%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW473^3 : 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 : n016.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 26.59s 7.20s
% Output : Refutation 28.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 417
% Syntax : Number of formulae : 836 ( 221 unt; 0 typ; 0 def)
% Number of atoms : 3452 ( 704 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 7085 ( 196 ~; 48 |; 172 &;5607 @)
% ( 0 <=>;1062 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 1530 (1530 >; 0 *; 0 +; 0 <<)
% Number of symbols : 83 ( 81 usr; 4 con; 0-3 aty)
% Number of variables : 2150 ( 64 ^;2016 !; 70 ?;2150 :)
% Comments :
%------------------------------------------------------------------------------
thf(x_a_type,type,
x_a: $tType ).
thf(com_type,type,
com: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(int_type,type,
int: $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_int_o_decl,type,
finite_card_int_o: ( ( int > $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_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(finite229719499nt_o_o_decl,type,
finite229719499nt_o_o: ( ( ( int > $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_int_o_decl,type,
finite_finite_int_o: ( ( int > $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_folding_one_a_decl,type,
finite_folding_one_a: ( x_a > x_a > x_a ) > ( ( x_a > $o ) > x_a ) > $o ).
thf(finite1282449217_pname_decl,type,
finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(finite1819937229idem_a_decl,type,
finite1819937229idem_a: ( x_a > x_a > x_a ) > ( ( x_a > $o ) > x_a ) > $o ).
thf(finite89670078_pname_decl,type,
finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(minus_minus_a_o_decl,type,
minus_minus_a_o: ( x_a > $o ) > ( x_a > $o ) > x_a > $o ).
thf(minus_minus_pname_o_decl,type,
minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $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(the_a_decl,type,
the_a: ( x_a > $o ) > x_a ).
thf(suc_decl,type,
suc: nat > nat ).
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(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_int_o_o_decl,type,
ord_less_eq_int_o_o: ( ( int > $o ) > $o ) > ( ( int > $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_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_int_o_o_decl,type,
collect_int_o_o: ( ( ( int > $o ) > $o ) > $o ) > ( ( int > $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_a_decl,type,
collect_a: ( x_a > $o ) > x_a > $o ).
thf(collect_pname_decl,type,
collect_pname: ( pname > $o ) > pname > $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_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_int_o_a_decl,type,
image_int_o_a: ( ( int > $o ) > x_a ) > ( ( int > $o ) > $o ) > x_a > $o ).
thf(image_int_o_pname_decl,type,
image_int_o_pname: ( ( int > $o ) > pname ) > ( ( int > $o ) > $o ) > pname > $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_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_int_o_decl,type,
image_a_int_o: ( x_a > int > $o ) > ( x_a > $o ) > ( int > $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_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_int_o_decl,type,
image_pname_int_o: ( pname > int > $o ) > ( pname > $o ) > ( int > $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(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(the_elem_a_decl,type,
the_elem_a: ( x_a > $o ) > x_a ).
thf(fequal_a_decl,type,
fequal_a: x_a > x_a > $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(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(79,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_533_all__not__in__conv) ).
thf(645,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)],[79]) ).
thf(269,axiom,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_insertI1) ).
thf(1322,plain,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(342,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_625_bot__unique) ).
thf(1586,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)],[342]) ).
thf(177,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_card__Diff1__le) ).
thf(1024,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(212,axiom,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Suc__n__not__le__n) ).
thf(1168,plain,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(388,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_393_insertI2) ).
thf(1767,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)],[388]) ).
thf(146,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_74_card__mono) ).
thf(893,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)],[146]) ).
thf(20,axiom,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ one_one_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_Suc__eq__plus1__left) ).
thf(468,plain,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ one_one_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(216,axiom,
( bot_bot_a_o
= ( collect_a
@ ^ [A: x_a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_empty__def) ).
thf(1179,plain,
( bot_bot_a_o
= ( collect_a
@ ^ [A: x_a] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(115,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_finite__induct) ).
thf(777,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(25,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_854_termination__basic__simps_I3_J) ).
thf(481,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)],[25]) ).
thf(330,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ! [C: x_a] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_le__funI) ).
thf(1559,plain,
! [A: x_a > $o,B: x_a > $o] :
( ! [C: x_a] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(200,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) ) )
= ( finite_finite_pname @ ( minus_minus_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_finite__Diff__insert) ).
thf(1105,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) ) )
= ( finite_finite_pname @ ( minus_minus_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(239,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_131_diff__commute) ).
thf(1237,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)],[239]) ).
thf(130,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_480_subsetI) ).
thf(846,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)],[130]) ).
thf(74,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_157_rev__finite__subset) ).
thf(628,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)],[74]) ).
thf(180,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_321_order__antisym__conv) ).
thf(1031,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)],[180]) ).
thf(85,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_n__not__Suc__n) ).
thf(666,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(407,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_227_finite__subset__image) ).
thf(1818,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)],[407]) ).
thf(228,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_851_diff__Suc__diff__eq1) ).
thf(1211,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)],[228]) ).
thf(59,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_789_add__left__cancel) ).
thf(582,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)],[59]) ).
thf(170,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ~ ( member_a @ B @ A )
=> ( member_a @ B @ ( minus_minus_a_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_DiffI) ).
thf(1005,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ~ ( member_a @ B @ A )
=> ( member_a @ B @ ( minus_minus_a_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(90,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_326_ord__eq__le__trans) ).
thf(683,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)],[90]) ).
thf(104,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_72_card__mono) ).
thf(730,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)],[104]) ).
thf(304,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_26_finite__imageI) ).
thf(1443,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)],[304]) ).
thf(191,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( A != bot_bot_pname_o )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_773_folding__one__idem_Osubset__idem) ).
thf(1073,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( A != bot_bot_pname_o )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(377,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_327_ord__eq__le__trans) ).
thf(1728,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)],[377]) ).
thf(344,axiom,
! [A: x_a,B: x_a > $o] :
( bot_bot_a_o
!= ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_empty__not__insert) ).
thf(1591,plain,
! [A: x_a,B: x_a > $o] :
( bot_bot_a_o
!= ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(71,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_793_add__left__imp__eq) ).
thf(614,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)],[71]) ).
thf(136,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( minus_minus_pname_o @ A @ C ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( minus_minus_pname_o @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_insert__Diff__if) ).
thf(861,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( minus_minus_pname_o @ A @ C ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( minus_minus_pname_o @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(10,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_66_card__image__le) ).
thf(440,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)],[10]) ).
thf(82,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_476_imageE) ).
thf(655,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)],[82]) ).
thf(398,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_449_le__funE) ).
thf(1793,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)],[398]) ).
thf(322,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_342_xt1_I4_J) ).
thf(1533,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)],[322]) ).
thf(214,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(1173,plain,
! [A: x_a,B: x_a] :
( ~ ( fequal_a @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(311,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_231_finite__subset__image) ).
thf(1486,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)],[311]) ).
thf(396,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_bot__least) ).
thf(1788,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(363,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_668_image__constant__conv) ).
thf(1655,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)],[363]) ).
thf(206,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_346_order__antisym) ).
thf(1137,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)],[206]) ).
thf(379,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_384_insert__iff) ).
thf(1735,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)],[379]) ).
thf(32,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_795_add__imp__eq) ).
thf(500,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)],[32]) ).
thf(251,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_23_finite__imageI) ).
thf(1275,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)],[251]) ).
thf(271,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_852_diff__Suc__diff__eq2) ).
thf(1327,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)],[271]) ).
thf(155,axiom,
! [A: ( int > $o ) > pname,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( finite_finite_pname @ ( image_int_o_pname @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite__imageI) ).
thf(945,plain,
! [A: ( int > $o ) > pname,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( finite_finite_pname @ ( image_int_o_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(282,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_12_finite__imageI) ).
thf(1354,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)],[282]) ).
thf(86,axiom,
! [A: ( int > $o ) > $o,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( ( ord_less_eq_int_o_o @ A @ B )
=> ( finite_finite_int_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_rev__finite__subset) ).
thf(670,plain,
! [A: ( int > $o ) > $o,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( ( ord_less_eq_int_o_o @ A @ B )
=> ( finite_finite_int_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(264,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_416_in__mono) ).
thf(1310,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)],[264]) ).
thf(42,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_one__reorient) ).
thf(533,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(241,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_364_linorder__le__cases) ).
thf(1243,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)],[241]) ).
thf(183,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_264_lift__Suc__mono__le) ).
thf(1046,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)],[183]) ).
thf(351,axiom,
! [A: x_a > $o,B: x_a > $o] : ( ord_less_eq_a_o @ ( minus_minus_a_o @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_Diff__subset) ).
thf(1613,plain,
! [A: x_a > $o,B: x_a > $o] : ( ord_less_eq_a_o @ ( minus_minus_a_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(284,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_insert__Diff__single) ).
thf(1359,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(347,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_332_xt1_I3_J) ).
thf(1601,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)],[347]) ).
thf(54,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_847_add__diff__assoc2) ).
thf(565,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)],[54]) ).
thf(320,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_472_subset__image__iff) ).
thf(1529,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)],[320]) ).
thf(402,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_446_le__funD) ).
thf(1803,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)],[402]) ).
thf(235,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ C @ ( insert_pname @ B @ A ) ) )
= ( minus_minus_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ C @ A ) ) @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_card__Diff__insert) ).
thf(1228,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ C @ ( insert_pname @ B @ A ) ) )
= ( minus_minus_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ C @ A ) ) @ one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(354,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_457_subset__insert) ).
thf(1623,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)],[354]) ).
thf(245,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_158_rev__finite__subset) ).
thf(1254,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)],[245]) ).
thf(256,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_506_equals0D) ).
thf(1287,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)],[256]) ).
thf(372,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(1709,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)],[372]) ).
thf(302,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_299_zero__induct__lemma) ).
thf(1430,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)],[302]) ).
thf(315,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_nat_Oinject) ).
thf(1511,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(409,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_666_image__constant) ).
