insert_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(532,axiom,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_imageI) ).
thf(2497,plain,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(381,axiom,
! [A: pname > $o,B: nat > pname,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_nat_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_finite__surj) ).
thf(1984,plain,
! [A: pname > $o,B: nat > pname,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_nat_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(338,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_less__eq__Suc__le) ).
thf(1852,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(637,axiom,
! [A: x_a > $o] :
( ( ord_less_eq_a_o @ A @ bot_bot_a_o )
= ( A = bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_subset__empty) ).
thf(2862,plain,
! [A: x_a > $o] :
( ( ord_less_eq_a_o @ A @ bot_bot_a_o )
= ( A = bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(233,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_order__eq__refl) ).
thf(1456,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(208,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_order__refl) ).
thf(1382,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(528,axiom,
! [A: x_a > $o,B: pname > x_a,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_pname_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_finite__surj) ).
thf(2487,plain,
! [A: x_a > $o,B: pname > x_a,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_pname_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(562,axiom,
! [A: ( x_a > $o ) > $o,B: x_a > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ B )
=> ( ( A @ bot_bot_a_o )
=> ( ! [D: x_a,E: x_a > $o] :
( ( finite_finite_a @ E )
=> ( ( member_a @ D @ B )
=> ( ~ ( member_a @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_a @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_finite__subset__induct) ).
thf(2598,plain,
! [A: ( x_a > $o ) > $o,B: x_a > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ B )
=> ( ( A @ bot_bot_a_o )
=> ( ! [D: x_a,E: x_a > $o] :
( ( finite_finite_a @ E )
=> ( ( member_a @ D @ B )
=> ( ~ ( member_a @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_a @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(255,axiom,
! [A: $o,B: $o] :
( ( ord_less_eq_o @ A @ B )
=> ( ( ord_less_eq_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_xt1_I5_J) ).
thf(1552,plain,
! [A: $o,B: $o] :
( ( ord_less_eq_o @ A @ B )
=> ( ( ord_less_eq_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(633,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( member_a @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_insertI2) ).
thf(2851,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( member_a @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(406,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_xt1_I3_J) ).
thf(2052,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(588,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_order__eq__iff) ).
thf(2697,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(379,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_rev__finite__subset) ).
thf(1979,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(39,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_less__not__refl) ).
thf(779,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(274,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_le__SucE) ).
thf(1627,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(491,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( nat_case_o @ $false @ ( ord_less_eq_nat @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_less__eq__nat_Osimps_I2_J) ).
thf(2370,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( nat_case_o @ $false @ ( ord_less_eq_nat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(316,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( finite_card_pname @ B ) ) )
& ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_card__insert__if) ).
thf(1779,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( finite_card_pname @ B ) ) )
& ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(441,axiom,
! [A: pname > $o,B: ( x_a > $o ) > pname,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_a_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_finite__surj) ).
thf(2208,plain,
! [A: pname > $o,B: ( x_a > $o ) > pname,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_a_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(90,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_nat__add__left__cancel__le) ).
thf(921,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(301,axiom,
! [A: ( pname > $o ) > $o] :
( ( finite297249702name_o @ A )
=> ( finite1066544169me_o_o
@ ( collect_pname_o_o
@ ^ [B: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).
thf(1712,plain,
! [A: ( pname > $o ) > $o] :
( ( finite297249702name_o @ A )
=> ( finite1066544169me_o_o
@ ( collect_pname_o_o
@ ^ [B: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(236,axiom,
! [A: nat,B: nat > $o] : ( member_nat @ A @ ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_insertI1) ).
thf(1466,plain,
! [A: nat,B: nat > $o] : ( member_nat @ A @ ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_termination__basic__simps_I2_J) ).
thf(674,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(161,axiom,
! [A: $o,B: $o] :
( ( ord_less_eq_o @ A @ B )
=> ( ( ord_less_eq_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_order__antisym) ).
thf(1167,plain,
! [A: $o,B: $o] :
( ( ord_less_eq_o @ A @ B )
=> ( ( ord_less_eq_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(542,axiom,
! [A: x_a > nat,B: x_a,C: x_a > $o] :
( ( image_a_nat @ A @ ( insert_a @ B @ C ) )
= ( insert_nat @ ( A @ B ) @ ( image_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_image__insert) ).
thf(2529,plain,
! [A: x_a > nat,B: x_a,C: x_a > $o] :
( ( image_a_nat @ A @ ( insert_a @ B @ C ) )
= ( insert_nat @ ( A @ B ) @ ( image_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(601,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_order__antisym__conv) ).
thf(2749,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(340,axiom,
! [A: pname > x_a > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a_o @ ( image_pname_a_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__imageI) ).
thf(1857,plain,
! [A: pname > x_a > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a_o @ ( image_pname_a_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(256,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B )
= ( plus_plus_nat @ ( minus_minus_nat @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_diff__add__assoc2) ).
thf(1563,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B )
= ( plus_plus_nat @ ( minus_minus_nat @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(4,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ B )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C = A )
| ( member_a_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_insert__compr__raw) ).
thf(657,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ B )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C = A )
| ( member_a_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(356,axiom,
! [A: ( nat > $o ) > $o,B: nat > nat > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o_o @ A @ ( image_nat_nat_o @ B @ C ) )
=> ( finite_finite_nat_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_finite__surj) ).
thf(1906,plain,
! [A: ( nat > $o ) > $o,B: nat > nat > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o_o @ A @ ( image_nat_nat_o @ B @ C ) )
=> ( finite_finite_nat_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(596,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( finite_card_a @ B ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_card__insert__if) ).
thf(2729,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( finite_card_a @ B ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(244,axiom,
! [A: ( pname > $o ) > nat,B: ( pname > $o ) > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_pname_o_nat @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_pname_o_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_finite__subset__image) ).
thf(1510,plain,
! [A: ( pname > $o ) > nat,B: ( pname > $o ) > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_pname_o_nat @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_pname_o_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(174,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_le__funD) ).
thf(1251,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(296,axiom,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
= ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_bot__unique) ).
thf(1698,plain,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
= ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(397,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_equalityD1) ).
thf(2028,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(539,axiom,
! [A: x_a > $o,B: ( nat > $o ) > x_a,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_nat_o_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_finite__surj) ).
thf(2524,plain,
! [A: x_a > $o,B: ( nat > $o ) > x_a,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_nat_o_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(30,axiom,
! [A: ( nat > $o ) > nat,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_o_nat @ A @ B ) ) @ ( finite_card_nat_o @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_card__image__le) ).
thf(733,plain,
! [A: ( nat > $o ) > nat,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_o_nat @ A @ B ) ) @ ( finite_card_nat_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(154,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_le__diff__iff) ).
thf(1146,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(312,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_in__mono) ).
thf(1754,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(646,axiom,
! [A: x_a > $o] :
( ( finite_finite_a @ A )
=> ( finite_finite_a_o
@ ( collect_a_o
@ ^ [B: x_a > $o] : ( ord_less_eq_a_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
thf(2904,plain,
! [A: x_a > $o] :
( ( finite_finite_a @ A )
=> ( finite_finite_a_o
@ ( collect_a_o
@ ^ [B: x_a > $o] : ( ord_less_eq_a_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(289,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_order__antisym) ).
thf(1680,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(157,axiom,
! [A: x_a > nat,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( insert_nat @ ( A @ B ) @ ( image_a_nat @ A @ C ) )
= ( image_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_insert__image) ).
thf(1154,plain,
! [A: x_a > nat,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( insert_nat @ ( A @ B ) @ ( image_a_nat @ A @ C ) )
= ( image_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(54,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( collect_nat @ B ) )
= ( collect_nat
@ ^ [C: nat] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_insert__Collect) ).
thf(819,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( collect_nat @ B ) )
= ( collect_nat
@ ^ [C: nat] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(107,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ~ ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( suc @ ( finite_card_a_o @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_card__insert__disjoint) ).
thf(975,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ~ ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( suc @ ( finite_card_a_o @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(615,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_set__eq__subset) ).
thf(2791,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(151,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_nat__add__left__commute) ).
thf(1125,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(529,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_card__insert__disjoint) ).
thf(2489,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(498,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ( ord_le1205211808me_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_pname_o @ B ) @ ( finite_card_pname_o @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_card__seteq) ).
thf(2393,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ( ord_le1205211808me_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_pname_o @ B ) @ ( finite_card_pname_o @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(365,axiom,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_pname_pname @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_image__subsetI) ).
thf(1929,plain,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_pname_pname @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(211,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
= ( ( A = B )
| ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_insert__iff) ).
thf(1388,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
= ( ( A = B )
| ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(75,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_less__zeroE) ).
thf(875,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(587,axiom,
! [A: pname,B: x_a > $o] :
( ( p @ ( insert_a @ ( mgt_call @ A ) @ B ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ A ) ) ) @ bot_bot_a_o ) )
=> ( p @ B @ ( insert_a @ ( mgt_call @ A ) @ bot_bot_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_assms_I2_J) ).
thf(2695,plain,
! [A: pname,B: x_a > $o] :
( ( p @ ( insert_a @ ( mgt_call @ A ) @ B ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ A ) ) ) @ bot_bot_a_o ) )
=> ( p @ B @ ( insert_a @ ( mgt_call @ A ) @ bot_bot_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(405,axiom,
! [A: pname > nat,B: nat > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_nat @ ( A @ D ) @ B ) )
=> ( ord_less_eq_nat_o @ ( image_pname_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_image__subsetI) ).
thf(2048,plain,
! [A: pname > nat,B: nat > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_nat @ ( A @ D ) @ B ) )
=> ( ord_less_eq_nat_o @ ( image_pname_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(636,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_insert__iff) ).
thf(2859,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(576,axiom,
! [A: nat > x_a,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_a_o @ ( image_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_image__mono) ).
thf(2657,plain,
! [A: nat > x_a,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_a_o @ ( image_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(632,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_a @ ( insert_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite_OinsertI) ).
thf(2849,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_a @ ( insert_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(392,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_le__add__diff) ).
thf(2016,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(536,axiom,
! [A: x_a] :
( ( collect_a @ ( fequal_a @ A ) )
= ( insert_a @ A @ bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_singleton__conv2) ).
thf(2514,plain,
! [A: x_a] :
( ( collect_a @ ( fequal_a @ A ) )
= ( insert_a @ A @ bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(321,axiom,
! [A: pname,B: pname] :
( ( member_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_singleton__iff) ).
thf(1795,plain,
! [A: pname,B: pname] :
( ( member_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(297,axiom,
! [A: nat > nat > $o,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_nat_o @ ( image_nat_nat_o @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_pigeonhole__infinite) ).
thf(1701,plain,
! [A: nat > nat > $o,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_nat_o @ ( image_nat_nat_o @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(299,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_order__antisym) ).
thf(1707,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( ( A
= ( suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( suc @ zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_add__is__1) ).
thf(787,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( ( A
= ( suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( suc @ zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(591,axiom,
! [A: nat > x_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( insert_a @ ( A @ B ) @ ( image_nat_a @ A @ C ) )
= ( image_nat_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_insert__image) ).
thf(2706,plain,
! [A: nat > x_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( insert_a @ ( A @ B ) @ ( image_nat_a @ A @ C ) )
= ( image_nat_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_lessE) ).
thf(704,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(643,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( B = C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_ord__eq__le__trans) ).
thf(2891,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( B = C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(471,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subsetD) ).
thf(2308,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(203,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_set__mp) ).
thf(1371,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(23,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_Zero__not__Suc) ).
thf(713,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(343,axiom,
! [A: x_a > pname,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_pname @ ( image_a_pname @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_pigeonhole__infinite) ).
thf(1865,plain,
! [A: x_a > pname,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_pname @ ( image_a_pname @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(353,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( collect_pname @ B ) )
= ( collect_pname
@ ^ [C: pname] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_insert__Collect) ).
thf(1897,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( collect_pname @ B ) )
= ( collect_pname
@ ^ [C: pname] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_termination__basic__simps_I1_J) ).
