%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP153^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 08:06:58 AM UTC 2026
% Result : Theorem 16.50s 5.35s
% Output : Refutation 17.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 232
% Syntax : Number of formulae : 466 ( 201 unt; 0 typ; 0 def)
% Number of atoms : 1385 ( 384 equ; 8 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 4009 ( 186 ~; 30 |; 129 &;3128 @)
% ( 0 <=>; 536 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 8 con; 0-3 aty)
% Number of variables : 1160 ( 70 ^;1066 !; 24 ?;1160 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1295299783od_a_a_type,type,
set_Pr1295299783od_a_a: $tType ).
thf(produc1990712039od_a_a_type,type,
produc1990712039od_a_a: $tType ).
thf(set_Pr1948701895od_a_a_type,type,
set_Pr1948701895od_a_a: $tType ).
thf(produc1572603623od_a_a_type,type,
produc1572603623od_a_a: $tType ).
thf(set_Pr2045688071_set_a_type,type,
set_Pr2045688071_set_a: $tType ).
thf(produc1691597095_set_a_type,type,
produc1691597095_set_a: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(set_set_a_type,type,
set_set_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(bNF_Ca850758276_set_a_decl,type,
bNF_Ca850758276_set_a: set_Product_prod_a_a > ( a > set_a ) > $o ).
thf(uminus1440301054od_a_a_decl,type,
uminus1440301054od_a_a: set_Product_prod_a_a > set_Product_prod_a_a ).
thf(uminus_uminus_set_a_decl,type,
uminus_uminus_set_a: set_a > set_a ).
thf(order_653178931r_on_a_decl,type,
order_653178931r_on_a: set_a > set_Product_prod_a_a > $o ).
thf(order_preorder_on_a_decl,type,
order_preorder_on_a: set_a > set_Product_prod_a_a > $o ).
thf(order_under_a_decl,type,
order_under_a: set_Product_prod_a_a > a > set_a ).
thf(bot_bot_a_o_decl,type,
bot_bot_a_o: a > $o ).
thf(bot_bo2131659635od_a_a_decl,type,
bot_bo2131659635od_a_a: set_Product_prod_a_a ).
thf(bot_bot_set_a_decl,type,
bot_bot_set_a: set_a ).
thf(ord_le486764743_set_a_decl,type,
ord_le486764743_set_a: produc1691597095_set_a > produc1691597095_set_a > $o ).
thf(ord_le1824328871od_a_a_decl,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(order_Greatest_set_a_decl,type,
order_Greatest_set_a: ( set_a > $o ) > set_a ).
thf(prefer436369274d_as_a_decl,type,
prefer436369274d_as_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(prefer161218362good_a_decl,type,
prefer161218362good_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(prefer1676310729than_a_decl,type,
prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(prefer1292084992ence_a_decl,type,
prefer1292084992ence_a: set_a > set_Product_prod_a_a > $o ).
thf(prefer719835986ence_a_decl,type,
prefer719835986ence_a: set_a > set_Product_prod_a_a > $o ).
thf(prefer580340847ioms_a_decl,type,
prefer580340847ioms_a: set_a > set_Product_prod_a_a > $o ).
thf(product_Pair_a_a_decl,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(produc1926412547_set_a_decl,type,
produc1926412547_set_a: produc1691597095_set_a > set_a ).
thf(produc918972485_set_a_decl,type,
produc918972485_set_a: produc1691597095_set_a > set_a ).
thf(product_swap_a_a_decl,type,
product_swap_a_a: product_prod_a_a > product_prod_a_a ).
thf(domain_a_a_decl,type,
domain_a_a: set_Product_prod_a_a > set_a ).
thf(id_on_a_decl,type,
id_on_a: set_a > set_Product_prod_a_a ).
thf(range_a_a_decl,type,
range_a_a: set_Product_prod_a_a > set_a ).
thf(refl_on_a_decl,type,
refl_on_a: set_a > set_Product_prod_a_a > $o ).
thf(total_on_a_decl,type,
total_on_a: set_a > set_Product_prod_a_a > $o ).