thf(1826,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)],[409]) ).
thf(253,axiom,
! [A: pname > int > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_int_o @ ( image_pname_int_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__imageI) ).
thf(1279,plain,
! [A: pname > int > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_int_o @ ( image_pname_int_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(220,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) @ ( finite_card_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_card__Diff1__le) ).
thf(1191,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) @ ( finite_card_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(18,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_797_add__right__imp__eq) ).
thf(460,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)],[18]) ).
thf(272,axiom,
! [A: ( int > $o ) > $o,B: pname > int > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_int_o_o @ A @ ( image_pname_int_o @ B @ C ) )
=> ( finite_finite_int_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_finite__surj) ).
thf(1330,plain,
! [A: ( int > $o ) > $o,B: pname > int > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_int_o_o @ A @ ( image_pname_int_o @ B @ C ) )
=> ( finite_finite_int_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(248,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_247_finite__subset__image) ).
thf(1264,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)],[248]) ).
thf(61,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_848_diff__add__assoc2) ).
thf(587,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)],[61]) ).
thf(72,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_folding__one_Oinsert__remove) ).
thf(619,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(325,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_419_set__rev__mp) ).
thf(1545,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)],[325]) ).
thf(133,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(853,plain,
! [A: x_a,B: x_a] :
( ( A != B )
| ( fequal_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(316,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_173_le__diff__iff) ).
thf(1514,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)],[316]) ).
thf(336,axiom,
~ ( member_a @ ( mgt_call @ pn ) @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
thf(1572,plain,
~ ( member_a @ ( mgt_call @ pn ) @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(359,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_180_finite__surj) ).
thf(1641,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)],[359]) ).
thf(406,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_382_insert__absorb2) ).
thf(1815,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)],[406]) ).
thf(285,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_6_finite__Collect__subsets) ).
thf(1362,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)],[285]) ).
thf(268,axiom,
! [A: x_a] :
~ ( member_a @ A @ bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_emptyE) ).
thf(1319,plain,
! [A: x_a] :
~ ( member_a @ A @ bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(370,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite1819937229idem_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ( A != bot_bot_a_o )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_folding__one__idem_Osubset__idem) ).
thf(1704,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite1819937229idem_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ( A != bot_bot_a_o )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(364,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_383_insert__commute) ).
thf(1664,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)],[364]) ).
thf(298,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
= ( ( member_pname @ A @ B )
& ~ ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_723_Diff__iff) ).
thf(1418,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
= ( ( member_pname @ A @ B )
& ~ ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(36,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ B )
= ( plus_plus_nat @ one_one_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_card_Oremove) ).
thf(514,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ B )
= ( plus_plus_nat @ one_one_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_diff__add__inverse) ).
thf(574,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(339,axiom,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(1581,plain,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(182,axiom,
! [A: x_a,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ( member_a @ A @ B )
=> ( ( ( ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) )
= bot_bot_a_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) )
!= bot_bot_a_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_folding__one_Oremove) ).
thf(1040,plain,
! [A: x_a,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ( member_a @ A @ B )
=> ( ( ( ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) )
= bot_bot_a_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) )
!= bot_bot_a_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(356,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_482_image__subsetI) ).
thf(1632,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)],[356]) ).
thf(91,axiom,
! [A: x_a > $o,B: ( int > $o ) > x_a,C: ( int > $o ) > $o] :
( ( finite_finite_int_o @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_int_o_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_finite__surj) ).
thf(687,plain,
! [A: x_a > $o,B: ( int > $o ) > x_a,C: ( int > $o ) > $o] :
( ( finite_finite_int_o @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_int_o_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(159,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_165_le__SucE) ).
thf(956,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)],[159]) ).
thf(319,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_312_order__eq__iff) ).
thf(1526,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)],[319]) ).
thf(83,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_153_finite__subset) ).
thf(660,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)],[83]) ).
thf(167,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_127_le__trans) ).
thf(998,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)],[167]) ).
thf(164,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Suc__n__not__n) ).
thf(988,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(293,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_164_Suc__leD) ).
thf(1405,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)],[293]) ).
thf(367,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_453_insert__subset) ).
thf(1697,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)],[367]) ).
thf(140,axiom,
! [A: ( int > $o ) > $o,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( ( ord_less_eq_int_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_int_o @ A ) @ ( finite_card_int_o @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_card__mono) ).
thf(877,plain,
! [A: ( int > $o ) > $o,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( ( ord_less_eq_int_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_int_o @ A ) @ ( finite_card_int_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(93,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_602_singleton__iff) ).
thf(692,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)],[93]) ).
thf(6,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_843_le__diff__conv2) ).
thf(428,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)],[6]) ).
thf(224,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_351_order__trans) ).
thf(1201,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)],[224]) ).
thf(41,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_116_finite__Collect__conjI) ).
thf(529,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)],[41]) ).
thf(275,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_440_insert__compr__raw) ).
thf(1338,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)],[275]) ).
thf(394,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_295_insertE) ).
thf(1783,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)],[394]) ).
thf(190,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_248_finite__subset__image) ).
thf(1067,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)],[190]) ).
thf(100,axiom,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_insert__Diff) ).
thf(714,plain,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(357,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_397_insert__absorb) ).
thf(1636,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)],[357]) ).
thf(226,axiom,
! [A: pname > $o] :
( ( A != bot_bot_pname_o )
= ( ? [B: pname,C: pname > $o] :
( ( A
= ( insert_pname @ B @ C ) )
& ~ ( member_pname @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_nonempty__iff) ).
thf(1206,plain,
! [A: pname > $o] :
( ( A != bot_bot_pname_o )
= ( ? [B: pname,C: pname > $o] :
( ( A
= ( insert_pname @ B @ C ) )
& ~ ( member_pname @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(15,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_135_finite__Collect__disjI) ).
thf(452,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)],[15]) ).
thf(233,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C )
=> ( ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_diff__single__insert) ).
thf(1223,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C )
=> ( ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(176,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_432_image__iff) ).
thf(1021,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)],[176]) ).
thf(335,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_352_order__trans) ).
thf(1570,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)],[335]) ).
thf(65,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_841_le__add__diff__inverse) ).
thf(598,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)],[65]) ).
thf(385,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_291_insertCI) ).
thf(1751,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)],[385]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_add__left__mono) ).
thf(561,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(75,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( ( finite_card_a @ ( minus_minus_a_o @ A @ B ) )
= ( minus_minus_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_card__Diff__subset) ).
thf(630,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( ( finite_card_a @ ( minus_minus_a_o @ A @ B ) )
= ( minus_minus_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(123,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_396_insertI2) ).
thf(825,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)],[123]) ).
thf(277,axiom,
! [A: x_a > $o,B: x_a > x_a > x_a,C: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ B @ C )
=> ( ( finite_finite_a @ A )
=> ( ( A != bot_bot_a_o )
=> ( ! [D: x_a,E: x_a] : ( member_a @ ( B @ D @ E ) @ ( insert_a @ D @ ( insert_a @ E @ bot_bot_a_o ) ) )
=> ( member_a @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_folding__one_Oclosed) ).
thf(1343,plain,
! [A: x_a > $o,B: x_a > x_a > x_a,C: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ B @ C )
=> ( ( finite_finite_a @ A )
=> ( ( A != bot_bot_a_o )
=> ( ! [D: x_a,E: x_a] : ( member_a @ ( B @ D @ E ) @ ( insert_a @ D @ ( insert_a @ E @ bot_bot_a_o ) ) )
=> ( member_a @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(408,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_289_subsetD) ).
thf(1824,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)],[408]) ).
thf(287,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_order__eq__refl) ).
thf(1370,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(73,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_615_image__empty) ).
thf(625,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)],[73]) ).
thf(141,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_331_xt1_I3_J) ).
thf(879,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)],[141]) ).
thf(39,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_832_add__leE) ).
thf(522,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)],[39]) ).
thf(413,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_322_order__antisym__conv) ).
thf(1836,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)],[413]) ).
thf(193,axiom,
! [A: pname,B: pname > $o] :
( ~ ( member_pname @ A @ B )
=> ( ( minus_minus_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ bot_bot_pname_o ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_Diff__insert__absorb) ).
thf(1079,plain,
! [A: pname,B: pname > $o] :
( ~ ( member_pname @ A @ B )
=> ( ( minus_minus_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ bot_bot_pname_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(113,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_182_finite__surj) ).
thf(757,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)],[113]) ).
thf(48,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_826_trans__le__add1) ).
thf(551,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)],[48]) ).
thf(254,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_311_order__eq__iff) ).
thf(1281,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)],[254]) ).
thf(257,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_83_card__seteq) ).
thf(1291,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)],[257]) ).
thf(381,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_474_image__mono) ).
thf(1740,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)],[381]) ).
thf(222,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( member_a @ A @ ( minus_minus_a_o @ B @ C ) )
= ( ( member_a @ A @ B )
& ~ ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_Diff__iff) ).
thf(1195,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( member_a @ A @ ( minus_minus_a_o @ B @ C ) )
= ( ( member_a @ A @ B )
& ~ ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(294,axiom,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
= ( ( A = bot_bot_pname_o )
| ? [B: pname > $o,C: pname] :
( ( A
= ( insert_pname @ C @ B ) )
& ( finite_finite_pname @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_finite_Osimps) ).
thf(1407,plain,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
= ( ( A = bot_bot_pname_o )
| ? [B: pname > $o,C: pname] :
( ( A
= ( insert_pname @ C @ B ) )
& ( finite_finite_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(292,axiom,
! [A: pname > $o,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ! [D: pname,E: pname] : ( member_pname @ ( B @ D @ E ) @ ( insert_pname @ D @ ( insert_pname @ E @ bot_bot_pname_o ) ) )
=> ( member_pname @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_folding__one_Oclosed) ).