thf(919,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(551,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_rev__finite__subset) ).
thf(2557,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(235,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ( ord_le1205211808me_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname_o @ A ) @ ( finite_card_pname_o @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_card__mono) ).
thf(1464,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ( ord_le1205211808me_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname_o @ A ) @ ( finite_card_pname_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(523,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_a_o @ B ) @ ( finite_card_a_o @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_card__seteq) ).
thf(2474,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_a_o @ B ) @ ( finite_card_a_o @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(98,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_less__eq__nat_Osimps_I1_J) ).
thf(947,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(429,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ( finite_finite_a @ ( collect_a @ B ) )
| ( finite_finite_a @ ( collect_a @ A ) ) )
=> ( finite_finite_a
@ ( collect_a
@ ^ [C: x_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_finite__Collect__conjI) ).
thf(2148,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ( finite_finite_a @ ( collect_a @ B ) )
| ( finite_finite_a @ ( collect_a @ A ) ) )
=> ( finite_finite_a
@ ( collect_a
@ ^ [C: x_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(487,axiom,
! [A: nat,B: nat] :
( ( member_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_singleton__iff) ).
thf(2358,plain,
! [A: nat,B: nat] :
( ( member_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(198,axiom,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o] :
( ~ ( finite_finite_a_o @ B )
=> ( ( finite_finite_nat @ ( image_a_o_nat @ A @ B ) )
=> ? [C: x_a > $o] :
( ( member_a_o @ C @ B )
& ~ ( finite_finite_a_o
@ ( collect_a_o
@ ^ [D: x_a > $o] :
( ( member_a_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_pigeonhole__infinite) ).
thf(1356,plain,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o] :
( ~ ( finite_finite_a_o @ B )
=> ( ( finite_finite_nat @ ( image_a_o_nat @ A @ B ) )
=> ? [C: x_a > $o] :
( ( member_a_o @ C @ B )
& ~ ( finite_finite_a_o
@ ( collect_a_o
@ ^ [D: x_a > $o] :
( ( member_a_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(36,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ( ( ord_less_nat @ B @ C )
=> ( A @ C @ B ) )
=> ( ( ( B = C )
=> ( A @ C @ B ) )
=> ( ( ( ord_less_nat @ C @ B )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_nat__less__cases) ).
thf(764,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ( ( ord_less_nat @ B @ C )
=> ( A @ C @ B ) )
=> ( ( ( B = C )
=> ( A @ C @ B ) )
=> ( ( ( ord_less_nat @ C @ B )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(488,axiom,
! [A: x_a > $o] :
( ( bot_bot_a_o
= ( collect_a @ A ) )
= ( ! [B: x_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_empty__Collect__eq) ).
thf(2361,plain,
! [A: x_a > $o] :
( ( bot_bot_a_o
= ( collect_a @ A ) )
= ( ! [B: x_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(538,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ ( insert_a @ A @ B ) )
= ( finite_finite_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_finite__insert) ).
thf(2521,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ ( insert_a @ A @ B ) )
= ( finite_finite_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(583,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( ~ ( member_a @ B @ C )
=> ( B = A ) )
=> ( member_a @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_insertCI) ).
thf(2679,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( ~ ( member_a @ B @ C )
=> ( B = A ) )
=> ( member_a @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(544,axiom,
! [A: x_a > pname,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( image_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_image__mono) ).
thf(2538,plain,
! [A: x_a > pname,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( image_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_diff__diff__right) ).
thf(1282,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ A @ ( minus_minus_nat @ C @ B ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(448,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
=> ( ( A != B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_insertE) ).
thf(2229,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
=> ( ( A != B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(505,axiom,
! [A: pname > $o,B: pname > pname,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_pname_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_finite__surj) ).
thf(2415,plain,
! [A: pname > $o,B: pname > pname,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_pname_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(196,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_insert__not__empty) ).
thf(1349,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(270,axiom,
! [A: ( pname > $o ) > x_a,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_a @ A @ B ) ) @ ( finite_card_pname_o @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_card__image__le) ).
thf(1603,plain,
! [A: ( pname > $o ) > x_a,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_a @ A @ B ) ) @ ( finite_card_pname_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(252,axiom,
! [A: nat > x_a,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_a @ ( image_nat_a @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_pigeonhole__infinite) ).
thf(1542,plain,
! [A: nat > x_a,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_a @ ( image_nat_a @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(305,axiom,
! [A: nat > pname,B: nat > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_nat_pname @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_finite__subset__image) ).
thf(1722,plain,
! [A: nat > pname,B: nat > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_nat_pname @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(420,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_pname @ B ) @ ( finite_card_pname @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_card__seteq) ).
thf(2116,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_pname @ B ) @ ( finite_card_pname @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(323,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_rev__finite__subset) ).
thf(1801,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(635,axiom,
! [A: x_a > $o,B: nat > x_a,C: nat > $o] :
( ( ord_less_eq_a_o @ A @ ( image_nat_a @ B @ C ) )
= ( ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ C )
& ( A
= ( image_nat_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_subset__image__iff) ).
thf(2856,plain,
! [A: x_a > $o,B: nat > x_a,C: nat > $o] :
( ( ord_less_eq_a_o @ A @ ( image_nat_a @ B @ C ) )
= ( ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ C )
& ( A
= ( image_nat_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(293,axiom,
! [A: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ A )
=> ( finite1676163439at_o_o
@ ( collect_nat_o_o
@ ^ [B: ( nat > $o ) > $o] : ( ord_less_eq_nat_o_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
thf(1690,plain,
! [A: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ A )
=> ( finite1676163439at_o_o
@ ( collect_nat_o_o
@ ^ [B: ( nat > $o ) > $o] : ( ord_less_eq_nat_o_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(377,axiom,
! [A: ( nat > $o ) > x_a,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_a @ A @ B ) ) @ ( finite_card_nat_o @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_card__image__le) ).
thf(1969,plain,
! [A: ( nat > $o ) > x_a,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_a @ A @ B ) ) @ ( finite_card_nat_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(595,axiom,
! [A: x_a > $o,B: x_a] :
( ( ( A @ B )
=> ( ( collect_a
@ ^ [C: x_a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_a @ B @ bot_bot_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_a
@ ^ [C: x_a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_Collect__conv__if) ).
thf(2721,plain,
! [A: x_a > $o,B: x_a] :
( ( ( A @ B )
=> ( ( collect_a
@ ^ [C: x_a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_a @ B @ bot_bot_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_a
@ ^ [C: x_a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(421,axiom,
! [A: pname > $o,B: nat,C: pname > nat,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_nat @ B @ ( image_pname_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_image__eqI) ).
thf(2119,plain,
! [A: pname > $o,B: nat,C: pname > nat,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_nat @ B @ ( image_pname_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_not__less__eq) ).
thf(784,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(569,axiom,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2637,plain,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(508,axiom,
! [A: nat,B: nat,C: nat > pname > $o] :
( ! [D: nat] : ( ord_less_eq_pname_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_pname_o @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_lift__Suc__mono__le) ).
thf(2422,plain,
! [A: nat,B: nat,C: nat > pname > $o] :
( ! [D: nat] : ( ord_less_eq_pname_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_pname_o @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(260,axiom,
! [A: x_a > nat > $o,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_nat_o @ ( image_a_nat_o @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_pigeonhole__infinite) ).
thf(1574,plain,
! [A: x_a > nat > $o,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_nat_o @ ( image_a_nat_o @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ B @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_diffs0__imp__equal) ).
thf(1011,plain,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ B @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(610,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_order__antisym) ).
thf(2774,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(247,axiom,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_mem__def) ).
thf(1524,plain,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(647,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_order__refl) ).
thf(2906,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(128,axiom,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
=> ( A = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_le__bot) ).
thf(1048,plain,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
=> ( A = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(265,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_xt1_I4_J) ).
thf(1589,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(115,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ ( collect_nat @ B ) )
| ( finite_finite_nat @ ( collect_nat @ A ) ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_finite__Collect__conjI) ).
thf(996,plain,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ ( collect_nat @ B ) )
| ( finite_finite_nat @ ( collect_nat @ A ) ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(366,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_le__add__diff__inverse) ).
thf(1933,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(259,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_insert__commute) ).
thf(1571,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(205,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ A @ B )
=> ( ( finite_finite_a_o @ B )
=> ( finite_finite_a_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_finite__subset) ).
thf(1376,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ A @ B )
=> ( ( finite_finite_a_o @ B )
=> ( finite_finite_a_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(625,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_equalityD1) ).
thf(2824,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(275,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_Suc__le__eq) ).
thf(1630,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(457,axiom,
! [A: pname,B: nat > pname,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_pname @ A @ ( image_nat_pname @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_rev__image__eqI) ).
thf(2261,plain,
! [A: pname,B: nat > pname,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_pname @ A @ ( image_nat_pname @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(342,axiom,
! [A: nat,B: nat > $o,C: nat] :
( ( insert_nat @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_insert__code) ).
thf(1862,plain,
! [A: nat,B: nat > $o,C: nat] :
( ( insert_nat @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(503,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ A ) @ ( finite_card_pname @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_card__mono) ).
thf(2410,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ A ) @ ( finite_card_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(122,axiom,
! [A: nat] :
( ( finite_card_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_eq_nat @ B @ A ) ) )
= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_card__Collect__le__nat) ).
thf(1029,plain,
! [A: nat] :
( ( finite_card_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_eq_nat @ B @ A ) ) )
= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(155,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_insert__absorb2) ).
thf(1149,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(455,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ~ ( member_nat @ B @ A )
=> ( ( ( insert_nat @ B @ C )
= ( insert_nat @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_insert__ident) ).
thf(2252,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ~ ( member_nat @ B @ A )
=> ( ( ( insert_nat @ B @ C )
= ( insert_nat @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(519,axiom,
! [A: pname > nat,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_nat @ ( A @ B ) @ ( image_pname_nat @ A @ C ) )
= ( image_pname_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_insert__image) ).
thf(2461,plain,
! [A: pname > nat,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_nat @ ( A @ B ) @ ( image_pname_nat @ A @ C ) )
= ( image_pname_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(478,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ( minus_minus_nat @ C @ B )
= A )
= ( C
= ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_le__imp__diff__is__add) ).
thf(2329,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ( minus_minus_nat @ C @ B )
= A )
= ( C
= ( plus_plus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(649,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_insertE) ).
thf(2911,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(292,axiom,
! [A: nat > x_a,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_a @ ( image_nat_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__imageI) ).
thf(1688,plain,
! [A: nat > x_a,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_a @ ( image_nat_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_less__or__eq__imp__le) ).
thf(890,plain,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(284,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_pname @ ( collect_pname @ A ) )
& ( finite_finite_pname @ ( collect_pname @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_finite__Collect__disjI) ).
thf(1667,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_pname @ ( collect_pname @ A ) )
& ( finite_finite_pname @ ( collect_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(514,axiom,
! [A: nat > pname > $o,B: nat > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_nat_pname_o @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_pname_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_finite__subset__image) ).
thf(2446,plain,
! [A: nat > pname > $o,B: nat > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_nat_pname_o @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_pname_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(604,axiom,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( image_pname_a @ A @ ( insert_pname @ B @ C ) )
= ( insert_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_image__insert) ).
thf(2757,plain,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( image_pname_a @ A @ ( insert_pname @ B @ C ) )
= ( insert_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(234,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_ord__le__eq__trans) ).
thf(1460,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(466,axiom,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_a_o_nat @ A @ B ) )
=> ? [D: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ D @ B )
& ( finite_finite_a_o @ D )
& ( C
= ( image_a_o_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_finite__subset__image) ).
thf(2289,plain,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_a_o_nat @ A @ B ) )
=> ? [D: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ D @ B )
& ( finite_finite_a_o @ D )
& ( C
= ( image_a_o_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(87,axiom,
! [A: nat,B: nat > $o] :
( bot_bot_nat_o
!= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_empty__not__insert) ).