thf(trans_a_decl,type,
trans_a: set_Product_prod_a_a > $o ).
thf(collec645855634od_a_a_decl,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(insert1116662519od_a_a_decl,type,
insert1116662519od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(insert_a_decl,type,
insert_a: a > set_a > set_a ).
thf(is_empty_a_decl,type,
is_empty_a: set_a > $o ).
thf(is_singleton_a_decl,type,
is_singleton_a: set_a > $o ).
thf(the_elem_a_decl,type,
the_elem_a: set_a > a ).
thf(member449909584od_a_a_decl,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(carrier_decl,type,
carrier: set_a ).
thf(relation_decl,type,
relation: set_Product_prod_a_a ).
thf(y_decl,type,
y: a ).
thf(z_decl,type,
z: a ).
thf(166,axiom,
! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_insertI1) ).
thf(760,plain,
! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(77,axiom,
! [A: a] : ( is_singleton_a @ ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_is__singletonI) ).
thf(468,plain,
! [A: a] : ( is_singleton_a @ ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1,conjecture,
( ( member_a @ z @ carrier )
& ( member_a @ y @ carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( member_a @ z @ carrier )
& ( member_a @ y @ carrier ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(234,plain,
~ ( ( member_a @ z @ carrier )
& ( member_a @ y @ carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(220,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A ) @ ( id_on_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Id__onI) ).
thf(941,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A ) @ ( id_on_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(209,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( ord_less_eq_set_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_subset__emptyI) ).
thf(909,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( ord_less_eq_set_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(36,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( A = bot_bo2131659635od_a_a )
=> ~ ( member449909584od_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_equals0D) ).
thf(333,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( A = bot_bo2131659635od_a_a )
=> ~ ( member449909584od_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(59,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ D @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_rational__preference_Ono__better__subset__pref) ).
thf(408,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ D @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(167,axiom,
prefer1292084992ence_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_preference__axioms) ).
thf(762,plain,
prefer1292084992ence_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(144,axiom,
! [A: set_a > $o,B: set_a,C: set_a > $o] :
( ( A @ B )
=> ( ! [D: set_a] :
( ( A @ D )
=> ( ord_less_eq_set_a @ D @ B ) )
=> ( ! [D: set_a] :
( ( A @ D )
=> ( ! [E: set_a] :
( ( A @ E )
=> ( ord_less_eq_set_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_set_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_GreatestI2__order) ).
thf(683,plain,
! [A: set_a > $o,B: set_a,C: set_a > $o] :
( ( A @ B )
=> ( ! [D: set_a] :
( ( A @ D )
=> ( ord_less_eq_set_a @ D @ B ) )
=> ( ! [D: set_a] :
( ( A @ D )
=> ( ! [E: set_a] :
( ( A @ E )
=> ( ord_less_eq_set_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_set_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(28,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_empty__iff) ).
thf(308,plain,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(159,axiom,
! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_singletonI) ).
thf(741,plain,
! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(69,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_equalityD2) ).
thf(440,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(133,axiom,
( bot_bot_set_a
= ( collect_a @ bot_bot_a_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_bot__set__def) ).
thf(655,plain,
( bot_bot_set_a
= ( collect_a @ bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(50,axiom,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( ( A = bot_bot_set_a )
| ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_subset__singletonD) ).
thf(384,plain,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( ( A = bot_bot_set_a )
| ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(178,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ D @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_rational__preference_Ono__better__thansubset__rel) ).
thf(797,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ D @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(150,axiom,
! [A: a,B: set_Product_prod_a_a,C: a > $o] :
( ( member_a @ A @ ( range_a_a @ B ) )
=> ( ! [D: a,E: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
=> ( C @ E ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_Range_Oinducts) ).
thf(715,plain,
! [A: a,B: set_Product_prod_a_a,C: a > $o] :
( ( member_a @ A @ ( range_a_a @ B ) )
=> ( ! [D: a,E: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
=> ( C @ E ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(222,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ? [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
& ~ ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_mk__disjoint__insert) ).
thf(945,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ? [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
& ~ ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(139,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( A = bot_bot_a_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Collect__empty__eq__bot) ).