thf(1402,plain,
! [A: pname > $o,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ! [D: pname,E: pname] : ( member_pname @ ( B @ D @ E ) @ ( insert_pname @ D @ ( insert_pname @ E @ bot_bot_pname_o ) ) )
=> ( member_pname @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(280,axiom,
! [A: ( int > $o ) > $o,B: ( int > $o ) > $o] :
( ( ord_less_eq_int_o_o @ A @ B )
=> ( ( finite_finite_int_o @ B )
=> ( finite_finite_int_o @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_finite__subset) ).
thf(1350,plain,
! [A: ( int > $o ) > $o,B: ( int > $o ) > $o] :
( ( ord_less_eq_int_o_o @ A @ B )
=> ( ( finite_finite_int_o @ B )
=> ( finite_finite_int_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_add__le__cancel__right) ).
thf(519,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(189,axiom,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_mem__def) ).
thf(1064,plain,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(202,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_222_finite__subset__image) ).
thf(1111,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)],[202]) ).
thf(374,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_636_singleton__conv) ).
thf(1719,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)],[374]) ).
thf(137,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_3_finite__Collect__subsets) ).
thf(869,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)],[137]) ).
thf(69,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_816_add__le__imp__le__left) ).
thf(610,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)],[69]) ).
thf(3,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_842_add__diff__assoc) ).
thf(420,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)],[3]) ).
thf(134,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_267_lift__Suc__mono__le) ).
thf(857,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)],[134]) ).
thf(95,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_175_eq__diff__iff) ).
thf(697,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)],[95]) ).
thf(237,axiom,
finite_finite_pname @ bot_bot_pname_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_finite_OemptyI) ).
thf(1234,plain,
finite_finite_pname @ bot_bot_pname_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(139,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_126_le__antisym) ).
thf(874,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)],[139]) ).
thf(208,axiom,
! [A: x_a,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ~ ( member_a @ A @ B )
=> ( ( B != bot_bot_a_o )
=> ( ( D @ ( insert_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_folding__one_Oinsert) ).
thf(1143,plain,
! [A: x_a,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ~ ( member_a @ A @ B )
=> ( ( B != bot_bot_a_o )
=> ( ( D @ ( insert_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(249,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ A @ B ) )
= ( minus_minus_nat @ ( finite_card_pname @ A ) @ ( finite_card_pname @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_card__Diff__subset) ).
thf(1270,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ A @ B ) )
= ( minus_minus_nat @ ( finite_card_pname @ A ) @ ( finite_card_pname @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(418,axiom,
! [A: x_a] :
( ( collect_a @ ( fequal_a @ A ) )
= ( insert_a @ A @ bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_singleton__conv2) ).
thf(1851,plain,
! [A: x_a] :
( ( collect_a @ ( fequal_a @ A ) )
= ( insert_a @ A @ bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(21,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_48_card__image__le) ).
thf(471,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)],[21]) ).
thf(194,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_228_finite__subset__image) ).
thf(1082,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)],[194]) ).
thf(153,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_99_card__insert__if) ).
thf(933,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)],[153]) ).
thf(300,axiom,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_ex__in__conv) ).
thf(1424,plain,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(78,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ C ) )
= ( ( ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C ) )
& ( ~ ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_subset__insert__iff) ).
thf(642,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ C ) )
= ( ( ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C ) )
& ( ~ ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(229,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_76_card__mono) ).
thf(1214,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)],[229]) ).
thf(383,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_389_insert__ident) ).
thf(1744,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)],[383]) ).
thf(148,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( minus_minus_a_o @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( member_a @ C @ A )
& ~ ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_set__diff__eq) ).
thf(901,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( minus_minus_a_o @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( member_a @ C @ A )
& ~ ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(23,axiom,
! [A: ( int > $o ) > x_a,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_int_o_a @ A @ B ) ) @ ( finite_card_int_o @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_card__image__le) ).
thf(476,plain,
! [A: ( int > $o ) > x_a,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_int_o_a @ A @ B ) ) @ ( finite_card_int_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(297,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_341_xt1_I4_J) ).
thf(1414,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)],[297]) ).
thf(40,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_137_finite__Collect__disjI) ).
thf(526,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)],[40]) ).
thf(415,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 )
=> ( ( minus_minus_a_o @ C @ ( minus_minus_a_o @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_double__diff) ).
thf(1842,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 )
=> ( ( minus_minus_a_o @ C @ ( minus_minus_a_o @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(368,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_47_finite_OinsertI) ).
thf(1700,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)],[368]) ).
thf(28,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_822_le__add2) ).
thf(489,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(174,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( minus_minus_a_o @ ( insert_a @ B @ A ) @ C )
= ( minus_minus_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_insert__Diff1) ).
thf(1016,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( minus_minus_a_o @ ( insert_a @ B @ A ) @ C )
= ( minus_minus_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(62,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_827_trans__le__add2) ).
thf(590,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)],[62]) ).
thf(127,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_mem__def) ).
thf(837,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(270,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_592_singletonE) ).
thf(1324,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)],[270]) ).
thf(163,axiom,
! [A: pname > $o,B: pname > $o] :
( ( minus_minus_pname_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
& ~ ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_727_set__diff__eq) ).
thf(985,plain,
! [A: pname > $o,B: pname > $o] :
( ( minus_minus_pname_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
& ~ ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(211,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ B )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_minus_pname_o @ D @ ( insert_pname @ C @ bot_bot_pname_o ) ) ) ) ) )
=> ( A @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_finite__empty__induct) ).
thf(1150,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ B )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_minus_pname_o @ D @ ( insert_pname @ C @ bot_bot_pname_o ) ) ) ) ) )
=> ( A @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(259,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_161_rev__finite__subset) ).
thf(1297,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)],[259]) ).
thf(290,axiom,
! [A: ( x_a > $o ) > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( A @ B )
=> ( ! [C: x_a,D: x_a > $o] :
( ( finite_finite_a @ D )
=> ( ( member_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_minus_a_o @ D @ ( insert_a @ C @ bot_bot_a_o ) ) ) ) ) )
=> ( A @ bot_bot_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_finite__empty__induct) ).
thf(1382,plain,
! [A: ( x_a > $o ) > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( A @ B )
=> ( ! [C: x_a,D: x_a > $o] :
( ( finite_finite_a @ D )
=> ( ( member_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_minus_a_o @ D @ ( insert_a @ C @ bot_bot_a_o ) ) ) ) ) )
=> ( A @ bot_bot_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(204,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( member_a @ A @ B )
=> ( ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= ( minus_minus_nat @ ( finite_card_a @ B ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_card__Diff__singleton) ).
thf(1131,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( member_a @ A @ B )
=> ( ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= ( minus_minus_nat @ ( finite_card_a @ B ) @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(328,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_409_equalityD1) ).
thf(1552,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)],[328]) ).
thf(185,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( minus_minus_nat @ ( finite_card_pname @ B ) @ one_one_nat ) ) )
& ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( finite_card_pname @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_card__Diff__singleton__if) ).
thf(1050,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( minus_minus_nat @ ( finite_card_pname @ B ) @ one_one_nat ) ) )
& ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( finite_card_pname @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(152,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_681_finite__subset__induct) ).
thf(911,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)],[152]) ).
thf(411,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_order__refl) ).
thf(1831,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(236,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( member_a @ A @ B )
=> ( ( suc @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) )
= ( finite_card_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_card__Suc__Diff1) ).
thf(1231,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( member_a @ A @ B )
=> ( ( suc @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) )
= ( finite_card_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(76,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_107_card__insert__disjoint) ).
thf(633,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)],[76]) ).
thf(119,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_102_card__insert__if) ).
thf(805,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)],[119]) ).
thf(34,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_831_add__leD1) ).
thf(508,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)],[34]) ).
thf(332,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_217_finite__surj) ).
thf(1563,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)],[332]) ).
thf(51,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_821_add__Suc__shift) ).
thf(558,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)],[51]) ).
thf(88,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_294_insertCI) ).
thf(674,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)],[88]) ).
thf(178,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_460_subset__insert) ).
thf(1026,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)],[178]) ).
thf(378,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_286_equalityI) ).
thf(1732,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)],[378]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_eq__imp__le) ).
thf(662,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(144,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_168_le__Suc__eq) ).
thf(888,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)],[144]) ).
thf(150,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_49_card__image__le) ).
thf(906,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)],[150]) ).
thf(5,axiom,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_diff__Suc__1) ).
thf(425,plain,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(209,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_150_finite__subset) ).
thf(1146,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)],[209]) ).
thf(310,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( finite_finite_a @ ( minus_minus_a_o @ A @ ( insert_a @ B @ C ) ) )
= ( finite_finite_a @ ( minus_minus_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_finite__Diff__insert) ).
thf(1483,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( finite_finite_a @ ( minus_minus_a_o @ A @ ( insert_a @ B @ C ) ) )
= ( finite_finite_a @ ( minus_minus_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(250,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_91_card__insert__le) ).
thf(1273,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)],[250]) ).
thf(384,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_479_subsetI) ).
thf(1747,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)],[384]) ).
thf(92,axiom,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_all__not__in__conv) ).
thf(689,plain,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(12,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( plus_plus_nat @ one_one_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_770_card_Oinsert__remove) ).
thf(444,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( plus_plus_nat @ one_one_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(288,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) ) @ ( finite_card_a @ ( minus_minus_a_o @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_diff__card__le__card__Diff) ).
thf(1374,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) ) @ ( finite_card_a @ ( minus_minus_a_o @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(66,axiom,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ A @ one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_Suc__eq__plus1) ).
thf(601,plain,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ A @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(261,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_372_insert__compr) ).
thf(1301,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)],[261]) ).
thf(345,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_443_le__fun__def) ).
thf(1595,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)],[345]) ).
thf(121,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_emptyE) ).
thf(819,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(149,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_178_diff__le__mono2) ).
thf(904,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)],[149]) ).
thf(412,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_347_order__antisym) ).
thf(1833,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)],[412]) ).
thf(4,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_812_add__mono) ).
thf(423,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)],[4]) ).
thf(171,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_149_finite__subset) ).
thf(1007,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)],[171]) ).