thf(912,plain,
! [A: nat,B: nat > $o] :
( bot_bot_nat_o
!= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(364,axiom,
! [A: nat] :
( ( ord_less_nat @ A )
= ( ord_less_eq_nat @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_less__eq__Suc__le__raw) ).
thf(1926,plain,
! [A: nat] :
( ( ord_less_nat @ A )
= ( ord_less_eq_nat @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(485,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_finite__subset) ).
thf(2350,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(102,axiom,
! [A: ( nat > $o ) > pname,B: ( nat > $o ) > $o] :
( ~ ( finite_finite_nat_o @ B )
=> ( ( finite_finite_pname @ ( image_nat_o_pname @ A @ B ) )
=> ? [C: nat > $o] :
( ( member_nat_o @ C @ B )
& ~ ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [D: nat > $o] :
( ( member_nat_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_pigeonhole__infinite) ).
thf(959,plain,
! [A: ( nat > $o ) > pname,B: ( nat > $o ) > $o] :
( ~ ( finite_finite_nat_o @ B )
=> ( ( finite_finite_pname @ ( image_nat_o_pname @ A @ B ) )
=> ? [C: nat > $o] :
( ( member_nat_o @ C @ B )
& ~ ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [D: nat > $o] :
( ( member_nat_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(57,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_diff__diff__left) ).
thf(827,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(427,axiom,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite_finite_pname @ ( image_pname_o_pname @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(2139,plain,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite_finite_pname @ ( image_pname_o_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(410,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_diff__is__0__eq) ).
thf(2064,plain,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(146,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_termination__basic__simps_I3_J) ).
thf(1113,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(567,axiom,
~ ( member_a @ ( mgt_call @ pn ) @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
thf(2633,plain,
~ ( member_a @ ( mgt_call @ pn ) @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(497,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_xt1_I5_J) ).
thf(2390,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(143,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_add__leE) ).
thf(1102,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(431,axiom,
! [A: pname > nat,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_pname_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_imageI) ).
thf(2156,plain,
! [A: pname > nat,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_pname_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(1,conjecture,
ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(653,plain,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(325,axiom,
! [A: $o,B: $o,C: $o] :
( ( ord_less_eq_o @ B @ C )
=> ( ( ord_less_eq_o @ A @ B )
=> ( ord_less_eq_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_xt1_I6_J) ).
thf(1805,plain,
! [A: $o,B: $o,C: $o] :
( ( ord_less_eq_o @ B @ C )
=> ( ( ord_less_eq_o @ A @ B )
=> ( ord_less_eq_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(639,axiom,
! [A: ( x_a > $o ) > x_a,B: ( x_a > $o ) > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_a_o_a @ A @ B ) )
=> ? [D: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ D @ B )
& ( finite_finite_a_o @ D )
& ( C
= ( image_a_o_a @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_finite__subset__image) ).
thf(2867,plain,
! [A: ( x_a > $o ) > x_a,B: ( x_a > $o ) > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_a_o_a @ A @ B ) )
=> ? [D: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ D @ B )
& ( finite_finite_a_o @ D )
& ( C
= ( image_a_o_a @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(214,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_set__eq__subset) ).
thf(1396,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(512,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ ( collect_pname @ B ) )
| ( finite_finite_pname @ ( collect_pname @ A ) ) )
=> ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_finite__Collect__conjI) ).
thf(2439,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ ( collect_pname @ B ) )
| ( finite_finite_pname @ ( collect_pname @ A ) ) )
=> ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(18,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_le__add1) ).
thf(695,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(526,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_bot__least) ).
thf(2481,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(563,axiom,
! [A: pname > x_a] :
( ( image_pname_a @ A @ bot_bot_pname_o )
= bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_image__empty) ).
thf(2620,plain,
! [A: pname > x_a] :
( ( image_pname_a @ A @ bot_bot_pname_o )
= bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(72,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_less__add__eq__less) ).
thf(868,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(561,axiom,
! [A: x_a > pname > $o,B: x_a > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_a_pname_o @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_pname_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_finite__subset__image) ).
thf(2592,plain,
! [A: x_a > pname > $o,B: x_a > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_a_pname_o @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_pname_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(116,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_less__irrefl__nat) ).
thf(1000,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(602,axiom,
! [A: pname > x_a,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_card__image__le) ).
thf(2752,plain,
! [A: pname > x_a,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(388,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ ( finite_card_nat @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_card__mono) ).
thf(2005,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ ( finite_card_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_nat__neq__iff) ).
thf(722,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(282,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_xt1_I5_J) ).
thf(1662,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(314,axiom,
! [A: ( nat > $o ) > nat,B: ( nat > $o ) > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_nat_o_nat @ A @ B ) )
=> ? [D: ( nat > $o ) > $o] :
( ( ord_less_eq_nat_o_o @ D @ B )
& ( finite_finite_nat_o @ D )
& ( C
= ( image_nat_o_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_finite__subset__image) ).
thf(1758,plain,
! [A: ( nat > $o ) > nat,B: ( nat > $o ) > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_nat_o_nat @ A @ B ) )
=> ? [D: ( nat > $o ) > $o] :
( ( ord_less_eq_nat_o_o @ D @ B )
& ( finite_finite_nat_o @ D )
& ( C
= ( image_nat_o_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(579,axiom,
( ( finite_card_a @ g )
= ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(2665,plain,
( ( finite_card_a @ g )
= ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(92,axiom,
! [A: pname,B: pname] :
( ( A != B )
| ( fequal_pname @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
thf(927,plain,
! [A: pname,B: pname] :
( ( A != B )
| ( fequal_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(450,axiom,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( ord_less_eq_nat_o_o @ A @ B )
=> ( ( finite_finite_nat_o @ B )
=> ( finite_finite_nat_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_finite__subset) ).
thf(2234,plain,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( ord_less_eq_nat_o_o @ A @ B )
=> ( ( finite_finite_nat_o @ B )
=> ( finite_finite_nat_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(51,axiom,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ one_one_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_Suc__eq__plus1__left) ).
thf(812,plain,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ one_one_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(384,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_xt1_I3_J) ).
thf(1990,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(239,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Suc__diff__diff) ).
thf(1472,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(650,axiom,
! [A: pname > x_a,B: pname > $o] :
( ( ( image_pname_a @ A @ B )
= bot_bot_a_o )
= ( B = bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_image__is__empty) ).
thf(2914,plain,
! [A: pname > x_a,B: pname > $o] :
( ( ( image_pname_a @ A @ B )
= bot_bot_a_o )
= ( B = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(622,axiom,
! [A: x_a,B: x_a > $o] :
( bot_bot_a_o
!= ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_empty__not__insert) ).
thf(2816,plain,
! [A: x_a,B: x_a > $o] :
( bot_bot_a_o
!= ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(45,axiom,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_card__image__le) ).
thf(795,plain,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(474,axiom,
! [A: nat,B: nat > nat] :
( ! [C: nat] : ( ord_less_eq_nat @ C @ ( B @ C ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] : ( ord_less_eq_nat @ ( B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_finite__less__ub) ).
thf(2318,plain,
! [A: nat,B: nat > nat] :
( ! [C: nat] : ( ord_less_eq_nat @ C @ ( B @ C ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] : ( ord_less_eq_nat @ ( B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(459,axiom,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_Collect__def) ).
thf(2271,plain,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(6,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_a_o @ ( insert_a_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite_OinsertI) ).
thf(663,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_a_o @ ( insert_a_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(574,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_subsetD) ).
thf(2652,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(522,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__antisym) ).
thf(2471,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(95,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_nat__add__left__cancel) ).
thf(939,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(193,axiom,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
= ( ? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_finite__nat__set__iff__bounded) ).
thf(1340,plain,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
= ( ? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(120,axiom,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_not__add__less1) ).
thf(1018,plain,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(554,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( insert_a @ A @ B ) )
= ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_insert__absorb2) ).
thf(2564,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( insert_a @ A @ B ) )
= ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(311,axiom,
! [A: nat > nat > $o,B: nat > $o,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_nat_o_o @ C @ ( image_nat_nat_o @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_nat_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_finite__subset__image) ).
thf(1748,plain,
! [A: nat > nat > $o,B: nat > $o,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_nat_o_o @ C @ ( image_nat_nat_o @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_nat_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(117,axiom,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_Collect__conv__if2) ).
thf(1003,plain,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(374,axiom,
! [A: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ A )
=> ( finite_finite_a_o_o
@ ( collect_a_o_o
@ ^ [B: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
thf(1961,plain,
! [A: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ A )
=> ( finite_finite_a_o_o
@ ( collect_a_o_o
@ ^ [B: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(493,axiom,
! [A: ( nat > $o ) > pname,B: ( nat > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_nat_o_pname @ A @ B ) )
=> ? [D: ( nat > $o ) > $o] :
( ( ord_less_eq_nat_o_o @ D @ B )
& ( finite_finite_nat_o @ D )
& ( C
= ( image_nat_o_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_finite__subset__image) ).
thf(2375,plain,
! [A: ( nat > $o ) > pname,B: ( nat > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_nat_o_pname @ A @ B ) )
=> ? [D: ( nat > $o ) > $o] :
( ( ord_less_eq_nat_o_o @ D @ B )
& ( finite_finite_nat_o @ D )
& ( C
= ( image_nat_o_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( ( insert_nat @ A @ bot_bot_nat_o )
= ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_singleton__inject) ).
thf(887,plain,
! [A: nat,B: nat] :
( ( ( insert_nat @ A @ bot_bot_nat_o )
= ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(257,axiom,
! [A: nat,B: nat] : ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_diff__less__Suc) ).
thf(1566,plain,
! [A: nat,B: nat] : ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(271,axiom,
! [A: $o,B: $o,C: $o] :
( ( C = B )
=> ( ( ord_less_eq_o @ B @ A )
=> ( ord_less_eq_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_ord__eq__le__trans) ).
thf(1605,plain,
! [A: $o,B: $o,C: $o] :
( ( C = B )
=> ( ( ord_less_eq_o @ B @ A )
=> ( ord_less_eq_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_Suc__less__eq) ).
thf(739,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(502,axiom,
! [A: pname] :
( ( collect_pname
@ ^ [B: pname] : ( B = A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_singleton__conv) ).
thf(2407,plain,
! [A: pname] :
( ( collect_pname
@ ^ [B: pname] : ( B = A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(555,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
!= bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_insert__not__empty) ).
thf(2567,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
!= bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(335,axiom,
! [A: pname > nat > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_nat_o @ ( image_pname_nat_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_finite__imageI) ).
thf(1845,plain,
! [A: pname > nat > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_nat_o @ ( image_pname_nat_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(322,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_order__antisym__conv) ).
thf(1798,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(468,axiom,
! [A: x_a > pname > $o,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite297249702name_o @ ( image_a_pname_o @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_pigeonhole__infinite) ).
thf(2298,plain,
! [A: x_a > pname > $o,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite297249702name_o @ ( image_a_pname_o @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(67,axiom,
! [A: nat > $o,B: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_finite__M__bounded__by__nat) ).
thf(855,plain,
! [A: nat > $o,B: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(593,axiom,
! [A: pname > x_a,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_a @ ( image_pname_a @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_pigeonhole__infinite) ).
thf(2715,plain,
! [A: pname > x_a,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_a @ ( image_pname_a @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(16,axiom,
finite_finite_nat @ bot_bot_nat_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_finite_OemptyI) ).
thf(690,plain,
finite_finite_nat @ bot_bot_nat_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(245,axiom,
! [A: ( nat > $o ) > nat,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( finite_finite_nat @ ( image_nat_o_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(1516,plain,
! [A: ( nat > $o ) > nat,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( finite_finite_nat @ ( image_nat_o_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(268,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_card__seteq) ).
thf(1598,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(172,axiom,
! [A: x_a > nat,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_nat @ ( image_a_nat @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_pigeonhole__infinite) ).
thf(1230,plain,
! [A: x_a > nat,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_nat @ ( image_a_nat @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(433,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Nat_Odiff__diff__eq) ).