thf(670,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( A = bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(206,axiom,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( A != B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_completeD) ).
thf(898,plain,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( A != B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(62,axiom,
! [A: a,B: a,C: set_a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( insert_a @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_a @ C @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_singleton__insert__inj__eq) ).
thf(417,plain,
! [A: a,B: a,C: set_a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( insert_a @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_a @ C @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(229,axiom,
! [A: product_prod_a_a,B: set_a] :
( ( member449909584od_a_a @ A @ ( id_on_a @ B ) )
=> ~ ! [C: a] :
( ( member_a @ C @ B )
=> ( A
!= ( product_Pair_a_a @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_Id__onE) ).
thf(973,plain,
! [A: product_prod_a_a,B: set_a] :
( ( member449909584od_a_a @ A @ ( id_on_a @ B ) )
=> ~ ! [C: a] :
( ( member_a @ C @ B )
=> ( A
!= ( product_Pair_a_a @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(11,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_subsetI) ).
thf(257,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(32,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_in__mono) ).
thf(320,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(103,axiom,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_empty__Collect__eq) ).
thf(565,plain,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(152,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_singleton__iff) ).
thf(724,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(105,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_order__class_Oorder_Oeq__iff) ).
thf(570,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(85,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ ( uminus_uminus_set_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_Compl__anti__mono) ).
thf(504,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ ( uminus_uminus_set_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(101,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_subset__empty) ).
thf(559,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(228,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_rational__preference_OcompleteD) ).
thf(969,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(34,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ ( insert1116662519od_a_a @ A @ C ) )
= ( ord_le1824328871od_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_subset__insert) ).
thf(325,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ ( insert1116662519od_a_a @ A @ C ) )
= ( ord_le1824328871od_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(22,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ ( uminus1440301054od_a_a @ ( insert1116662519od_a_a @ B @ bot_bo2131659635od_a_a ) ) )
= ( ~ ( member449909584od_a_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_subset__Compl__singleton) ).
thf(289,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ ( uminus1440301054od_a_a @ ( insert1116662519od_a_a @ B @ bot_bo2131659635od_a_a ) ) )
= ( ~ ( member449909584od_a_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ? [C: set_Product_prod_a_a] :
( ( B
= ( insert1116662519od_a_a @ A @ C ) )
& ~ ( member449909584od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_mk__disjoint__insert) ).
thf(261,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ? [C: set_Product_prod_a_a] :
( ( B
= ( insert1116662519od_a_a @ A @ C ) )
& ~ ( member449909584od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(183,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_in__mono) ).
thf(817,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(207,axiom,
! [A: a,B: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ~ ( member_a @ A @ ( prefer161218362good_a @ B @ carrier @ relation ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_at__lst__asgd__not__ge) ).
thf(902,plain,
! [A: a,B: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ~ ( member_a @ A @ ( prefer161218362good_a @ B @ carrier @ relation ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(214,axiom,
! [A: a,B: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) @ ( prefer1676310729than_a @ B @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ B @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_nbt__nest) ).
thf(924,plain,
! [A: a,B: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) @ ( prefer1676310729than_a @ B @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ B @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(112,axiom,
! [A: set_a] : ( trans_a @ ( id_on_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_trans__Id__on) ).
thf(591,plain,
! [A: set_a] : ( trans_a @ ( id_on_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(129,axiom,
( is_empty_a
= ( ^ [A: set_a] : ( A = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Set_Ois__empty__def) ).
thf(646,plain,
( is_empty_a
= ( ^ [A: set_a] : ( A = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(40,axiom,
! [A: a,B: set_a,C: a] :
( ( ( insert_a @ A @ B )
= ( insert_a @ C @ bot_bot_set_a ) )
= ( ( A = C )
& ( ord_less_eq_set_a @ B @ ( insert_a @ C @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_singleton__insert__inj__eq_H) ).
thf(348,plain,
! [A: a,B: set_a,C: a] :
( ( ( insert_a @ A @ B )
= ( insert_a @ C @ bot_bot_set_a ) )
= ( ( A = C )
& ( ord_less_eq_set_a @ B @ ( insert_a @ C @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(181,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ B @ ( prefer1676310729than_a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_worse__in__no__better) ).