thf(105,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_613_image__is__empty) ).
thf(732,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)],[105]) ).
thf(352,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_262_finite__subset__image) ).
thf(1615,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)],[352]) ).
thf(129,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_insert__absorb) ).
thf(843,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(109,axiom,
! [A: ( int > $o ) > x_a,B: ( int > $o ) > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_int_o_a @ A @ B ) )
=> ? [D: ( int > $o ) > $o] :
( ( ord_less_eq_int_o_o @ D @ B )
& ( finite_finite_int_o @ D )
& ( C
= ( image_int_o_a @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_finite__subset__image) ).
thf(743,plain,
! [A: ( int > $o ) > x_a,B: ( int > $o ) > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_int_o_a @ A @ B ) )
=> ? [D: ( int > $o ) > $o] :
( ( ord_less_eq_int_o_o @ D @ B )
& ( finite_finite_int_o @ D )
& ( C
= ( image_int_o_a @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(57,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_747_diff__Suc__eq__diff__pred) ).
thf(577,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)],[57]) ).
thf(399,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_596_doubleton__eq__iff) ).
thf(1795,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)],[399]) ).
thf(318,axiom,
! [A: x_a > int > $o,B: x_a > $o,C: ( int > $o ) > $o] :
( ( finite_finite_int_o @ C )
=> ( ( ord_less_eq_int_o_o @ C @ ( image_a_int_o @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_int_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_finite__subset__image) ).
thf(1520,plain,
! [A: x_a > int > $o,B: x_a > $o,C: ( int > $o ) > $o] :
( ( finite_finite_int_o @ C )
=> ( ( ord_less_eq_int_o_o @ C @ ( image_a_int_o @ A @ B ) )
=> ? [D: x_a > $o] :
( ( ord_less_eq_a_o @ D @ B )
& ( finite_finite_a @ D )
& ( C
= ( image_a_int_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(246,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( member_pname @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_DiffD2) ).
thf(1256,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( member_pname @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(46,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_838_diff__diff__right) ).
thf(545,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)],[46]) ).
thf(395,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_450_subset__insertI) ).
thf(1786,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)],[395]) ).
thf(371,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_160_rev__finite__subset) ).
thf(1707,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)],[371]) ).
thf(265,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_202_finite__surj) ).
thf(1312,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)],[265]) ).
thf(187,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_insert__Diff) ).
thf(1058,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(273,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_132_finite__Collect__disjI) ).
thf(1332,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)],[273]) ).
thf(247,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_folding__one_Oremove) ).
thf(1258,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(156,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( member_a @ A @ ( minus_minus_a_o @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_DiffE) ).
thf(947,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( member_a @ A @ ( minus_minus_a_o @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(283,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_523_empty__Collect__eq) ).
thf(1356,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)],[283]) ).
thf(87,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_204_finite__surj) ).
thf(672,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)],[87]) ).
thf(387,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_415_in__mono) ).
thf(1765,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)],[387]) ).
thf(196,axiom,
! [A: ( int > $o ) > $o,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( ( ord_less_eq_int_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_int_o @ B ) @ ( finite_card_int_o @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_card__seteq) ).
thf(1090,plain,
! [A: ( int > $o ) > $o,B: ( int > $o ) > $o] :
( ( finite_finite_int_o @ B )
=> ( ( ord_less_eq_int_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_int_o @ B ) @ ( finite_card_int_o @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(366,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_678_finite__subset__induct) ).
thf(1675,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)],[366]) ).
thf(44,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_845_le__imp__diff__is__add) ).
thf(540,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)],[44]) ).
thf(67,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_801_nat__add__left__cancel) ).
thf(604,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)],[67]) ).
thf(227,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_order__refl) ).
thf(1209,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(184,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_189_finite__surj) ).
thf(1048,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)],[184]) ).
thf(343,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(1589,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)],[343]) ).
thf(375,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_406_set__eq__subset) ).
thf(1722,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)],[375]) ).
thf(289,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_230_finite__subset__image) ).
thf(1376,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)],[289]) ).
thf(263,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_510_Collect__empty__eq) ).
thf(1307,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)],[263]) ).
thf(337,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_412_equalityD2) ).
thf(1574,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)],[337]) ).
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(419,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(390,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_437_insert__compr__raw) ).
thf(1771,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)],[390]) ).
thf(107,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_167_Suc__le__mono) ).
thf(737,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)],[107]) ).
thf(401,axiom,
! [A: pname > x_a,B: pname > $o,C: pname > $o] : ( ord_less_eq_a_o @ ( minus_minus_a_o @ ( image_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) @ ( image_pname_a @ A @ ( minus_minus_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_image__diff__subset) ).
thf(1801,plain,
! [A: pname > x_a,B: pname > $o,C: pname > $o] : ( ord_less_eq_a_o @ ( minus_minus_a_o @ ( image_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) @ ( image_pname_a @ A @ ( minus_minus_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(8,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_800_nat__add__assoc) ).
thf(434,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)],[8]) ).
thf(365,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_430_equalityE) ).
thf(1667,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)],[365]) ).
thf(120,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( ( member_a @ B @ C )
=> ( ( minus_minus_a_o @ ( insert_a @ B @ A ) @ C )
= ( minus_minus_a_o @ A @ C ) ) )
& ( ~ ( member_a @ B @ C )
=> ( ( minus_minus_a_o @ ( insert_a @ B @ A ) @ C )
= ( insert_a @ B @ ( minus_minus_a_o @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_insert__Diff__if) ).
thf(811,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( ( member_a @ B @ C )
=> ( ( minus_minus_a_o @ ( insert_a @ B @ A ) @ C )
= ( minus_minus_a_o @ A @ C ) ) )
& ( ~ ( member_a @ B @ C )
=> ( ( minus_minus_a_o @ ( insert_a @ B @ A ) @ C )
= ( insert_a @ B @ ( minus_minus_a_o @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(306,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( plus_plus_nat @ one_one_nat @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_card_Oinsert__remove) ).
thf(1471,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( plus_plus_nat @ one_one_nat @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(30,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_136_finite__Collect__disjI) ).
thf(494,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)],[30]) ).
thf(103,axiom,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_equals0D) ).
thf(726,plain,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(26,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_820_add__Suc) ).
thf(483,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)],[26]) ).
thf(96,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( member_a @ B @ C )
=> ( ~ ( member_a @ B @ A )
=> ( ( finite_card_a @ ( minus_minus_a_o @ C @ ( insert_a @ B @ A ) ) )
= ( minus_minus_nat @ ( finite_card_a @ ( minus_minus_a_o @ C @ A ) ) @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_751_card__Diff__insert) ).
thf(700,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( member_a @ B @ C )
=> ( ~ ( member_a @ B @ A )
=> ( ( finite_card_a @ ( minus_minus_a_o @ C @ ( insert_a @ B @ A ) ) )
= ( minus_minus_nat @ ( finite_card_a @ ( minus_minus_a_o @ C @ A ) ) @ one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(329,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_357_xt1_I5_J) ).
thf(1556,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)],[329]) ).
thf(188,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ B ) )
= ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_finite__Diff2) ).
thf(1061,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ B ) )
= ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(179,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_186_finite__surj) ).
thf(1029,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)],[179]) ).
thf(147,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_221_finite__subset__image) ).
thf(895,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)],[147]) ).
thf(213,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_27_finite__imageI) ).
thf(1171,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)],[213]) ).
thf(162,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_206_finite__surj) ).
thf(983,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)],[162]) ).
thf(223,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_169_not__less__eq__eq) ).
thf(1198,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)],[223]) ).
thf(307,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_81_card__seteq) ).
thf(1474,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)],[307]) ).
thf(160,axiom,
! [A: ( int > $o ) > $o] :
( ( finite_finite_int_o @ A )
=> ( finite229719499nt_o_o
@ ( collect_int_o_o
@ ^ [B: ( int > $o ) > $o] : ( ord_less_eq_int_o_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
thf(959,plain,
! [A: ( int > $o ) > $o] :
( ( finite_finite_int_o @ A )
=> ( finite229719499nt_o_o
@ ( collect_int_o_o
@ ^ [B: ( int > $o ) > $o] : ( ord_less_eq_int_o_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(124,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_249_finite__subset__image) ).
thf(827,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)],[124]) ).
thf(360,axiom,
! [A: x_a > $o] :
( ( the_elem_a @ A )
= ( the_a
@ ^ [B: x_a] :
( A
= ( insert_a @ B @ bot_bot_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_the__elem__def) ).
thf(1643,plain,
! [A: x_a > $o] :
( ( the_elem_a @ A )
= ( the_a
@ ^ [B: x_a] :
( A
= ( insert_a @ B @ bot_bot_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(215,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_folding__one__idem_Oinsert__idem) ).
thf(1176,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(53,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_808_add__right__mono) ).
thf(563,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)],[53]) ).
thf(168,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( minus_minus_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_insert__Diff1) ).
thf(1000,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( minus_minus_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(308,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_758_folding__one_Oinsert) ).
thf(1477,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(286,axiom,
! [A: x_a,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ( ( ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) )
= bot_bot_a_o )
=> ( ( D @ ( insert_a @ A @ B ) )
= A ) )
& ( ( ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) )
!= bot_bot_a_o )
=> ( ( D @ ( insert_a @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_folding__one_Oinsert__remove) ).
thf(1364,plain,
! [A: x_a,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ( ( ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) )
= bot_bot_a_o )
=> ( ( D @ ( insert_a @ A @ B ) )
= A ) )
& ( ( ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) )
!= bot_bot_a_o )
=> ( ( D @ ( insert_a @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(132,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_38_finite__imageI) ).
thf(851,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)],[132]) ).
thf(33,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_819_add__Suc__right) ).
thf(505,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)],[33]) ).
thf(7,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_844_le__add__diff__inverse2) ).
thf(431,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)],[7]) ).
thf(403,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
!= bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_insert__not__empty) ).