thf(2160,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(652,axiom,
! [A: x_a > $o,B: x_a] : ( ord_less_eq_a_o @ A @ ( insert_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_subset__insertI) ).
thf(2920,plain,
! [A: x_a > $o,B: x_a] : ( ord_less_eq_a_o @ A @ ( insert_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(589,axiom,
! [A: x_a,B: pname > x_a,C: pname > $o] :
( ( member_a @ A @ ( image_pname_a @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_image__iff) ).
thf(2700,plain,
! [A: x_a,B: pname > x_a,C: pname > $o] :
( ( member_a @ A @ ( image_pname_a @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(24,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_trans__le__add2) ).
thf(717,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(344,axiom,
! [A: x_a > $o] :
( ( collect_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Collect__def) ).
thf(1869,plain,
! [A: x_a > $o] :
( ( collect_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(317,axiom,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_subset__insertI) ).
thf(1785,plain,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(329,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_le__refl) ).
thf(1830,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(251,axiom,
! [A: x_a > $o,B: nat,C: x_a > nat,D: x_a] :
( ( B
= ( C @ D ) )
=> ( ( member_a @ D @ A )
=> ( member_nat @ B @ ( image_a_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_image__eqI) ).
thf(1538,plain,
! [A: x_a > $o,B: nat,C: x_a > nat,D: x_a] :
( ( B
= ( C @ D ) )
=> ( ( member_a @ D @ A )
=> ( member_nat @ B @ ( image_a_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(403,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_le__imp__less__Suc) ).
thf(2044,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(85,axiom,
! [A: ( pname > $o ) > $o] :
( ( collect_pname_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Collect__def) ).
thf(907,plain,
! [A: ( pname > $o ) > $o] :
( ( collect_pname_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(600,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_in__mono) ).
thf(2747,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_diff__add__inverse) ).
thf(1053,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(319,axiom,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ( ord_less_eq_nat_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_nat_o @ B ) @ ( finite_card_nat_o @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_card__seteq) ).
thf(1790,plain,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ( ord_less_eq_nat_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_nat_o @ B ) @ ( finite_card_nat_o @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(303,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_not__less__eq__eq) ).
thf(1716,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(516,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_nat_o @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_subset__insertI2) ).
thf(2454,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_nat_o @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(187,axiom,
! [A: ( nat > $o ) > $o,B: nat > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ B )
=> ( ( A @ bot_bot_nat_o )
=> ( ! [D: nat,E: nat > $o] :
( ( finite_finite_nat @ E )
=> ( ( member_nat @ D @ B )
=> ( ~ ( member_nat @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_nat @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_finite__subset__induct) ).
thf(1300,plain,
! [A: ( nat > $o ) > $o,B: nat > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ B )
=> ( ( A @ bot_bot_nat_o )
=> ( ! [D: nat,E: nat > $o] :
( ( finite_finite_nat @ E )
=> ( ( member_nat @ D @ B )
=> ( ~ ( member_nat @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_nat @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(232,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( member_nat @ C @ B )
=> ( member_nat @ C @ A ) )
=> ( ord_less_eq_nat_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_subsetI) ).
thf(1452,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( member_nat @ C @ B )
=> ( member_nat @ C @ A ) )
=> ( ord_less_eq_nat_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(277,axiom,
! [A: pname,B: nat > pname,C: nat > $o] :
( ( member_pname @ A @ ( image_nat_pname @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( B @ D ) )
=> ~ ( member_nat @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_imageE) ).
thf(1637,plain,
! [A: pname,B: nat > pname,C: nat > $o] :
( ( member_pname @ A @ ( image_nat_pname @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( B @ D ) )
=> ~ ( member_nat @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(585,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_equalityI) ).
thf(2688,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(461,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( insert_pname @ B @ A ) )
= ( ord_less_eq_pname_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_subset__insert) ).
thf(2276,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( insert_pname @ B @ A ) )
= ( ord_less_eq_pname_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(445,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_xt1_I4_J) ).
thf(2219,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(137,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ B @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_diff__less__mono2) ).
thf(1085,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ B @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(281,axiom,
! [A: pname > nat > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_nat_o @ ( image_pname_nat_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_pigeonhole__infinite) ).
thf(1658,plain,
! [A: pname > nat > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_nat_o @ ( image_pname_nat_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(182,axiom,
! [A: x_a > nat,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_card__image__le) ).
thf(1285,plain,
! [A: x_a > nat,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(307,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_nat__le__linear) ).
thf(1738,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(33,axiom,
! [A: ( pname > $o ) > nat,B: ( pname > $o ) > $o] :
( ~ ( finite297249702name_o @ B )
=> ( ( finite_finite_nat @ ( image_pname_o_nat @ A @ B ) )
=> ? [C: pname > $o] :
( ( member_pname_o @ C @ B )
& ~ ( finite297249702name_o
@ ( collect_pname_o
@ ^ [D: pname > $o] :
( ( member_pname_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_pigeonhole__infinite) ).
thf(744,plain,
! [A: ( pname > $o ) > nat,B: ( pname > $o ) > $o] :
( ~ ( finite297249702name_o @ B )
=> ( ( finite_finite_nat @ ( image_pname_o_nat @ A @ B ) )
=> ? [C: pname > $o] :
( ( member_pname_o @ C @ B )
& ~ ( finite297249702name_o
@ ( collect_pname_o
@ ^ [D: pname > $o] :
( ( member_pname_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(380,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ A @ ( suc @ ( minus_minus_nat @ C @ B ) ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_diff__Suc__diff__eq1) ).
thf(1981,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ A @ ( suc @ ( minus_minus_nat @ C @ B ) ) )
= ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(546,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( B = C )
=> ( ( ord_less_eq_a_o @ A @ C )
=> ( ord_less_eq_a_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_xt1_I3_J) ).
thf(2543,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( B = C )
=> ( ( ord_less_eq_a_o @ A @ C )
=> ( ord_less_eq_a_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(475,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_diff__Suc__Suc) ).
thf(2320,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(70,axiom,
! [A: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_empty__subsetI) ).
thf(864,plain,
! [A: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(28,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat @ ( collect_nat @ A ) )
& ( finite_finite_nat @ ( collect_nat @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_finite__Collect__disjI) ).
thf(727,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat @ ( collect_nat @ A ) )
& ( finite_finite_nat @ ( collect_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(285,axiom,
! [A: nat > x_a > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_a_o @ ( image_nat_a_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(1670,plain,
! [A: nat > x_a > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_a_o @ ( image_nat_a_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(177,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_le__funD) ).
thf(1272,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(113,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ? [C: nat] :
( B
= ( suc @ ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_less__imp__Suc__add) ).
thf(991,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ? [C: nat] :
( B
= ( suc @ ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(407,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ ( insert_nat @ A @ B ) @ C )
= ( ( member_nat @ A @ C )
& ( ord_less_eq_nat_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_insert__subset) ).
thf(2056,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ ( insert_nat @ A @ B ) @ C )
= ( ( member_nat @ A @ C )
& ( ord_less_eq_nat_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(217,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subsetD) ).
thf(1404,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(197,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_le__add__diff__inverse2) ).
thf(1353,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(462,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_linorder__linear) ).
thf(2279,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(373,axiom,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_finite__subset__image) ).
thf(1955,plain,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(630,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_equalityD2) ).
thf(2843,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(428,axiom,
! [A: pname > $o] :
( ( ( collect_pname @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_Collect__empty__eq) ).
thf(2145,plain,
! [A: pname > $o] :
( ( ( collect_pname @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_not__less__less__Suc__eq) ).
thf(1094,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(108,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_add__le__mono1) ).
thf(978,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(333,axiom,
! [A: pname > $o] :
( ( bot_bot_pname_o
= ( collect_pname @ A ) )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_empty__Collect__eq) ).
thf(1839,plain,
! [A: pname > $o] :
( ( bot_bot_pname_o
= ( collect_pname @ A ) )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(525,axiom,
! [A: x_a > nat,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_nat_o @ ( image_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_image__mono) ).
thf(2479,plain,
! [A: x_a > nat,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_nat_o @ ( image_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(418,axiom,
! [A: $o,B: $o] :
( ( ord_less_eq_o @ A @ B )
=> ( ( ord_less_eq_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_order__antisym__conv) ).
thf(2088,plain,
! [A: $o,B: $o] :
( ( ord_less_eq_o @ A @ B )
=> ( ( ord_less_eq_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(163,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_order__antisym) ).
thf(1180,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(376,axiom,
! [A: pname,B: pname > $o,C: pname] :
( ( insert_pname @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_insert__code) ).
thf(1966,plain,
! [A: pname,B: pname > $o,C: pname] :
( ( insert_pname @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(158,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ A @ B )
=> ( ( finite297249702name_o @ B )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_finite__subset) ).
thf(1157,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ A @ B )
=> ( ( finite297249702name_o @ B )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(220,axiom,
! [A: pname > x_a > $o,B: pname > $o,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_a_o_o @ C @ ( image_pname_a_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_a_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_finite__subset__image) ).
thf(1412,plain,
! [A: pname > x_a > $o,B: pname > $o,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_a_o_o @ C @ ( image_pname_a_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_a_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(477,axiom,
! [A: x_a,B: x_a > $o] :
( ( B = bot_bot_a_o )
=> ~ ( member_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_equals0D) ).
thf(2325,plain,
! [A: x_a,B: x_a > $o] :
( ( B = bot_bot_a_o )
=> ~ ( member_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(165,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_eq__imp__le) ).
thf(1189,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(482,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Suc__le__mono) ).
thf(2342,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(638,axiom,
! [A: x_a > $o,B: nat > x_a,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_nat_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_finite__surj) ).
thf(2865,plain,
! [A: x_a > $o,B: nat > x_a,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_nat_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(368,axiom,
! [A: ( nat > $o ) > $o,B: pname > nat > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_nat_o_o @ A @ ( image_pname_nat_o @ B @ C ) )
=> ( finite_finite_nat_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_finite__surj) ).
thf(1940,plain,
! [A: ( nat > $o ) > $o,B: pname > nat > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_nat_o_o @ A @ ( image_pname_nat_o @ B @ C ) )
=> ( finite_finite_nat_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(511,axiom,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o] :
( ~ ( finite_finite_a_o @ B )
=> ( ( finite_finite_pname @ ( image_a_o_pname @ A @ B ) )
=> ? [C: x_a > $o] :
( ( member_a_o @ C @ B )
& ~ ( finite_finite_a_o
@ ( collect_a_o
@ ^ [D: x_a > $o] :
( ( member_a_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_pigeonhole__infinite) ).
thf(2435,plain,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o] :
( ~ ( finite_finite_a_o @ B )
=> ( ( finite_finite_pname @ ( image_a_o_pname @ A @ B ) )
=> ? [C: x_a > $o] :
( ( member_a_o @ C @ B )
& ~ ( finite_finite_a_o
@ ( collect_a_o
@ ^ [D: x_a > $o] :
( ( member_a_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(605,axiom,
! [A: x_a > $o] :
( ( ord_less_eq_a_o @ A @ bot_bot_a_o )
=> ( A = bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_le__bot) ).
thf(2760,plain,
! [A: x_a > $o] :
( ( ord_less_eq_a_o @ A @ bot_bot_a_o )
=> ( A = bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(222,axiom,
! [A: x_a > x_a,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_a @ ( image_a_a @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_pigeonhole__infinite) ).
thf(1421,plain,
! [A: x_a > x_a,B: x_a > $o] :
( ~ ( finite_finite_a @ B )
=> ( ( finite_finite_a @ ( image_a_a @ A @ B ) )
=> ? [C: x_a] :
( ( member_a @ C @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [D: x_a] :
( ( member_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(391,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_Suc__le__D) ).
thf(2013,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(565,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_ord__le__eq__trans) ).
thf(2626,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(486,axiom,
! [A: pname > pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_pname_pname_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_finite__subset__image) ).
thf(2352,plain,
! [A: pname > pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_pname_pname_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_less__not__refl3) ).