thf(806,plain,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ B @ ( prefer1676310729than_a @ B @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(42,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_order__subst2) ).
thf(353,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(79,axiom,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_old_Oprod_Oexhaust) ).
thf(480,plain,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(19,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( insert1116662519od_a_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_insert__absorb) ).
thf(280,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( insert1116662519od_a_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(201,axiom,
! [A: a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( insert_a @ A @ B ) @ C )
= ( ( member_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_insert__subset) ).
thf(877,plain,
! [A: a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( insert_a @ A @ B ) @ C )
= ( ( member_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(156,axiom,
prefer719835986ence_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_rational__preference__axioms) ).
thf(734,plain,
prefer719835986ence_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(225,axiom,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_insert__ident) ).
thf(956,plain,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(172,axiom,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_at__lst__asgd__ge) ).
thf(774,plain,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(54,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( order_preorder_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_preference_Otrans__refl) ).
thf(396,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( order_preorder_on_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(60,axiom,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( ( A = bot_bot_set_a )
| ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_subset__singleton__iff) ).
thf(411,plain,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( ( A = bot_bot_set_a )
| ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(7,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a] : ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_insertI1) ).
thf(243,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a] : ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(192,axiom,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_bot__empty__eq) ).
thf(849,plain,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(27,axiom,
trans_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_trans__empty) ).
thf(307,plain,
trans_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(23,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ B )
=> ( ord_le1824328871od_a_a @ ( insert1116662519od_a_a @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_insert__subsetI) ).
thf(292,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ B )
=> ( ord_le1824328871od_a_a @ ( insert1116662519od_a_a @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ B @ bot_bo2131659635od_a_a ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_singleton__iff) ).
thf(248,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ B @ bot_bo2131659635od_a_a ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_eq__refl) ).
thf(380,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(15,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ B @ C ) )
= ( ( A = B )
| ( member449909584od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_insert__iff) ).
thf(270,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ B @ C ) )
= ( ( A = B )
| ( member449909584od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(136,axiom,
! [A: set_Product_prod_a_a,B: a,C: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ord_less_eq_set_a @ ( order_under_a @ A @ B ) @ ( order_under_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_under__incr) ).
thf(661,plain,
! [A: set_Product_prod_a_a,B: a,C: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ord_less_eq_set_a @ ( order_under_a @ A @ B ) @ ( order_under_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(94,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_old_Oprod_Oinducts) ).
thf(534,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(161,axiom,
! [A: a,B: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_strict__not__refl__weak) ).
thf(746,plain,
! [A: a,B: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(184,axiom,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ B @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_no__better__thansubset__rel) ).
thf(820,plain,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ B @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(65,axiom,
! [A: set_a,B: a] : ( ord_less_eq_set_a @ A @ ( insert_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_subset__insertI) ).
thf(429,plain,
! [A: set_a,B: a] : ( ord_less_eq_set_a @ A @ ( insert_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(17,axiom,
! [A: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ bot_bo2131659635od_a_a )
= ( A = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_subset__empty) ).
thf(275,plain,
! [A: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ bot_bo2131659635od_a_a )
= ( A = bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(154,axiom,
! [A: a] :
( ( member_a @ A @ carrier )
=> ! [B: a] :
( ( member_a @ B @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_compl) ).
thf(729,plain,
! [A: a] :
( ( member_a @ A @ carrier )
=> ! [B: a] :
( ( member_a @ B @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(80,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_ord__le__eq__trans) ).
thf(484,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(35,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ A @ B )
=> ( ~ ( member449909584od_a_a @ A @ C )
=> ( ( ( insert1116662519od_a_a @ A @ B )
= ( insert1116662519od_a_a @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_insert__ident) ).
thf(329,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ A @ B )
=> ( ~ ( member449909584od_a_a @ A @ C )
=> ( ( ( insert1116662519od_a_a @ A @ B )
= ( insert1116662519od_a_a @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(205,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) )
=> ( total_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_total__onI) ).