thf(1805,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
!= bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(77,axiom,
! [A: pname > int > $o,B: pname > $o,C: ( int > $o ) > $o] :
( ( finite_finite_int_o @ C )
=> ( ( ord_less_eq_int_o_o @ C @ ( image_pname_int_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_int_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_finite__subset__image) ).
thf(636,plain,
! [A: pname > int > $o,B: pname > $o,C: ( int > $o ) > $o] :
( ( finite_finite_int_o @ C )
=> ( ( ord_less_eq_int_o_o @ C @ ( image_pname_int_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_int_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(94,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_159_rev__finite__subset) ).
thf(695,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)],[94]) ).
thf(242,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_356_xt1_I5_J) ).
thf(1245,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)],[242]) ).
thf(16,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_846_diff__add__assoc) ).
thf(455,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)],[16]) ).
thf(142,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_171_Suc__diff__diff) ).
thf(883,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)],[142]) ).
thf(355,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_223_finite__subset__image) ).
thf(1626,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)],[355]) ).
thf(181,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_232_finite__subset__image) ).
thf(1034,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)],[181]) ).
thf(341,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_388_insert__code) ).
thf(1583,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)],[341]) ).
thf(404,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_487_assms_I3_J) ).
thf(1809,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)],[404]) ).
thf(262,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_392_insert__ident) ).
thf(1304,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)],[262]) ).
thf(225,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_144_finite__insert) ).
thf(1203,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)],[225]) ).
thf(47,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_837_diff__cancel2) ).
thf(548,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)],[47]) ).
thf(252,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_le__refl) ).
thf(1277,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(314,axiom,
! [A: pname > $o,B: ( int > $o ) > pname,C: ( int > $o ) > $o] :
( ( finite_finite_int_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_int_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_finite__surj) ).
thf(1509,plain,
! [A: pname > $o,B: ( int > $o ) > pname,C: ( int > $o ) > $o] :
( ( finite_finite_int_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_int_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(110,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_174_Nat_Odiff__diff__eq) ).
thf(749,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)],[110]) ).
thf(154,axiom,
! [A: ( int > $o ) > pname,B: ( int > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_int_o_pname @ A @ B ) )
=> ? [D: ( int > $o ) > $o] :
( ( ord_less_eq_int_o_o @ D @ B )
& ( finite_finite_int_o @ D )
& ( C
= ( image_int_o_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_finite__subset__image) ).
thf(939,plain,
! [A: ( int > $o ) > pname,B: ( int > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_int_o_pname @ A @ B ) )
=> ? [D: ( int > $o ) > $o] :
( ( ord_less_eq_int_o_o @ D @ B )
& ( finite_finite_int_o @ D )
& ( C
= ( image_int_o_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(49,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_nat__add__commute) ).
thf(553,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(22,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_825_nat__add__left__cancel__le) ).
thf(473,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)],[22]) ).
thf(192,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( minus_minus_a_o @ A @ ( insert_a @ B @ C ) )
= ( minus_minus_a_o @ ( minus_minus_a_o @ A @ ( insert_a @ B @ bot_bot_a_o ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_Diff__insert2) ).
thf(1076,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( minus_minus_a_o @ A @ ( insert_a @ B @ C ) )
= ( minus_minus_a_o @ ( minus_minus_a_o @ A @ ( insert_a @ B @ bot_bot_a_o ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(116,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_220_finite__subset__image) ).
thf(795,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)],[116]) ).
thf(89,axiom,
! [A: x_a > $o] :
( ( minus_minus_a_o @ A @ A )
= bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_Diff__cancel) ).
thf(680,plain,
! [A: x_a > $o] :
( ( minus_minus_a_o @ A @ A )
= bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(205,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_456_insert__subset) ).
thf(1134,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)],[205]) ).
thf(80,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_436_rev__image__eqI) ).
thf(648,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)],[80]) ).
thf(17,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_830_add__leD2) ).
thf(458,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)],[17]) ).
thf(217,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( suc @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) )
= ( finite_card_pname @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_card__Suc__Diff1) ).
thf(1181,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( suc @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) )
= ( finite_card_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(416,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_317_order__eq__refl) ).
thf(1845,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)],[416]) ).
thf(326,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( ord_less_eq_a_o @ A @ ( insert_a @ B @ C ) )
= ( ( ( member_a @ B @ A )
=> ( ord_less_eq_a_o @ ( minus_minus_a_o @ A @ ( insert_a @ B @ bot_bot_a_o ) ) @ C ) )
& ( ~ ( member_a @ B @ A )
=> ( ord_less_eq_a_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_subset__insert__iff) ).
thf(1547,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( ord_less_eq_a_o @ A @ ( insert_a @ B @ C ) )
= ( ( ( member_a @ B @ A )
=> ( ord_less_eq_a_o @ ( minus_minus_a_o @ A @ ( insert_a @ B @ bot_bot_a_o ) ) @ C ) )
& ( ~ ( member_a @ B @ A )
=> ( ord_less_eq_a_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(400,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_373_insert__Collect) ).
thf(1798,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)],[400]) ).
thf(169,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_75_card__mono) ).
thf(1003,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)],[169]) ).
thf(58,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_828_add__le__mono1) ).
thf(580,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)],[58]) ).
thf(346,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_468_image__insert) ).
thf(1598,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)],[346]) ).
thf(98,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_298_insertE) ).
thf(705,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)],[98]) ).
thf(334,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_337_ord__le__eq__trans) ).
thf(1566,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)],[334]) ).
thf(348,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_empty__subsetI) ).
thf(1605,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(393,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_470_insert__image) ).
thf(1780,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)],[393]) ).
thf(234,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_387_insert__iff) ).
thf(1225,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)],[234]) ).
thf(291,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_5_finite__Collect__subsets) ).
thf(1400,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)],[291]) ).
thf(158,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_diff__le__self) ).
thf(954,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(244,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_361_xt1_I6_J) ).
thf(1252,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)],[244]) ).
thf(373,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_630_Collect__conv__if) ).
thf(1711,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)],[373]) ).
thf(397,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_660_subset__singletonD) ).
thf(1790,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)],[397]) ).
thf(405,axiom,
! [A: pname] :
( ( member_pname @ A @ u )
=> ( wt @ ( the_com @ ( body @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_assms_I4_J) ).
thf(1813,plain,
! [A: pname] :
( ( member_pname @ A @ u )
=> ( wt @ ( the_com @ ( body @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(219,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_82_card__seteq) ).
thf(1188,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)],[219]) ).
thf(60,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_840_le__add__diff) ).
thf(585,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)],[60]) ).
thf(101,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_172_diff__Suc__Suc) ).
thf(717,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)],[101]) ).
thf(128,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_176_diff__diff__cancel) ).
thf(840,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)],[128]) ).
thf(238,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_94_card__insert__le) ).
thf(1235,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)],[238]) ).
thf(157,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_300_Suc__le__D) ).
thf(951,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)],[157]) ).
thf(232,axiom,
! [A: x_a] :
~ ( member_a @ A @ bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_empty__iff) ).
thf(1220,plain,
! [A: x_a] :
~ ( member_a @ A @ bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(380,axiom,
! [A: x_a,B: x_a > $o] : ( member_a @ A @ ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_insertI1) ).
thf(1738,plain,
! [A: x_a,B: x_a > $o] : ( member_a @ A @ ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(231,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_177_diff__le__mono) ).
thf(1218,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)],[231]) ).
thf(324,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_152_finite__subset) ).
thf(1543,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)],[324]) ).
thf(417,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_682_assms_I2_J) ).
thf(1849,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)],[417]) ).
thf(97,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_69_card__image__le) ).
thf(703,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)],[97]) ).
thf(369,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_423_set__mp) ).
thf(1702,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)],[369]) ).
thf(255,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( minus_minus_nat @ ( finite_card_pname @ B ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_card__Diff__singleton) ).
thf(1284,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( minus_minus_nat @ ( finite_card_pname @ B ) @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(313,axiom,
! [A: x_a,B: x_a > $o] :
( ~ ( member_a @ A @ B )
=> ( ( minus_minus_a_o @ ( insert_a @ A @ B ) @ ( insert_a @ A @ bot_bot_a_o ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_Diff__insert__absorb) ).
thf(1506,plain,
! [A: x_a,B: x_a > $o] :
( ~ ( member_a @ A @ B )
=> ( ( minus_minus_a_o @ ( insert_a @ A @ B ) @ ( insert_a @ A @ bot_bot_a_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(301,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( member_a @ A @ ( minus_minus_a_o @ B @ C ) )
=> ( member_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_DiffD1) ).
thf(1427,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( member_a @ A @ ( minus_minus_a_o @ B @ C ) )
=> ( member_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(312,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_4_finite__Collect__subsets) ).
thf(1504,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)],[312]) ).
thf(207,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_80_card__seteq) ).
thf(1140,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)],[207]) ).
thf(64,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_802_nat__add__right__cancel) ).
thf(595,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)],[64]) ).
thf(70,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_le__add1) ).
thf(612,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(31,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_839_le__diff__conv) ).
thf(497,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)],[31]) ).
thf(135,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_265_lift__Suc__mono__le) ).
thf(859,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)],[135]) ).
thf(240,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_595_singletonE) ).
thf(1240,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)],[240]) ).
thf(414,axiom,
! [A: x_a,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite1819937229idem_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ( B != bot_bot_a_o )
=> ( ( D @ ( insert_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_folding__one__idem_Oinsert__idem) ).
thf(1839,plain,
! [A: x_a,B: x_a > $o,C: x_a > x_a > x_a,D: ( x_a > $o ) > x_a] :
( ( finite1819937229idem_a @ C @ D )
=> ( ( finite_finite_a @ B )
=> ( ( B != bot_bot_a_o )
=> ( ( D @ ( insert_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(50,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_add__le__imp__le__right) ).
thf(556,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(296,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_420_set__rev__mp) ).
thf(1412,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)],[296]) ).
thf(317,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_84_card__seteq) ).
thf(1517,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)],[317]) ).