thf(931,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(640,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ ( insert_a @ A @ B ) @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_insert__mono) ).
thf(2885,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ ( insert_a @ A @ B ) @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(371,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ B ) @ ( finite_card_pname @ ( insert_pname @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_card__insert__le) ).
thf(1949,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ B ) @ ( finite_card_pname @ ( insert_pname @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(626,axiom,
! [A: x_a > nat > $o,B: x_a > $o,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_nat_o_o @ C @ ( image_a_nat_o @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_nat_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_finite__subset__image) ).
thf(2828,plain,
! [A: x_a > nat > $o,B: x_a > $o,C: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ C )
=> ( ( ord_less_eq_nat_o_o @ C @ ( image_a_nat_o @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_nat_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(472,axiom,
! [A: nat > nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_nat_o @ ( image_nat_nat_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__imageI) ).
thf(2310,plain,
! [A: nat > nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_nat_o @ ( image_nat_nat_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(84,axiom,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( ( finite_finite_nat_o @ ( collect_nat_o @ B ) )
| ( finite_finite_nat_o @ ( collect_nat_o @ A ) ) )
=> ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [C: nat > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_finite__Collect__conjI) ).
thf(903,plain,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( ( finite_finite_nat_o @ ( collect_nat_o @ B ) )
| ( finite_finite_nat_o @ ( collect_nat_o @ A ) ) )
=> ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [C: nat > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( suc @ A ) @ B )
= ( plus_plus_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_add__Suc__shift) ).
thf(844,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( suc @ A ) @ B )
= ( plus_plus_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(447,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_insert__compr__raw) ).
thf(2226,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(572,axiom,
! [A: x_a > pname,B: x_a > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_a_pname @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_finite__subset__image) ).
thf(2643,plain,
! [A: x_a > pname,B: x_a > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_a_pname @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(179,axiom,
! [A: x_a,B: nat > x_a,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_a @ A @ ( image_nat_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_rev__image__eqI) ).
thf(1276,plain,
! [A: x_a,B: nat > x_a,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_a @ A @ ( image_nat_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(513,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( ( ( insert_pname @ B @ C )
= ( insert_pname @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_insert__ident) ).
thf(2443,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( ( ( insert_pname @ B @ C )
= ( insert_pname @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(175,axiom,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [B: nat > $o] : ( ord_less_eq_nat_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
thf(1253,plain,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [B: nat > $o] : ( ord_less_eq_nat_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(103,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_linorder__neqE__nat) ).
thf(963,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(464,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_equalityD2) ).
thf(2283,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(634,axiom,
! [A: x_a > $o,B: pname > x_a,C: pname > $o] :
( ( ord_less_eq_a_o @ A @ ( image_pname_a @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_pname_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_subset__image__iff) ).
thf(2853,plain,
! [A: x_a > $o,B: pname > x_a,C: pname > $o] :
( ( ord_less_eq_a_o @ A @ ( image_pname_a @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_pname_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(355,axiom,
! [A: pname,B: pname] :
( ( ( insert_pname @ A @ bot_bot_pname_o )
= ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_singleton__inject) ).
thf(1903,plain,
! [A: pname,B: pname] :
( ( ( insert_pname @ A @ bot_bot_pname_o )
= ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(396,axiom,
! [A: nat > $o,B: pname > nat,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_pname_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_finite__surj) ).
thf(2026,plain,
! [A: nat > $o,B: pname > nat,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_pname_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(326,axiom,
! [A: nat > pname,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_pname @ A @ B ) ) @ ( finite_card_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_card__image__le) ).
thf(1822,plain,
! [A: nat > pname,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_pname @ A @ B ) ) @ ( finite_card_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(424,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
= ( ( ord_less_eq_nat_o @ A @ B )
& ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_order__eq__iff) ).
thf(2130,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
= ( ( ord_less_eq_nat_o @ A @ B )
& ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(540,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_empty__subsetI) ).
thf(2526,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(430,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_nat_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_xt1_I4_J) ).
thf(2152,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_nat_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_Suc__lessD) ).
thf(896,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(34,axiom,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o] :
( ~ ( finite297249702name_o @ B )
=> ( ( finite_finite_pname @ ( image_pname_o_pname @ A @ B ) )
=> ? [C: pname > $o] :
( ( member_pname_o @ C @ B )
& ~ ( finite297249702name_o
@ ( collect_pname_o
@ ^ [D: pname > $o] :
( ( member_pname_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_pigeonhole__infinite) ).
thf(748,plain,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o] :
( ~ ( finite297249702name_o @ B )
=> ( ( finite_finite_pname @ ( image_pname_o_pname @ A @ B ) )
=> ? [C: pname > $o] :
( ( member_pname_o @ C @ B )
& ~ ( finite297249702name_o
@ ( collect_pname_o
@ ^ [D: pname > $o] :
( ( member_pname_o @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(132,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_less__diff__conv) ).
thf(1062,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(543,axiom,
! [A: ( nat > $o ) > x_a,B: ( nat > $o ) > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_nat_o_a @ A @ B ) )
=> ? [D: ( nat > $o ) > $o] :
( ( ord_less_eq_nat_o_o @ D @ B )
& ( finite_finite_nat_o @ D )
& ( C
= ( image_nat_o_a @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_finite__subset__image) ).
thf(2532,plain,
! [A: ( nat > $o ) > x_a,B: ( nat > $o ) > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_nat_o_a @ A @ B ) )
=> ? [D: ( nat > $o ) > $o] :
( ( ord_less_eq_nat_o_o @ D @ B )
& ( finite_finite_nat_o @ D )
& ( C
= ( image_nat_o_a @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(390,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_n__not__Suc__n) ).
thf(2009,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(415,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_order__refl) ).
thf(2081,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(495,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_le__diff__conv) ).
thf(2384,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(617,axiom,
! [A: x_a > $o,B: x_a] :
( ( ord_less_eq_a_o @ A @ ( insert_a @ B @ bot_bot_a_o ) )
=> ( ( A = bot_bot_a_o )
| ( A
= ( insert_a @ B @ bot_bot_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_subset__singletonD) ).
thf(2796,plain,
! [A: x_a > $o,B: x_a] :
( ( ord_less_eq_a_o @ A @ ( insert_a @ B @ bot_bot_a_o ) )
=> ( ( A = bot_bot_a_o )
| ( A
= ( insert_a @ B @ bot_bot_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(8,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ ( insert_a_o @ A @ B ) )
= ( finite_finite_a_o @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_finite__insert) ).
thf(667,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ ( insert_a_o @ A @ B ) )
= ( finite_finite_a_o @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(227,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( B = C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_ord__eq__le__trans) ).
thf(1440,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( B = C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(166,axiom,
! [A: nat > pname,B: pname > $o,C: nat > $o] :
( ! [D: nat] :
( ( member_nat @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_nat_pname @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_image__subsetI) ).
thf(1193,plain,
! [A: nat > pname,B: pname > $o,C: nat > $o] :
( ! [D: nat] :
( ( member_nat @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_nat_pname @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(439,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o
@ ( collect_a_o
@ ^ [C: x_a > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a_o @ ( collect_a_o @ A ) )
& ( finite_finite_a_o @ ( collect_a_o @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_finite__Collect__disjI) ).
thf(2183,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o
@ ( collect_a_o
@ ^ [C: x_a > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a_o @ ( collect_a_o @ A ) )
& ( finite_finite_a_o @ ( collect_a_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(352,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_ord__eq__le__trans) ).
thf(1893,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(385,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ~ ( member_nat @ B @ C )
=> ( B = A ) )
=> ( member_nat @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_insertCI) ).
thf(1994,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ~ ( member_nat @ B @ C )
=> ( B = A ) )
=> ( member_nat @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(612,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_insert__compr) ).
thf(2779,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(127,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_diff__add__inverse2) ).
thf(1045,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(47,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_nat__add__right__cancel) ).
thf(800,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( ( suc @ zero_zero_nat )
= ( plus_plus_nat @ A @ B ) )
= ( ( ( A
= ( suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( suc @ zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_one__is__add) ).
thf(832,plain,
! [A: nat,B: nat] :
( ( ( suc @ zero_zero_nat )
= ( plus_plus_nat @ A @ B ) )
= ( ( ( A
= ( suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( suc @ zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(14,axiom,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_not__add__less2) ).
thf(684,plain,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(531,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_xt1_I5_J) ).
thf(2494,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(228,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( member_pname @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_set__rev__mp) ).
thf(1444,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( member_pname @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(651,axiom,
! [A: pname > x_a,B: pname > $o] :
( ( bot_bot_a_o
= ( image_pname_a @ A @ B ) )
= ( B = bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_empty__is__image) ).
thf(2917,plain,
! [A: pname > x_a,B: pname > $o] :
( ( bot_bot_a_o
= ( image_pname_a @ A @ B ) )
= ( B = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(564,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( collect_a @ B ) )
= ( collect_a
@ ^ [C: x_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_insert__Collect) ).
thf(2623,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( collect_a @ B ) )
= ( collect_a
@ ^ [C: x_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(357,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_equalityI) ).
thf(1908,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(422,axiom,
! [A: pname > pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_pname_pname @ A @ C ) )
= ( image_pname_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_insert__image) ).
thf(2123,plain,
! [A: pname > pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_pname_pname @ A @ C ) )
= ( image_pname_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(465,axiom,
! [A: nat > $o,B: ( x_a > $o ) > nat,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_a_o_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_finite__surj) ).
thf(2287,plain,
! [A: nat > $o,B: ( x_a > $o ) > nat,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_a_o_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(278,axiom,
! [A: pname > $o,B: pname] :
( ( ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_pname @ B @ bot_bot_pname_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_Collect__conv__if2) ).
thf(1642,plain,
! [A: pname > $o,B: pname] :
( ( ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_pname @ B @ bot_bot_pname_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(180,axiom,
! [A: x_a > nat,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_imageI) ).
thf(1280,plain,
! [A: x_a > nat,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(261,axiom,
! [A: pname > pname > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_pigeonhole__infinite) ).
thf(1578,plain,
! [A: pname > pname > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(288,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ( ord_le1205211808me_o_o @ A @ B )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_rev__finite__subset) ).
thf(1678,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ( ord_le1205211808me_o_o @ A @ B )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(456,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( B = A ) )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_insertCI) ).
thf(2255,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( B = A ) )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(594,axiom,
! [A: pname] :
( ( member_pname @ A @ u )
=> ( wt @ ( the_com @ ( body @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_assms_I4_J) ).
thf(2719,plain,
! [A: pname] :
( ( member_pname @ A @ u )
=> ( wt @ ( the_com @ ( body @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(253,axiom,
! [A: nat > pname,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_pname @ ( image_nat_pname @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_pigeonhole__infinite) ).
thf(1546,plain,
! [A: nat > pname,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_pname @ ( image_nat_pname @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(273,axiom,
! [A: nat > pname,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_pname @ ( A @ B ) @ ( image_nat_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_imageI) ).
thf(1625,plain,
! [A: nat > pname,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_pname @ ( A @ B ) @ ( image_nat_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(382,axiom,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_finite__Collect__le__nat) ).
thf(1986,plain,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(248,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_bot__least) ).
thf(1527,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_le__neq__implies__less) ).
thf(790,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(469,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( insert_pname @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite_OinsertI) ).
thf(2302,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( insert_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(537,axiom,
! [A: pname > $o,B: x_a,C: pname > x_a,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_a @ B @ ( image_pname_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_image__eqI) ).
thf(2517,plain,
! [A: pname > $o,B: x_a,C: pname > x_a,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_a @ B @ ( image_pname_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_less__Suc__eq) ).
thf(1097,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(60,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_nat_Osimps_I2_J) ).
thf(835,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(266,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_mem__def) ).
thf(1593,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(207,axiom,
! [A: nat > $o,B: nat > nat,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_nat_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_finite__surj) ).