thf(889,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) )
=> ( total_on_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(98,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_old_Oprod_Oinject) ).
thf(551,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(190,axiom,
( prefer1292084992ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) )
& ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) )
& ( order_preorder_on_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_preference__def) ).
thf(842,plain,
( prefer1292084992ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) )
& ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) )
& ( order_preorder_on_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(90,axiom,
! [A: a,B: a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_singleton__inject) ).
thf(522,plain,
! [A: a,B: a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(187,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ B @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_no__better__subset__pref) ).
thf(830,plain,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ B @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(31,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_insertI2) ).
thf(317,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(131,axiom,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Collect__mem__eq) ).
thf(650,plain,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(113,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ ( uminus_uminus_set_a @ B ) )
= ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_Compl__subset__Compl__iff) ).
thf(593,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ ( uminus_uminus_set_a @ B ) )
= ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(233,axiom,
! [A: a,B: set_Product_prod_a_a] :
( ( member_a @ A @ ( range_a_a @ B ) )
=> ~ ! [C: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_RangeE) ).
thf(989,plain,
! [A: a,B: set_Product_prod_a_a] :
( ( member_a @ A @ ( range_a_a @ B ) )
=> ~ ! [C: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(231,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ ( prefer1676310729than_a @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_rational__preference_Oworse__in__no__better) ).
thf(980,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ ( prefer1676310729than_a @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(57,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( refl_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_preference_Oreflexivity) ).
thf(403,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( refl_on_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(174,axiom,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_insert__iff) ).
thf(783,plain,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(63,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) )
=> ( trans_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_transI) ).
thf(420,plain,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) )
=> ( trans_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(203,axiom,
( ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ y @ z ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
thf(884,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ y @ z ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(99,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( total_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_rational__preference_Ototal) ).
thf(554,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( total_on_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(127,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_equalityD1) ).
thf(637,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(81,axiom,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_indiff__trans) ).
thf(489,plain,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(142,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_bot_Oextremum) ).
thf(679,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(97,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_Collect__mono) ).
thf(547,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(53,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_bot_Oextremum__uniqueI) ).
thf(393,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(146,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ ( uminus_uminus_set_a @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_subset__Compl__self__eq) ).
thf(701,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ ( uminus_uminus_set_a @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(158,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_subsetD) ).
thf(738,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(73,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_subset__refl) ).
thf(457,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(48,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_ord__eq__le__subst) ).
thf(371,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(117,axiom,
( trans_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_trans__def) ).
thf(605,plain,
( trans_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(4,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_emptyE) ).
thf(237,plain,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(219,axiom,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_all__not__in__conv) ).
thf(938,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(13,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_subset__iff) ).
thf(266,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(87,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_ord__le__eq__subst) ).
thf(508,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(29,axiom,
! [A: set_Product_prod_a_a] :
( ( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A ) )
= ( A = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_all__not__in__conv) ).
thf(311,plain,
! [A: set_Product_prod_a_a] :
( ( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A ) )
= ( A = bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(213,axiom,
! [A: a,B: set_Product_prod_a_a] :
( ( member_a @ A @ ( range_a_a @ B ) )
=> ~ ! [C: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_Range_Ocases) ).
thf(921,plain,
! [A: a,B: set_Product_prod_a_a] :
( ( member_a @ A @ ( range_a_a @ B ) )
=> ~ ! [C: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(134,axiom,
! [A: a] : ( refl_on_a @ ( insert_a @ A @ bot_bot_set_a ) @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ A ) @ bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_refl__on__singleton) ).
thf(657,plain,
! [A: a] : ( refl_on_a @ ( insert_a @ A @ bot_bot_set_a ) @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ A ) @ bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(55,axiom,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_transD) ).
thf(398,plain,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(92,axiom,
! [A: a] : ( total_on_a @ ( insert_a @ A @ bot_bot_set_a ) @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ A ) @ bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_total__on__singleton) ).
thf(530,plain,
! [A: a] : ( total_on_a @ ( insert_a @ A @ bot_bot_set_a ) @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ A ) @ bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(204,axiom,
order_preorder_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_trans__refl) ).