thf(114,axiom,
! [A: ( x_a > $o ) > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( A @ bot_bot_a_o )
=> ( ! [C: x_a,D: x_a > $o] :
( ( finite_finite_a @ D )
=> ( ~ ( member_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_a @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_finite__induct) ).
thf(759,plain,
! [A: ( x_a > $o ) > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( A @ bot_bot_a_o )
=> ( ! [C: x_a,D: x_a > $o] :
( ( finite_finite_a @ D )
=> ( ~ ( member_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_a @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(201,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( member_a @ A @ B )
=> ( ( finite_card_a @ B )
= ( plus_plus_nat @ one_one_nat @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_card_Oremove) ).
thf(1108,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( member_a @ A @ B )
=> ( ( finite_card_a @ B )
= ( plus_plus_nat @ one_one_nat @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(299,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ( member_pname @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_DiffD1) ).
thf(1421,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ( member_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(19,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_835_diff__diff__left) ).
thf(465,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)],[19]) ).
thf(267,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( minus_minus_a_o @ A @ ( insert_a @ B @ C ) )
= ( minus_minus_a_o @ ( minus_minus_a_o @ A @ C ) @ ( insert_a @ B @ bot_bot_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_Diff__insert) ).
thf(1316,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( minus_minus_a_o @ A @ ( insert_a @ B @ C ) )
= ( minus_minus_a_o @ ( minus_minus_a_o @ A @ C ) @ ( insert_a @ B @ bot_bot_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(362,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_225_finite__subset__image) ).
thf(1649,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)],[362]) ).
thf(14,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_829_add__le__mono) ).
thf(450,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)],[14]) ).
thf(230,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_187_finite__surj) ).
thf(1216,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)],[230]) ).
thf(145,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_pname @ A ) @ ( finite_card_pname @ B ) ) @ ( finite_card_pname @ ( minus_minus_pname_o @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_diff__card__le__card__Diff) ).
thf(891,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_pname @ A ) @ ( finite_card_pname @ B ) ) @ ( finite_card_pname @ ( minus_minus_pname_o @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(361,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_621_le__bot) ).
thf(1646,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)],[361]) ).
thf(161,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ! [C: pname] : ( A @ ( insert_pname @ C @ bot_bot_pname_o ) )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( D != bot_bot_pname_o )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_782_finite__ne__induct) ).
thf(961,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ! [C: pname] : ( A @ ( insert_pname @ C @ bot_bot_pname_o ) )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( D != bot_bot_pname_o )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(37,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_853_termination__basic__simps_I4_J) ).
thf(517,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)],[37]) ).
thf(276,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_266_lift__Suc__mono__le) ).
thf(1341,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)],[276]) ).
thf(358,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_362_xt1_I6_J) ).
thf(1639,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)],[358]) ).
thf(199,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_DiffE) ).
thf(1101,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(81,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_empty__iff) ).
thf(652,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(166,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_card__insert) ).
thf(995,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(55,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_53_card__image__le) ).
thf(568,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)],[55]) ).
thf(35,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_115_finite__Collect__conjI) ).
thf(510,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)],[35]) ).
thf(392,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_589_singleton__inject) ).
thf(1777,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)],[392]) ).
thf(258,axiom,
! [A: x_a > $o] :
( ( minus_minus_a_o @ bot_bot_a_o @ A )
= bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_empty__Diff) ).
thf(1294,plain,
! [A: x_a > $o] :
( ( minus_minus_a_o @ bot_bot_a_o @ A )
= bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(303,axiom,
! [A: x_a > $o] :
( ( finite_finite_a @ A )
= ( ( A = bot_bot_a_o )
| ? [B: x_a > $o,C: x_a] :
( ( A
= ( insert_a @ C @ B ) )
& ( finite_finite_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_finite_Osimps) ).
thf(1440,plain,
! [A: x_a > $o] :
( ( finite_finite_a @ A )
= ( ( A = bot_bot_a_o )
| ? [B: x_a > $o,C: x_a] :
( ( A
= ( insert_a @ C @ B ) )
& ( finite_finite_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(221,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_183_finite__surj) ).
thf(1193,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)],[221]) ).
thf(24,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_791_add__right__cancel) ).
thf(478,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)],[24]) ).
thf(349,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_611_subset__empty) ).
thf(1607,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)],[349]) ).
thf(43,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_114_finite__Collect__conjI) ).
thf(536,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)],[43]) ).
thf(279,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_44_finite_OinsertI) ).
thf(1348,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)],[279]) ).
thf(111,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_119_Suc__diff__le) ).
thf(752,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)],[111]) ).
thf(391,axiom,
! [A: x_a,B: x_a > x_a > x_a,C: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ B @ C )
=> ( ( C @ ( insert_a @ A @ bot_bot_a_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_folding__one_Osingleton) ).
thf(1774,plain,
! [A: x_a,B: x_a > x_a > x_a,C: ( x_a > $o ) > x_a] :
( ( finite_folding_one_a @ B @ C )
=> ( ( C @ ( insert_a @ A @ bot_bot_a_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(13,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_diff__add__inverse2) ).
thf(447,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(376,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_147_finite__insert) ).
thf(1725,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)],[376]) ).
thf(338,axiom,
! [A: x_a] :
( ( the_elem_a @ ( insert_a @ A @ bot_bot_a_o ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_the__elem__eq) ).
thf(1578,plain,
! [A: x_a] :
( ( the_elem_a @ ( insert_a @ A @ bot_bot_a_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(125,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( member_a @ A @ ( minus_minus_a_o @ B @ C ) )
=> ~ ( member_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_DiffD2) ).
thf(833,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( member_a @ A @ ( minus_minus_a_o @ B @ C ) )
=> ~ ( member_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(210,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_11_finite__imageI) ).
thf(1148,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)],[210]) ).
thf(243,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_111_finite__Collect__conjI) ).
thf(1248,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)],[243]) ).
thf(386,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_633_Collect__conv__if2) ).
thf(1757,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)],[386]) ).
thf(309,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_card__insert) ).
thf(1480,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(106,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_166_le__SucI) ).
thf(735,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)],[106]) ).
thf(198,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_280_pigeonhole__infinite) ).
thf(1097,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)],[198]) ).
thf(126,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_10_finite__imageI) ).
thf(835,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)],[126]) ).
thf(117,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_2_finite__Collect__subsets) ).
thf(801,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)],[117]) ).
thf(266,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_129_nat__le__linear) ).
thf(1314,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)],[266]) ).
thf(331,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_461_subset__insertI2) ).
thf(1561,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)],[331]) ).
thf(295,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( minus_minus_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_finite__Diff) ).
thf(1410,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( minus_minus_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(186,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_205_finite__surj) ).
thf(1056,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)],[186]) ).
thf(102,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ( member_a @ A @ B )
=> ( ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= ( minus_minus_nat @ ( finite_card_a @ B ) @ one_one_nat ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= ( finite_card_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_card__Diff__singleton__if) ).
thf(720,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ( member_a @ A @ B )
=> ( ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= ( minus_minus_nat @ ( finite_card_a @ B ) @ one_one_nat ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( minus_minus_a_o @ B @ ( insert_a @ A @ bot_bot_a_o ) ) )
= ( finite_card_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(9,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_836_diff__cancel) ).
thf(437,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)],[9]) ).
thf(274,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_617_empty__is__image) ).
thf(1335,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)],[274]) ).
thf(278,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_290_subsetD) ).
thf(1346,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)],[278]) ).
thf(350,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_369_insert__compr) ).
thf(1610,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)],[350]) ).
thf(143,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_184_finite__surj) ).
thf(886,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)],[143]) ).
thf(382,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_427_subset__trans) ).
thf(1742,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)],[382]) ).
thf(197,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_283_image__eqI) ).
thf(1093,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)],[197]) ).
thf(108,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_529_ex__in__conv) ).
thf(740,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)],[108]) ).
thf(281,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_188_finite__surj) ).
thf(1352,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)],[281]) ).
thf(321,axiom,
finite_finite_pname @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1532,plain,
finite_finite_pname @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(323,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_226_finite__subset__image) ).
thf(1537,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)],[323]) ).
thf(327,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o,D: x_a > $o] :
( ( ord_less_eq_a_o @ C @ D )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_a_o @ ( minus_minus_a_o @ C @ B ) @ ( minus_minus_a_o @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_Diff__mono) ).
thf(1550,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o,D: x_a > $o] :
( ( ord_less_eq_a_o @ C @ D )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_a_o @ ( minus_minus_a_o @ C @ B ) @ ( minus_minus_a_o @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(122,axiom,
! [A: x_a > $o] :
( ( minus_minus_a_o @ A @ bot_bot_a_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_Diff__empty) ).
thf(822,plain,
! [A: x_a > $o] :
( ( minus_minus_a_o @ A @ bot_bot_a_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(131,axiom,
finite_finite_a @ bot_bot_a_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_finite_OemptyI) ).
thf(850,plain,
finite_finite_a @ bot_bot_a_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(260,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_151_finite__subset) ).
thf(1299,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)],[260]) ).
thf(11,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_51_card__image__le) ).
thf(442,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)],[11]) ).
thf(138,axiom,
! [A: x_a > $o] :
( ( A != bot_bot_a_o )
= ( ? [B: x_a,C: x_a > $o] :
( ( A
= ( insert_a @ B @ C ) )
& ~ ( member_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_nonempty__iff) ).
thf(871,plain,
! [A: x_a > $o] :
( ( A != bot_bot_a_o )
= ( ? [B: x_a,C: x_a > $o] :
( ( A
= ( insert_a @ B @ C ) )
& ~ ( member_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(353,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( ord_less_eq_a_o @ ( minus_minus_a_o @ A @ ( insert_a @ B @ bot_bot_a_o ) ) @ C )
=> ( ( member_a @ B @ A )
=> ( ord_less_eq_a_o @ A @ ( insert_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_diff__single__insert) ).