thf(1380,plain,
! [A: nat > $o,B: nat > nat,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ A @ ( image_nat_nat @ B @ C ) )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(440,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [D: pname,E: pname > $o] :
( ( finite_finite_pname @ E )
=> ( ( member_pname @ D @ B )
=> ( ~ ( member_pname @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_pname @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_finite__subset__induct) ).
thf(2186,plain,
! [A: ( pname > $o ) > $o,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [D: pname,E: pname > $o] :
( ( finite_finite_pname @ E )
=> ( ( member_pname @ D @ B )
=> ( ~ ( member_pname @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_pname @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(506,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( ord_less_eq_nat_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_xt1_I6_J) ).
thf(2417,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( ord_less_eq_nat_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(131,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( finite_card_a_o @ B ) ) )
& ( ~ ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( suc @ ( finite_card_a_o @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_card__insert__if) ).
thf(1056,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( finite_card_a_o @ B ) ) )
& ( ~ ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( suc @ ( finite_card_a_o @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(501,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ! [C: pname] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_le__fun__def) ).
thf(2404,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ! [C: pname] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(446,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
= ( ( A = B )
| ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_insert__iff) ).
thf(2223,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
= ( ( A = B )
| ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(133,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ ( suc @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_less__trans__Suc) ).
thf(1065,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ ( suc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(401,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_Suc__le__lessD) ).
thf(2040,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(226,axiom,
! [A: x_a,B: x_a] :
( ( A != B )
| ( fequal_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).
thf(1436,plain,
! [A: x_a,B: x_a] :
( ( A != B )
| ( fequal_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(341,axiom,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
= ( ? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_finite__nat__set__iff__bounded__le) ).
thf(1859,plain,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
= ( ? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(412,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_insert__commute) ).
thf(2070,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(557,axiom,
! [A: x_a,B: x_a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_a_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_singletonE) ).
thf(2572,plain,
! [A: x_a,B: x_a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_a_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(300,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_order__trans) ).
thf(1710,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Suc__leD) ).
thf(1197,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(309,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_set__mp) ).
thf(1742,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(548,axiom,
! [A: nat > x_a,B: nat,C: nat > $o] :
( ( image_nat_a @ A @ ( insert_nat @ B @ C ) )
= ( insert_a @ ( A @ B ) @ ( image_nat_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_image__insert) ).
thf(2549,plain,
! [A: nat > x_a,B: nat,C: nat > $o] :
( ( image_nat_a @ A @ ( insert_nat @ B @ C ) )
= ( insert_a @ ( A @ B ) @ ( image_nat_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(61,axiom,
! [A: nat > $o] :
( ( ! [B: nat] :
~ ( member_nat @ B @ A ) )
= ( A = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_all__not__in__conv) ).
thf(839,plain,
! [A: nat > $o] :
( ( ! [B: nat] :
~ ( member_nat @ B @ A ) )
= ( A = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(156,axiom,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ( ord_less_eq_nat_o_o @ A @ B )
=> ( finite_finite_nat_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_rev__finite__subset) ).
thf(1152,plain,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ( ord_less_eq_nat_o_o @ A @ B )
=> ( finite_finite_nat_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(206,axiom,
! [A: nat > $o] : ( ord_less_eq_nat_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_order__refl) ).
thf(1378,plain,
! [A: nat > $o] : ( ord_less_eq_nat_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(254,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_order__trans) ).
thf(1550,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(55,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_nat__add__assoc) ).
thf(822,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(363,axiom,
finite_finite_pname @ bot_bot_pname_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_finite_OemptyI) ).
thf(1925,plain,
finite_finite_pname @ bot_bot_pname_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_trans__le__add1) ).
thf(850,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(17,axiom,
! [A: nat > nat,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_nat @ ( image_nat_nat @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_pigeonhole__infinite) ).
thf(691,plain,
! [A: nat > nat,B: nat > $o] :
( ~ ( finite_finite_nat @ B )
=> ( ( finite_finite_nat @ ( image_nat_nat @ A @ B ) )
=> ? [C: nat] :
( ( member_nat @ C @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(349,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_in__mono) ).
thf(1885,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(73,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_termination__basic__simps_I4_J) ).
thf(871,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(215,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_diff__le__mono) ).
thf(1399,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(149,axiom,
! [A: nat > $o] :
( ( collect_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Collect__def) ).
thf(1120,plain,
! [A: nat > $o] :
( ( collect_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(619,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_le__funD) ).
thf(2803,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_o @ ( B @ A ) @ ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(250,axiom,
! [A: nat > x_a > $o,B: nat > $o,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_a_o_o @ C @ ( image_nat_a_o @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_a_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_finite__subset__image) ).
thf(1532,plain,
! [A: nat > x_a > $o,B: nat > $o,C: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ C )
=> ( ( ord_less_eq_a_o_o @ C @ ( image_nat_a_o @ A @ B ) )
=> ? [D: nat > $o] :
( ( ord_less_eq_nat_o @ D @ B )
& ( finite_finite_nat @ D )
& ( C
= ( image_nat_a_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( C @ A ) @ B ) @ ( C @ ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_mono__nat__linear__lb) ).
thf(860,plain,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( C @ A ) @ B ) @ ( C @ ( plus_plus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(631,axiom,
! [A: nat,B: nat,C: nat > x_a > $o] :
( ! [D: nat] : ( ord_less_eq_a_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_a_o @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_lift__Suc__mono__le) ).
thf(2847,plain,
! [A: nat,B: nat,C: nat > x_a > $o] :
( ! [D: nat] : ( ord_less_eq_a_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_a_o @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(645,axiom,
! [A: x_a > nat,B: x_a > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_a_nat @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_finite__subset__image) ).
thf(2898,plain,
! [A: x_a > nat,B: x_a > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_a_nat @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(209,axiom,
! [A: x_a > pname,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_pname @ ( image_a_pname @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(1384,plain,
! [A: x_a > pname,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_pname @ ( image_a_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(262,axiom,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ( ord_less_eq_nat_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat_o @ A ) @ ( finite_card_nat_o @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_card__mono) ).
thf(1582,plain,
! [A: ( nat > $o ) > $o,B: ( nat > $o ) > $o] :
( ( finite_finite_nat_o @ B )
=> ( ( ord_less_eq_nat_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat_o @ A ) @ ( finite_card_nat_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(458,axiom,
! [A: pname > nat,B: pname > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_pname_nat @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_finite__subset__image) ).
thf(2265,plain,
! [A: pname > nat,B: pname > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( image_pname_nat @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_add__diff__inverse) ).
thf(982,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(224,axiom,
! [A: ( pname > $o ) > $o,B: pname > pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_pname_pname_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_finite__surj) ).
thf(1431,plain,
! [A: ( pname > $o ) > $o,B: pname > pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_pname_pname_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(190,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ B )
= ( plus_plus_nat @ A @ ( minus_minus_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_diff__add__assoc) ).
thf(1331,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ B )
= ( plus_plus_nat @ A @ ( minus_minus_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(603,axiom,
! [A: x_a > pname,B: x_a,C: x_a > $o] :
( ( image_a_pname @ A @ ( insert_a @ B @ C ) )
= ( insert_pname @ ( A @ B ) @ ( image_a_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_image__insert) ).
thf(2754,plain,
! [A: x_a > pname,B: x_a,C: x_a > $o] :
( ( image_a_pname @ A @ ( insert_a @ B @ C ) )
= ( insert_pname @ ( A @ B ) @ ( image_a_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(48,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_diff__cancel) ).
thf(803,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(202,axiom,
! [A: x_a > pname,B: pname > $o,C: x_a > $o] :
( ! [D: x_a] :
( ( member_a @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_a_pname @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_image__subsetI) ).
thf(1367,plain,
! [A: x_a > pname,B: pname > $o,C: x_a > $o] :
( ! [D: x_a] :
( ( member_a @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_a_pname @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(641,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_subset__trans) ).
thf(2887,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(393,axiom,
! [A: pname > pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__imageI) ).
thf(2018,plain,
! [A: pname > pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(408,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ ( insert_nat @ A @ B ) )
= ( finite_finite_nat @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_finite__insert) ).
thf(2059,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ ( insert_nat @ A @ B ) )
= ( finite_finite_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(627,axiom,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_insert__absorb) ).
thf(2834,plain,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(231,axiom,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Suc__n__not__le__n) ).
thf(1449,plain,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(237,axiom,
! [A: ( x_a > $o ) > $o,B: pname > x_a > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_a_o_o @ A @ ( image_pname_a_o @ B @ C ) )
=> ( finite_finite_a_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_finite__surj) ).
thf(1468,plain,
! [A: ( x_a > $o ) > $o,B: pname > x_a > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_a_o_o @ A @ ( image_pname_a_o @ B @ C ) )
=> ( finite_finite_a_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(437,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_ord__le__eq__trans) ).
thf(2177,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(94,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_Suc__neq__Zero) ).
thf(935,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(370,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_order__eq__refl) ).
thf(1945,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(452,axiom,
! [A: nat > $o] : ( ord_less_eq_nat_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_subset__refl) ).
thf(2238,plain,
! [A: nat > $o] : ( ord_less_eq_nat_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_less__SucI) ).
thf(1037,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(37,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_add__lessD1) ).
thf(775,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(360,axiom,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_insertI1) ).
thf(1917,plain,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(11,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_le__add2) ).
thf(676,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(119,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
!= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_insert__not__empty) ).
thf(1014,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
!= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_less__antisym) ).
thf(972,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(609,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ~ ( member_a @ B @ C )
=> ( ~ ( member_a @ B @ A )
=> ( ( ( insert_a @ B @ C )
= ( insert_a @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_insert__ident) ).
thf(2771,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ~ ( member_a @ B @ C )
=> ( ~ ( member_a @ B @ A )
=> ( ( ( insert_a @ B @ C )
= ( insert_a @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(3012,plain,
$false,
inference(e,[status(thm)],[2163,2889,1633,2412,2559,777,1295,1686,1322,1665,2822,2630,1586,2452,809,1879,1337,2295,760,2787,1850,2499,2210,730,2381,2659,994,1401,2676,1728,873,2099,2837,878,1692,1855,2077,1596,1406,2808,1522,2908,2062,1971,1793,1705,1756,2035,1872,1327,945,2042,1507,1164,797,1919,1988,2459,670,2575,898,1835,2216,2348,2046,2763,1391,782,2020,1475,2173,1803,1887,2432,1914,1650,1921,1601,1386,2400,2067,1529,2654,1409,1287,2735,2339,2274,1826,1832,2126,1132,2703,2667,719,949,2745,2571,2552,1890,2767,881,1568,2158,1875,1100,1847,817,2691,2169,1087,969,2373,1115,2635,1362,1963,1489,924,2794,1714,1373,1334,2540,2777,1051,2456,2007,1911,2782,1109,2469,1418,2236,2555,806,2335,966,1183,2073,2508,687,2367,2281,866,1394,2137,660,2002,1433,1447,2483,956,1622,2424,1345,988,2799,2639,1696,2586,942,678,793,1470,2737,2232,2000,1199,2364,2083,1067,1274,1091,1255,1123,1824,2528,2396,1883,1900,910,825,1343,2805,2249,1021,1042,952,1676,2133,2032,815,916,2477,1178,1951,665,830,1159,2345,682,710,2769,1106,2464,847,1032,1837,1365,2670,852,2663,2332,2820,1787,2181,1210,1656,1079,2213,2547,1128,2492,1740,842,742,2840,2685,2895,2577,725,980,1425,1672,1719,857,1360,1936,697,1234,2709,1227,2638,1118,1683,884,1942,2323,1292,2561,2312,1584,1744,1082,2023,901,2419,2240,1842,2038,1446,1207,2085,2649,1039,1776,985,701,1478,1297,2304,2387,654,2505,2497,1984,1852,2862,1456,1382,2487,2598,1552,2851,2052,2697,1979,779,1627,2370,1779,2208,921,1712,1466,674,1167,2529,2749,1857,1563,657,1906,2729,1510,1251,1698,2028,2524,733,1146,1754,2904,1680,1154,819,975,2791,1125,2489,2393,1929,1388,875,2695,2048,2859,2657,2849,2016,2514,1795,1701,1707,787,2706,704,2891,2308,1371,713,1865,1897,919,2557,1464,2474,947,2148,2358,1356,764,2361,2521,2679,2538,1282,2229,2415,1349,1603,1542,1722,2116,1801,2856,1690,1969,2721,2119,784,2637,2422,1574,1011,2774,1524,2906,1048,1589,996,1933,1571,1376,2824,1630,2261,1862,2410,1029,1149,2252,2461,2329,2911,1688,890,1667,2446,2757,1460,2289,912,1926,2350,959,827,2139,2064,1113,2633,2390,1102,2156,653,1805,2867,1396,2439,695,2481,2620,868,2592,1000,2752,2005,722,1662,1758,2665,927,2234,812,1990,1472,2914,2816,795,2318,2271,663,2652,2471,939,1340,1018,2564,1748,1003,1961,2375,887,1566,1605,739,2407,2567,1845,1798,2298,855,2715,690,1516,1598,1230,2160,2920,2700,717,1869,1785,1830,1538,2044,907,2747,1053,1790,1716,2454,1300,1452,1637,2688,2276,2219,1085,1658,1285,1738,744,1981,2543,2320,864,727,1670,1272,991,2056,1404,1353,2279,1955,2843,2145,1094,978,1839,2479,2088,1180,1966,1157,1412,2325,1189,2342,2865,1940,2435,2760,1421,2013,2626,2352,931,2885,1949,2828,2310,903,844,2226,2643,1276,2443,1253,963,2283,2853,1903,2026,1822,2130,2526,2152,896,748,1062,2532,2009,2081,2384,2796,667,1440,1193,2183,1893,1994,2779,1045,800,832,684,2494,1444,2917,2623,1908,2123,2287,1642,1280,1578,1678,2255,2719,1546,1625,1986,1527,790,2302,2517,1097,835,1593,1380,2186,2417,1056,2404,2223,1065,2040,1436,1859,2070,2572,1710,1197,1742,2549,839,1152,1378,1550,822,1925,850,691,1885,871,1399,1120,2803,1532,860,2847,2898,1384,1582,2265,982,1431,1331,2754,803,1367,2887,2018,2059,2834,1449,1468,2177,935,1945,2238,1037,775,1917,676,1014,972,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473^2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.23 % Computer : n013.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 16:05:21 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.82/1.32 % [INFO] Parsing done (519ms).