thf(1621,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( ord_less_eq_a_o @ ( minus_minus_a_o @ A @ ( insert_a @ B @ bot_bot_a_o ) ) @ C )
=> ( ( member_a @ B @ A )
=> ( ord_less_eq_a_o @ A @ ( insert_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(68,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_824_le__iff__add) ).
thf(607,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)],[68]) ).
thf(410,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_subset__refl) ).
thf(1829,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(203,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_25_finite__imageI) ).
thf(1129,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)],[203]) ).
thf(340,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(1582,plain,
ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(175,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( member_pname @ B @ ( minus_minus_pname_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_DiffI) ).
thf(1019,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( member_pname @ B @ ( minus_minus_pname_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(151,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_599_singleton__iff) ).
thf(908,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)],[151]) ).
thf(165,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_110_card__insert__disjoint) ).
thf(992,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)],[165]) ).
thf(27,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_787_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(486,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)],[27]) ).
thf(118,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_307_linorder__linear) ).
thf(803,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)],[118]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Suc__inject) ).
thf(1009,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(218,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_336_ord__le__eq__trans) ).
thf(1184,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)],[218]) ).
thf(333,axiom,
member_pname @ pn @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(1565,plain,
member_pname @ pn @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(45,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_52_card__image__le) ).
thf(543,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)],[45]) ).
thf(305,axiom,
! [A: ( x_a > $o ) > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( B != bot_bot_a_o )
=> ( ! [C: x_a] : ( A @ ( insert_a @ C @ bot_bot_a_o ) )
=> ( ! [C: x_a,D: x_a > $o] :
( ( finite_finite_a @ D )
=> ( ( D != bot_bot_a_o )
=> ( ~ ( member_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_a @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_779_finite__ne__induct) ).
thf(1449,plain,
! [A: ( x_a > $o ) > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( B != bot_bot_a_o )
=> ( ! [C: x_a] : ( A @ ( insert_a @ C @ bot_bot_a_o ) )
=> ( ! [C: x_a,D: x_a > $o] :
( ( finite_finite_a @ D )
=> ( ( D != bot_bot_a_o )
=> ( ~ ( member_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_a @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(63,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_799_nat__add__left__commute) ).
thf(592,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)],[63]) ).
thf(99,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_246_finite__subset__image) ).
thf(708,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)],[99]) ).
thf(173,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_434_imageI) ).
thf(1014,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)],[173]) ).
thf(389,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_464_insert__mono) ).
thf(1769,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)],[389]) ).
thf(112,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_73_card__mono) ).
thf(755,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)],[112]) ).
thf(29,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_806_add__le__cancel__left) ).
thf(491,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)],[29]) ).
thf(195,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_424_set__mp) ).
thf(1088,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)],[195]) ).
thf(1927,plain,
$false,
inference(e,[status(thm)],[645,1322,1586,1024,1168,1767,893,468,1179,777,481,1559,1105,1237,846,628,1031,666,1818,1211,582,1005,683,730,1443,1073,1728,1591,614,861,440,655,1793,1533,1173,1486,1788,1655,1137,1735,500,1275,1327,945,1354,670,1310,533,1243,1046,1613,1359,1601,565,1529,1803,1228,1623,1254,1287,1709,1430,1511,1826,1279,1191,460,1330,1264,587,619,1545,853,1514,1572,1641,1815,1362,1319,1704,1664,1418,514,574,1581,1040,1632,687,956,1526,660,998,988,1405,1697,877,692,428,1201,529,1338,1783,1067,714,1636,1206,452,1223,1021,1570,598,1751,561,630,825,1343,1824,1370,625,879,522,1836,1079,757,551,1281,1291,1740,1195,1407,1402,1350,519,1064,1111,1719,869,610,420,857,697,1234,874,1143,1270,1851,471,1082,933,1424,642,1214,1744,901,476,1414,526,1842,1700,489,1016,590,837,1324,985,1150,1297,1382,1131,1552,1050,911,1831,1231,633,805,508,1563,558,674,1026,1732,662,888,906,425,1146,1483,1273,1747,689,444,1374,601,1301,1595,819,904,1833,423,1007,732,1615,843,743,577,1795,1520,1256,545,1786,1707,1312,1058,1332,1258,947,1356,672,1765,1090,1675,540,604,1209,1048,1589,1722,1376,1307,1574,419,1771,737,1801,434,1667,811,1471,494,726,483,700,1556,1061,1029,895,1171,983,1198,1474,959,827,1643,1176,563,1000,1477,1364,851,505,431,1805,636,695,1245,455,883,1626,1034,1583,1809,1304,1203,548,1277,1509,749,939,553,473,1076,795,680,1134,648,458,1181,1845,1547,1798,1003,580,1598,705,1566,1605,1780,1225,1400,954,1252,1711,1790,1813,1188,585,717,840,1235,951,1220,1738,1218,1543,1849,703,1702,1284,1506,1427,1504,1140,595,612,497,859,1240,1839,556,1412,1517,759,1108,1421,465,1316,1649,450,1216,891,1646,961,517,1341,1639,1101,652,995,568,510,1777,1294,1440,1193,478,1607,536,1348,752,1774,447,1725,1578,833,1148,1248,1757,1480,735,1097,835,801,1314,1561,1410,1056,720,437,1335,1346,1610,886,1742,1093,740,1352,1532,1537,1550,822,850,1299,442,871,1621,607,1829,1129,1582,1019,908,992,486,803,1009,1184,1565,543,1449,592,708,1014,1769,755,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473^3 : 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
% 0.10/0.22 % Computer : n016.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 16:10:49 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.01/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.72/1.37 % [INFO] Parsing done (558ms).
% 2.72/1.38 % [INFO] Running in sequential loop mode.
% 3.74/1.76 % [INFO] eprover registered as external prover.
% 3.74/1.77 % [INFO] Scanning for conjecture ...
% 4.18/1.98 % [INFO] Found a conjecture (or negated_conjecture) and 1214 axioms. Running axiom selection ...
% 5.31/2.23 % [INFO] Axiom selection finished. Selected 416 axioms (removed 798 axioms).
% 6.20/2.56 % [INFO] Problem is higher-order (TPTP THF).
% 6.20/2.58 % [INFO] Type checking passed.
% 6.20/2.59 % [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 ...
% 26.33/7.19 % External prover 'e' found a proof!
% 26.33/7.19 % [INFO] Killing All external provers ...
% 26.33/7.19 % Time passed: 6816ms (effective reasoning time: 5804ms)
% 26.33/7.19 % 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)>
% 26.59/7.20 % Axioms used in derivation (416): fact_131_diff__commute, fact_660_subset__singletonD, fact_24_finite__imageI, fact_126_le__antisym, fact_83_card__seteq, fact_650_card__Diff1__le, fact_804_add__le__cancel__right, fact_283_image__eqI, fact_129_nat__le__linear, fact_551_Diff__insert__absorb, fact_227_finite__subset__image, fact_181_finite__surj, fact_747_diff__Suc__eq__diff__pred, fact_179_diff__le__self, fact_232_finite__subset__image, fact_321_order__antisym__conv, fact_767_card_Oinsert__remove, fact_125_n__not__Suc__n, fact_295_insertE, fact_851_diff__Suc__diff__eq1, fact_832_add__leE, fact_327_ord__eq__le__trans, fact_783_the__elem__def, fact_846_diff__add__assoc, fact_696_the__elem__eq, fact_290_subsetD, fact_151_finite__subset, fact_392_insert__ident, fact_379_mem__def, fact_11_finite__imageI, fact_519_empty__iff, fact_403_subset__refl, fact_723_Diff__iff, fact_299_zero__induct__lemma, fact_175_eq__diff__iff, fact_763_card_Oremove, fact_38_finite__imageI, fact_167_Suc__le__mono, fact_615_image__empty, fact_298_insertE, fact_485_le__funI, fact_84_card__seteq, fact_468_image__insert, fact_150_finite__subset, fact_826_trans__le__add1, fact_657_finite__Diff__insert, fact_388_insert__code, fact_304_order__refl, fact_711_DiffI, fact_636_singleton__conv, fact_646_card__insert, fact_672_card__Diff__subset, fact_25_finite__imageI, fact_694_finite_Osimps, fact_773_folding__one__idem_Osubset__idem, fact_548_Diff__insert__absorb, fact_487_assms_I3_J, fact_596_doubleton__eq__iff, conj_3, fact_9_finite__imageI, fact_740_card__Diff__singleton, fact_831_add__leD1, fact_579_insert__Diff__if, fact_50_card__image__le, fact_182_finite__surj, fact_229_finite__subset__image, fact_702_nonempty__iff, fact_362_xt1_I6_J, fact_513_Diff__cancel, fact_393_insertI2, fact_520_empty__iff, fact_202_finite__surj, fact_844_le__add__diff__inverse2, fact_613_image__is__empty, fact_307_linorder__linear, fact_294_insertCI, fact_357_xt1_I5_J, fact_745_one__reorient, fact_26_finite__imageI, fact_286_equalityI, fact_157_rev__finite__subset, fact_246_finite__subset__image, fact_839_le__diff__conv, fact_592_singletonE, fact_27_finite__imageI, fact_754_card__Diff__insert, fact_850_Suc__eq__plus1, fact_639_singleton__conv2, fact_719_DiffD1, fact_80_card__seteq, fact_820_add__Suc, fact_797_add__right__imp__eq, fact_849_Suc__eq__plus1__left, fact_291_insertCI, fact_317_order__eq__refl, fact_499_finite_OemptyI, fact_808_add__right__mono, fact_449_le__funE, fact_585_Diff__mono, fact_378_mem__def, fact_116_finite__Collect__conjI, fact_228_finite__subset__image, fact_533_all__not__in__conv, fact_396_insertI2, fact_529_ex__in__conv, fact_437_insert__compr__raw, fact_115_finite__Collect__conjI, fact_759_folding__one_Oclosed, fact_373_insert__Collect, fact_668_image__constant__conv, fact_245_finite__subset__image, fact_825_nat__add__left__cancel__le, fact_778_folding__one__idem_Oinsert__idem, fact_706_DiffE, fact_547_insert__Diff, fact_810_add__left__mono, fact_666_image__constant, fact_123_nat_Oinject, fact_427_subset__trans, fact_731_folding__one_Oinsert__remove, fact_305_order__refl, fact_322_order__antisym__conv, fact_799_nat__add__left__commute, fact_492_emptyE, fact_649_card__insert, fact_683_finite__empty__induct, fact_457_subset__insert, fact_544_insert__Diff, fact_10_finite__imageI, fact_722_Diff__iff, fact_177_diff__le__mono, fact_690_finite__induct, fact_81_card__seteq, fact_289_subsetD, fact_461_subset__insertI2, fact_66_card__image__le, fact_119_Suc__diff__le, fact_526_empty__Diff, fact_231_finite__subset__image, fact_621_le__bot, fact_821_add__Suc__shift, fact_837_diff__cancel2, fact_173_le__diff__iff, fact_114_finite__Collect__conjI, fact_91_card__insert__le, fact_99_card__insert__if, fact_183_finite__surj, fact_184_finite__surj, fact_178_diff__le__mono2, fact_156_rev__finite__subset, fact_739_card__Diff__singleton__if, fact_248_finite__subset__image, fact_217_finite__surj, fact_5_finite__Collect__subsets, fact_588_Diff__subset, fact_412_equalityD2, conj_2, fact_389_insert__ident, fact_280_pigeonhole__infinite, fact_847_add__diff__assoc2, fact_699_nonempty__iff, fact_127_le__trans, fact_137_finite__Collect__disjI, fact_152_finite__subset, fact_266_lift__Suc__mono__le, fact_2_finite__Collect__subsets, fact_74_card__mono, fact_606_empty__not__insert, fact_446_le__funD, fact_653_card__Diff1__le, fact_834_diff__add__inverse, fact_758_folding__one_Oinsert, fact_691_finite_Osimps, fact_161_rev__finite__subset, fact_838_diff__diff__right, fact_351_order__trans, fact_801_nat__add__left__cancel, fact_464_insert__mono, fact_122_Suc__inject, fact_47_finite_OinsertI, fact_169_not__less__eq__eq, fact_829_add__le__mono, fact_453_insert__subset, fact_746_diff__Suc__1, fact_645_card__Suc__Diff1, fact_654_finite__Diff__insert, fact_793_add__left__imp__eq, fact_460_subset__insert, fact_153_finite__subset, fact_337_ord__le__eq__trans, fact_677_diff__card__le__card__Diff, fact_341_xt1_I4_J, fact_424_set__mp, fact_52_card__image__le, fact_493_emptyE, fact_176_diff__diff__cancel, fact_23_finite__imageI, fact_312_order__eq__iff, fact_356_xt1_I5_J, fact_450_subset__insertI, fact_474_image__mono, fact_49_card__image__le, fact_409_equalityD1, fact_219_finite__subset__image, fact_12_finite__imageI, fact_824_le__iff__add, fact_506_equals0D, fact_342_xt1_I4_J, fact_575_insert__Diff1, fact_300_Suc__le__D, fact_476_imageE, fact_53_card__image__le, fact_642_card__Suc__Diff1, fact_4_finite__Collect__subsets, fact_440_insert__compr__raw, fact_149_finite__subset, fact_419_set__rev__mp, fact_840_le__add__diff, fact_732_folding__one_Oremove, fact_174_Nat_Odiff__diff__eq, fact_728_folding__one_Oinsert__remove, fact_186_finite__surj, fact_384_insert__iff, fact_552_insert__Diff__single, fact_852_diff__Suc__diff__eq2, fact_848_diff__add__assoc2, fact_812_add__mono, fact_710_DiffI, fact_540_empty__def, fact_180_finite__surj, fact_629_bot__least, fact_124_Suc__n__not__n, fact_226_finite__subset__image, fact_791_add__right__cancel, fact_172_diff__Suc__Suc, fact_814_add__le__imp__le__right, fact_802_nat__add__right__cancel, fact_364_linorder__le__cases, fact_534_all__not__in__conv, fact_111_finite__Collect__conjI, help_fequal_2_1_fequal_000t__a_T, fact_365_insertI1, fact_603_insert__not__empty, fact_659_image__diff__subset, fact_220_finite__subset__image, fact_507_equals0D, fact_387_insert__iff, fact_397_insert__absorb, fact_130_le__refl, fact_755_folding__one_Oinsert, fact_159_rev__finite__subset, fact_602_singleton__iff, fact_147_finite__insert, fact_170_Suc__n__not__le__n, fact_102_card__insert__if, fact_205_finite__surj, fact_383_insert__commute, fact_265_lift__Suc__mono__le, fact_748_folding__one_Osingleton, fact_264_lift__Suc__mono__le, fact_168_le__Suc__eq, fact_630_Collect__conv__if, fact_406_set__eq__subset, fact_382_insert__absorb2, fact_187_finite__surj, fact_72_card__mono, fact_480_subsetI, fact_144_finite__insert, fact_496_finite__Diff, fact_819_add__Suc__right, fact_617_empty__is__image, fact_188_finite__surj, fact_718_DiffD1, fact_48_card__image__le, fact_148_finite__subset, fact_267_lift__Suc__mono__le, fact_823_le__add1, fact_576_insert__Diff__if, fact_762_folding__one_Oclosed, fact_714_DiffD2, fact_835_diff__diff__left, fact_44_finite_OinsertI, fact_555_Diff__insert2, fact_795_add__imp__eq, fact_775_folding__one__idem_Oinsert__idem, fact_472_subset__image__iff, fact_558_Diff__insert, fact_51_card__image__le, fact_223_finite__subset__image, fact_743_card__Diff__singleton, fact_841_le__add__diff__inverse, fact_479_subsetI, fact_224_finite__subset__image, fact_368_insertI1, fact_510_Collect__empty__eq, fact_564_diff__single__insert, fact_735_folding__one_Oremove, fact_203_finite__surj, fact_262_finite__subset__image, conj_1, fact_816_add__le__imp__le__left, fact_171_Suc__diff__diff, fact_110_card__insert__disjoint, fact_1_finite__Collect__subsets, fact_76_card__mono, fact_443_le__fun__def, fact_828_add__le__mono1, fact_845_le__imp__diff__is__add, fact_132_finite__Collect__disjI, fact_434_imageI, help_fequal_1_1_fequal_000t__a_T, fact_523_empty__Collect__eq, fact_456_insert__subset, fact_751_card__Diff__insert, fact_372_insert__compr, fact_352_order__trans, fact_715_DiffD2, fact_798_nat__add__commute, fact_79_card__seteq, fact_160_rev__finite__subset, fact_128_eq__imp__le, fact_827_trans__le__add2, fact_682_assms_I2_J, fact_247_finite__subset__image, fact_571_finite__Diff2, fact_204_finite__surj, fact_430_equalityE, fact_185_finite__surj, fact_589_singleton__inject, fact_681_finite__subset__induct, fact_225_finite__subset__image, fact_676_diff__card__le__card__Diff, fact_843_le__diff__conv2, fact_707_DiffE, fact_568_subset__insert__iff, fact_230_finite__subset__image, fact_766_card_Oremove, fact_416_in__mono, fact_595_singletonE, fact_822_le__add2, fact_673_card__Diff__subset, fact_3_finite__Collect__subsets, fact_833_diff__add__inverse2, fact_806_add__le__cancel__left, fact_789_add__left__cancel, fact_249_finite__subset__image, fact_164_Suc__leD, fact_736_card__Diff__singleton__if, fact_800_nat__add__assoc, fact_107_card__insert__disjoint, fact_436_rev__image__eqI, fact_678_finite__subset__induct, fact_316_order__eq__refl, fact_782_finite__ne__induct, fact_842_add__diff__assoc, fact_633_Collect__conv__if2, conj_4, fact_415_in__mono, fact_787_ab__semigroup__add__class_Oadd__ac_I1_J, fact_73_card__mono, fact_572_insert__Diff1, fact_770_card_Oinsert__remove, fact_136_finite__Collect__disjI, fact_565_subset__insert__iff, fact_326_ord__eq__le__trans, fact_82_card__seteq, fact_221_finite__subset__image, fact_687_finite__induct, fact_361_xt1_I6_J, fact_530_ex__in__conv, fact_423_set__mp, fact_774_folding__one__idem_Osubset__idem, fact_346_order__antisym, fact_830_add__leD2, fact_470_insert__image, fact_0_assms_I1_J, fact_165_le__SucE, fact_836_diff__cancel, fact_853_termination__basic__simps_I4_J, conj_5, fact_189_finite__surj, fact_69_card__image__le, fact_135_finite__Collect__disjI, conj_0, fact_516_Diff__empty, fact_206_finite__surj, fact_331_xt1_I3_J, fact_420_set__rev__mp, fact_347_order__antisym, fact_482_image__subsetI, fact_222_finite__subset__image, fact_599_singleton__iff, fact_6_finite__Collect__subsets, fact_166_le__SucI, fact_703_assms_I4_J, fact_611_subset__empty, fact_332_xt1_I3_J, fact_625_bot__unique, fact_503_empty__subsetI, fact_75_card__mono, fact_854_termination__basic__simps_I3_J, fact_432_image__iff, fact_369_insert__compr, fact_336_ord__le__eq__trans, fact_500_finite_OemptyI, fact_561_diff__single__insert, fact_582_double__diff, fact_726_set__diff__eq, fact_311_order__eq__iff, fact_686_finite__empty__induct, fact_71_card__mono, fact_779_finite__ne__induct, fact_727_set__diff__eq, fact_400_insert__absorb, fact_94_card__insert__le, fact_158_rev__finite__subset
% 26.59/7.20 % No. of inferences in proof: 836
% 26.59/7.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6816 ms resp. 5804 ms w/o parsing
% 28.38/7.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 28.38/7.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------