% 2.82/1.34 % [INFO] Running in sequential loop mode.
% 4.21/1.73 % [INFO] eprover registered as external prover.
% 4.21/1.74 % [INFO] Scanning for conjecture ...
% 4.78/1.90 % [INFO] Found a conjecture (or negated_conjecture) and 718 axioms. Running axiom selection ...
% 5.32/2.04 % [INFO] Axiom selection finished. Selected 650 axioms (removed 68 axioms).
% 6.70/2.42 % [INFO] Problem is higher-order (TPTP THF).
% 6.70/2.45 % [INFO] Type checking passed.
% 6.70/2.45 % [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 ...
% 30.90/7.87 % External prover 'e' found a proof!
% 30.90/7.87 % [INFO] Killing All external provers ...
% 30.90/7.87 % Time passed: 7494ms (effective reasoning time: 6523ms)
% 30.90/7.87 % 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)>
% 30.90/7.87 % Axioms used in derivation (650): fact_628_less__SucE, fact_539_ord__eq__le__trans, fact_461_empty__not__insert, fact_508_xt1_I5_J, fact_513_order__trans, fact_658_less__eq__Suc__le, fact_155_finite__subset__image, fact_183_lift__Suc__mono__le, fact_359_subsetI, fact_348_image__mono, fact_310_rev__image__eqI, fact_692_Zero__neq__Suc, fact_166_finite__subset__image, fact_180_finite__subset__image, fact_555_linorder__linear, fact_31_card__image__le, fact_208_pigeonhole__infinite, fact_43_card__mono, fact_644_termination__basic__simps_I5_J, fact_171_finite__subset__image, fact_51_card__seteq, fact_598_le__imp__diff__is__add, fact_47_card__mono, fact_411_empty__Collect__eq, fact_139_finite__surj, fact_245_insert__absorb2, fact_614_finite__Collect__less__nat, fact_248_insert__commute, fact_164_finite__subset__image, fact_127_diff__diff__cancel, fact_618_less__add__eq__less, fact_678_less__zeroE, fact_185_lift__Suc__mono__le, fact_260_insertI2, fact_639_less__imp__le__nat, fact_371_order__refl, fact_651_nat__less__cases, fact_179_finite__subset__image, fact_219_subsetD, fact_684_diff__is__0__eq_H, fact_562_assms_I2_J, fact_512_order__trans, fact_178_finite__subset__image, fact_636_not__less__eq, fact_505_xt1_I5_J, fact_11_finite__imageI, fact_529_ord__le__eq__trans, fact_213_image__eqI, fact_655_less__add__Suc1, fact_621_trans__less__add2, fact_190_pigeonhole__infinite, fact_501_xt1_I6_J, fact_672_inc__induct, fact_604_le__diff__conv, fact_33_card__image__le, fact_302_image__iff, fact_390_finite_OemptyI, fact_265_insert__absorb, fact_306_imageI, fact_282_set__rev__mp, fact_654_finite__M__bounded__by__nat, fact_275_equalityD2, fact_277_equalityD2, fact_393_empty__subsetI, fact_15_finite__imageI, fact_603_le__add__diff, fact_122_Suc__diff__diff, fact_186_lift__Suc__mono__le, fact_676_Suc__lessE, fact_677_lessE, fact_686_One__nat__def, fact_345_subset__image__iff, fact_346_subset__image__iff, fact_469_empty__is__image, fact_199_pigeonhole__infinite, fact_374_le__fun__def, fact_299_equalityE, fact_667_less__diff__conv, fact_665_diff__less__Suc, fact_376_le__fun__def, fact_367_order__refl, fact_214_image__eqI, fact_136_finite__surj, fact_540_order__antisym__conv, fact_458_insert__not__empty, fact_372_finite__nat__set__iff__bounded__le, fact_659_less__Suc__eq__le, fact_192_pigeonhole__infinite, fact_652_finite__nat__set__iff__bounded, fact_444_bot__least, fact_109_rev__finite__subset, fact_698_le__0__eq, fact_626_Suc__less__SucD, fact_338_insert__image, fact_419_empty__def, conj_3, fact_177_finite__subset__image, fact_110_rev__finite__subset, fact_159_finite__subset__image, fact_450_singletonE, fact_126_eq__diff__iff, fact_638_le__neq__implies__less, fact_605_diff__diff__right, fact_206_pigeonhole__infinite, fact_163_finite__subset__image, fact_296_subset__trans, fact_511_order__trans, fact_9_finite__imageI, fact_541_order__antisym__conv, fact_616_termination__basic__simps_I2_J, fact_506_xt1_I5_J, fact_360_image__subsetI, fact_499_linorder__le__cases, fact_187_pigeonhole__infinite, fact_582_diff__cancel, fact_418_all__not__in__conv, fact_223_insertCI, fact_39_card__image__le, fact_311_rev__image__eqI, fact_398_Collect__empty__eq, fact_464_subset__empty, fact_252_insert__iff, fact_78_Suc__diff__le, fact_93_finite__Collect__disjI, fact_125_Nat_Odiff__diff__eq, fact_522_xt1_I4_J, fact_578_nat__add__commute, fact_246_insert__absorb2, fact_395_equals0D, fact_365_image__subsetI, fact_304_imageI, fact_484_singleton__conv, fact_354_imageE, fact_251_insert__iff, fact_120_not__less__eq__eq, fact_321_subset__insertI, fact_34_card__image__le, fact_216_equalityI, fact_226_insertE, fact_378_le__funD, fact_162_finite__subset__image, fact_477_Collect__conv__if2, fact_209_pigeonhole__infinite, fact_64_card__insert__if, fact_389_finite_OemptyI, fact_95_finite__Collect__disjI, fact_280_in__mono, fact_381_le__funE, fact_519_order__antisym, fact_642_diff__less__mono2, fact_674_bounded__nat__set__is__finite, fact_96_finite__Collect__disjI, fact_689_minus__nat_Odiff__0, fact_687_diffs0__imp__equal, fact_188_pigeonhole__infinite, fact_623_nat__add__left__cancel__less, fact_645_less__not__refl, fact_594_add__leE, fact_611_termination__basic__simps_I4_J, fact_333_insert__mono, fact_640_le__eq__less__or__eq, fact_637_less__or__eq__imp__le, fact_132_finite__surj, fact_57_card__insert__le, fact_350_image__mono, fact_579_diff__add__inverse2, fact_152_finite__surj, fact_63_card__insert__if, fact_40_card__image__le, fact_82_nat_Oinject, fact_392_empty__subsetI, fact_609_diff__Suc__diff__eq1, fact_142_finite__surj, fact_106_finite__subset, fact_635_less__Suc__eq, fact_550_order__eq__iff, fact_634_Suc__less__eq, fact_663_le__less__Suc__eq, fact_558_finite__subset__induct, fact_670_less__eq__Suc__le__raw, fact_103_finite__subset, fact_433_le__bot, fact_575_nat__add__left__cancel, fact_149_finite__surj, fact_259_insert__ident, fact_449_singletonE, fact_156_finite__subset__image, fact_584_le__add2, fact_13_finite__imageI, fact_355_imageE, fact_225_insertE, fact_361_image__subsetI, fact_624_not__add__less2, fact_62_card__insert__if, fact_534_xt1_I3_J, fact_255_insert__code, fact_675_less__mono__imp__le__mono, fact_545_order__eq__refl, fact_650_less__not__refl3, fact_648_less__irrefl__nat, fact_548_order__eq__refl, fact_694_Suc__not__Zero, fact_436_bot__unique, fact_335_image__insert, fact_457_singleton__iff, fact_317_insert__compr__raw, fact_580_diff__add__inverse, fact_112_rev__finite__subset, fact_10_finite__imageI, fact_75_finite__Collect__conjI, fact_503_xt1_I6_J, fact_65_card__insert__if, fact_325_subset__insert, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_619_add__less__mono, fact_257_insert__ident, fact_88_nat__le__linear, fact_526_ord__le__eq__trans, fact_140_finite__surj, fact_682_one__is__add, fact_438_bot__unique, fact_625_not__add__less1, fact_89_le__refl, fact_566_finite__less__ub, fact_90_diff__commute, fact_130_diff__le__self, fact_305_imageI, fact_602_le__add__diff__inverse, fact_228_zero__induct__lemma, fact_331_insert__mono, fact_210_pigeonhole__infinite, fact_510_order__trans, fact_494_subset__singletonD, fact_69_card__insert__disjoint, fact_364_image__subsetI, fact_200_pigeonhole__infinite, fact_272_equalityD1, fact_301_equalityE, fact_221_subsetD, help_fequal_1_1_fequal_000tc__Com__Opname_T, fact_169_finite__subset__image, fact_596_add__diff__assoc2, fact_583_diff__cancel2, fact_5_finite__Collect__subsets, fact_294_Collect__def, fact_229_Suc__le__D, conj_2, fact_527_ord__le__eq__trans, fact_278_in__mono, fact_268_subset__refl, fact_203_pigeonhole__infinite, fact_170_finite__subset__image, fact_357_subsetI, fact_281_set__rev__mp, fact_424_empty__def, fact_629_less__trans__Suc, fact_114_rev__finite__subset, fact_285_set__mp, fact_370_order__refl, fact_407_empty__Collect__eq, fact_20_finite__imageI, fact_79_finite__Collect__le__nat, fact_525_ord__le__eq__trans, fact_56_card__insert__le, fact_271_set__eq__subset, fact_168_finite__subset__image, fact_154_finite__surj, fact_324_insert__subset, fact_576_nat__add__assoc, fact_515_order__antisym, fact_2_finite__Collect__subsets, fact_232_insertI1, fact_577_nat__add__left__commute, fact_212_image__eqI, fact_669_less__diff__iff, fact_632_less__antisym, fact_287_mem__def, fact_507_xt1_I5_J, fact_128_diff__le__mono, fact_343_insert__image, fact_292_Collect__def, fact_662_Suc__leI, fact_242_insert__Collect, fact_554_order__eq__iff, fact_362_image__subsetI, fact_123_diff__Suc__Suc, fact_70_card__insert__disjoint, fact_470_Collect__conv__if, fact_320_subset__insertI, fact_668_diff__less__mono, fact_72_finite__Collect__conjI, fact_523_xt1_I4_J, fact_218_equalityI, fact_237_insert__compr, fact_336_image__insert, fact_266_subset__refl, fact_270_set__eq__subset, fact_688_diff__self__eq__0, fact_588_trans__le__add1, fact_312_rev__image__eqI, fact_353_imageE, fact_68_card__insert__disjoint, fact_585_le__add1, fact_35_card__image__le, fact_151_finite__surj, fact_27_finite_OinsertI, fact_244_insert__Collect, fact_50_card__seteq, fact_7_finite__imageI, fact_291_Collect__def, fact_87_eq__imp__le, fact_630_Suc__lessI, fact_121_Suc__n__not__le__n, fact_542_order__antisym__conv, fact_581_diff__diff__left, fact_264_insert__absorb, fact_12_finite__imageI, fact_533_xt1_I3_J, fact_141_finite__surj, fact_369_order__refl, fact_383_emptyE, fact_283_set__rev__mp, fact_443_bot__least, fact_402_Collect__empty__eq, fact_157_finite__subset__image, fact_373_assms_I3_J, fact_253_insert__iff, fact_547_order__eq__refl, fact_476_Collect__conv__if2, fact_289_mem__def, fact_172_finite__subset__image, fact_643_less__imp__diff__less, fact_553_order__eq__iff, fact_38_card__image__le, fact_607_Suc__eq__plus1__left, fact_105_finite__subset, fact_250_insert__commute, fact_108_finite__subset, fact_52_card__seteq, fact_77_finite__Collect__conjI, fact_323_insert__subset, fact_4_finite__Collect__subsets, fact_111_rev__finite__subset, fact_455_singleton__iff, fact_472_Collect__conv__if, fact_653_card__Collect__less__nat, fact_627_Suc__lessD, fact_404_empty__iff, fact_92_finite__Collect__disjI, fact_391_finite_OemptyI, fact_489_singleton__conv2, fact_673_less__imp__Suc__add, fact_329_subset__insertI2, fact_173_finite__subset__image, fact_341_insert__image, fact_337_image__insert, fact_254_insert__code, fact_462_empty__not__insert, fact_412_empty__Collect__eq, fact_693_nat_Osimps_I3_J, fact_601_add__diff__assoc, fact_695_nat_Osimps_I2_J, fact_532_xt1_I3_J, fact_86_le__trans, fact_551_order__eq__iff, fact_196_pigeonhole__infinite, fact_21_finite__imageI, fact_330_subset__insertI2, fact_396_equals0D, fact_622_trans__less__add1, fact_349_image__mono, fact_204_pigeonhole__infinite, fact_471_Collect__conv__if, fact_482_singleton__conv, fact_498_image__constant__conv, fact_680_zero__less__Suc, fact_535_ord__eq__le__trans, fact_671_mono__nat__linear__lb, fact_589_trans__le__add2, fact_133_finite__surj, fact_94_finite__Collect__disjI, fact_568_diff__Suc__eq__diff__pred, help_fequal_2_1_fequal_000t__a_T, fact_30_card__image__le, fact_382_le__funE, fact_319_subset__insertI, fact_25_finite_OinsertI, fact_205_pigeonhole__infinite, fact_258_insert__ident, fact_167_finite__subset__image, fact_220_subsetD, fact_201_pigeonhole__infinite, fact_175_finite__subset__image, fact_150_finite__surj, fact_574_nat__add__right__cancel, fact_344_subset__image__iff, fact_664_Suc__le__lessD, fact_403_Collect__empty__eq, fact_356_imageE, fact_681_add__is__1, fact_385_emptyE, fact_181_finite__subset__image, fact_633_not__less__less__Suc__eq, fact_536_ord__eq__le__trans, fact_691_Suc__neq__Zero, fact_16_finite__imageI, fact_28_finite_OinsertI, fact_243_insert__Collect, fact_262_insertI2, fact_102_finite__insert, fact_599_le__add__diff__inverse2, fact_597_diff__add__assoc, fact_696_Zero__not__Suc, fact_115_Suc__leD, fact_153_finite__surj, fact_274_equalityD1, fact_286_set__mp, fact_448_singleton__inject, fact_610_termination__basic__simps_I3_J, fact_71_card__insert__disjoint, fact_284_set__mp, fact_308_rev__image__eqI, fact_468_image__empty, fact_124_le__diff__iff, fact_456_singleton__iff, fact_608_diff__Suc__diff__eq2, fact_307_imageI, fact_414_ex__in__conv, fact_351_image__mono, fact_137_finite__surj, fact_238_insert__compr, fact_22_finite__imageI, fact_496_subset__singletonD, fact_182_lift__Suc__mono__le, fact_143_finite__surj, fact_537_ord__eq__le__trans, fact_377_le__funD, fact_490_singleton__conv2, fact_571_add__Suc__right, fact_261_insertI2, fact_160_finite__subset__image, fact_631_less__SucI, fact_590_add__le__mono1, fact_174_finite__subset__image, fact_91_finite__Collect__disjI, fact_269_set__eq__subset, fact_592_add__leD2, fact_279_in__mono, fact_135_finite__surj, fact_453_doubleton__eq__iff, fact_227_insertE, fact_573_add__Suc__shift, fact_194_pigeonhole__infinite, fact_113_rev__finite__subset, fact_528_ord__le__eq__trans, fact_699_less__eq__nat_Osimps_I1_J, fact_191_pigeonhole__infinite, fact_293_Collect__def, fact_683_diff__add__0, fact_612_lessI, fact_509_xt1_I5_J, fact_478_Collect__conv__if2, fact_215_image__eqI, fact_145_finite__surj, fact_397_equals0D, conj_1, fact_500_xt1_I6_J, fact_165_finite__subset__image, fact_1_finite__Collect__subsets, fact_600_le__diff__conv2, fact_416_all__not__in__conv, fact_516_order__antisym, fact_405_empty__iff, fact_463_empty__not__insert, fact_100_finite__insert, help_fequal_1_1_fequal_000t__a_T, fact_45_card__mono, fact_556_finite__subset__induct, fact_198_pigeonhole__infinite, fact_211_image__eqI, fact_520_xt1_I4_J, fact_660_Suc__le__eq, fact_315_insert__compr__raw, fact_591_add__le__mono, fact_217_equalityI, fact_197_pigeonhole__infinite, fact_606_Suc__eq__plus1, fact_417_all__not__in__conv, fact_543_order__antisym__conv, fact_224_insertCI, fact_570_less__eq__nat_Osimps_I2_J, fact_48_card__seteq, fact_184_lift__Suc__mono__le, fact_193_pigeonhole__infinite, fact_235_insert__compr, fact_80_card__Collect__le__nat, fact_646_nat__neq__iff, fact_679_le0, fact_615_termination__basic__simps_I1_J, fact_423_empty__def, fact_431_le__bot, fact_451_singletonE, fact_104_finite__subset, fact_661_le__imp__less__Suc, fact_36_card__image__le, fact_247_insert__absorb2, fact_273_equalityD1, fact_587_nat__add__left__cancel__le, fact_452_doubleton__eq__iff, fact_37_card__image__le, fact_53_card__seteq, fact_85_le__antisym, fact_384_emptyE, fact_549_order__eq__refl, fact_322_insert__subset, fact_340_insert__image, fact_530_xt1_I3_J, fact_276_equalityD2, fact_524_xt1_I4_J, fact_641_nat__less__le, fact_44_card__mono, fact_685_diff__is__0__eq, fact_290_Collect__def, fact_375_le__fun__def, fact_83_Suc__n__not__n, fact_298_subset__trans, fact_572_add__Suc, fact_502_xt1_I6_J, fact_76_finite__Collect__conjI, fact_263_insert__absorb, fact_465_subset__empty, fact_441_bot__least, fact_363_image__subsetI, fact_138_finite__surj, fact_3_finite__Collect__subsets, fact_531_xt1_I3_J, fact_256_insert__code, fact_617_add__lessD1, fact_58_card__insert__le, fact_459_insert__not__empty, fact_231_insertI1, fact_620_add__less__mono1, fact_586_le__iff__add, fact_544_order__antisym__conv, fact_483_singleton__conv, fact_666_add__diff__inverse, fact_318_insert__compr__raw, fact_647_linorder__neqE__nat, fact_342_insert__image, fact_358_subsetI, fact_380_le__funE, fact_406_empty__iff, fact_119_le__Suc__eq, fact_288_mem__def, fact_195_pigeonhole__infinite, fact_567_assms_I4_J, fact_158_finite__subset__image, fact_118_Suc__le__mono, conj_4, fact_454_doubleton__eq__iff, fact_303_imageI, fact_202_pigeonhole__infinite, fact_415_ex__in__conv, fact_434_le__bot, fact_239_insert__Collect, fact_657_less__iff__Suc__add, fact_316_insert__compr__raw, fact_26_finite_OinsertI, fact_368_order__refl, fact_569_diff__Suc__1, fact_326_subset__insert, fact_334_image__insert, fact_99_finite__insert, fact_84_n__not__Suc__n, fact_189_pigeonhole__infinite, fact_0_assms_I1_J, fact_379_le__funD, fact_81_Suc__inject, fact_73_finite__Collect__conjI, fact_649_less__not__refl2, fact_295_Collect__def, fact_517_order__antisym, fact_146_finite__surj, fact_460_insert__not__empty, fact_107_finite__subset, fact_101_finite__insert, fact_297_subset__trans, fact_467_image__is__empty, fact_504_xt1_I6_J, fact_19_finite__imageI, fact_49_card__seteq, fact_366_image__subsetI, fact_18_finite__imageI, fact_447_singleton__inject, fact_394_empty__subsetI, fact_538_ord__eq__le__trans, fact_29_card__image__le, fact_46_card__mono, conj_0, fact_593_add__leD1, fact_230_insertI1, fact_267_subset__refl, fact_161_finite__subset__image, fact_495_subset__singletonD, fact_148_finite__surj, fact_116_le__SucE, fact_439_bot__unique, fact_300_equalityE, conj_5, fact_207_pigeonhole__infinite, fact_552_order__eq__iff, fact_613_Suc__mono, fact_557_finite__subset__induct, fact_41_card__image__le, fact_521_xt1_I4_J, fact_131_finite__surj, fact_42_card__mono, fact_690_diff__0__eq__0, fact_327_subset__insert, fact_17_finite__imageI, fact_656_less__add__Suc2, fact_74_finite__Collect__conjI, fact_352_imageE, fact_8_finite__imageI, fact_309_rev__image__eqI, fact_236_insert__compr, fact_249_insert__commute, fact_6_finite__Collect__subsets, fact_339_insert__image, fact_595_diff__add__assoc2, fact_514_order__trans, fact_134_finite__surj, fact_328_subset__insertI2, fact_222_insertCI, fact_446_singleton__inject, fact_59_card__insert__le, fact_129_diff__le__mono2, fact_546_order__eq__refl, fact_144_finite__surj, fact_518_order__antisym, fact_332_insert__mono, fact_466_subset__empty, fact_14_finite__imageI, fact_147_finite__surj, fact_347_subset__image__iff, fact_176_finite__subset__image, fact_117_le__SucI, fact_497_image__constant, fact_413_ex__in__conv, fact_32_card__image__le
% 30.90/7.87 % No. of inferences in proof: 1304
% 30.90/7.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7494 ms resp. 6523 ms w/o parsing
% 32.25/8.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.25/8.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------