thf(888,plain,
order_preorder_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(215,axiom,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( uminus_uminus_set_a @ ( insert_a @ B @ bot_bot_set_a ) ) )
= ( ~ ( member_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_subset__Compl__singleton) ).
thf(926,plain,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( uminus_uminus_set_a @ ( insert_a @ B @ bot_bot_set_a ) ) )
= ( ~ ( member_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(125,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_order__refl) ).
thf(633,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(44,axiom,
( bNF_Ca850758276_set_a
= ( ^ [A: set_Product_prod_a_a,B: a > set_a] :
! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( ord_less_eq_set_a @ ( B @ C ) @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_relChain__def) ).
thf(360,plain,
( bNF_Ca850758276_set_a
= ( ^ [A: set_Product_prod_a_a,B: a > set_a] :
! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( ord_less_eq_set_a @ ( B @ C ) @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(177,axiom,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_insertE) ).
thf(794,plain,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(110,axiom,
( ( id_on_a @ bot_bot_set_a )
= bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Id__on__empty) ).
thf(586,plain,
( ( id_on_a @ bot_bot_set_a )
= bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(208,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_refl__onD2) ).
thf(906,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(194,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( A != bot_bot_set_a )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ~ ( member_a @ C @ ( prefer161218362good_a @ D @ A @ B ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_rational__preference_Oat__lst__asgd__not__ge) ).
thf(856,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( A != bot_bot_set_a )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ~ ( member_a @ C @ ( prefer161218362good_a @ D @ A @ B ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(70,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer1292084992ence_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_rational__preference_Oaxioms_I1_J) ).
thf(444,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer1292084992ence_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(109,axiom,
! [A: set_a] : ( refl_on_a @ A @ ( id_on_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_refl__on__Id__on) ).
thf(584,plain,
! [A: set_a] : ( refl_on_a @ A @ ( id_on_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(102,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Collect__mono__iff) ).
thf(562,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(21,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_subsetD) ).
thf(286,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(160,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ ( uminus_uminus_set_a @ B ) )
= ( ~ ( member_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_Compl__iff) ).
thf(743,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ ( uminus_uminus_set_a @ B ) )
= ( ~ ( member_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(108,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_ord__eq__le__trans) ).
thf(579,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(200,axiom,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_at__least__as__goodD) ).
thf(875,plain,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(186,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rational__preference_Ostrict__not__refl__weak) ).
thf(826,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(128,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_rational__preference_Ostrict__trans) ).
thf(641,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(106,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( uminus1440301054od_a_a @ B ) )
= ( ~ ( member449909584od_a_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_Compl__iff) ).
thf(572,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( uminus1440301054od_a_a @ B ) )
= ( ~ ( member449909584od_a_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(120,axiom,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_strict__trans) ).
thf(611,plain,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(149,axiom,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( member_a @ B @ ( range_a_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_Range_Ointros) ).
thf(713,plain,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( member_a @ B @ ( range_a_a @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(3,axiom,
order_653178931r_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_lnear__order__on__empty) ).
thf(236,plain,
order_653178931r_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(147,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( prefer436369274d_as_a @ B @ carrier @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_as__good__as__sameIff) ).
thf(704,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( prefer436369274d_as_a @ B @ carrier @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(143,axiom,
! [A: set_Product_prod_a_a] : ( total_on_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_total__on__empty) ).
thf(681,plain,
! [A: set_Product_prod_a_a] : ( total_on_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(45,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_set__eq__subset) ).
thf(362,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(8,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ B @ C ) )
=> ( ( A != B )
=> ( member449909584od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_insertE) ).
thf(245,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ B @ C ) )
=> ( ( A != B )
=> ( member449909584od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(121,axiom,
refl_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_refl__on__empty) ).
thf(616,plain,
refl_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(196,axiom,
! [A: a,B: a,C: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier )
& ( member_a @ C @ carrier ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_weak__is__transitive) ).
thf(863,plain,
! [A: a,B: a,C: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier )
& ( member_a @ C @ carrier ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(202,axiom,
! [A: a,B: set_a,C: a,D: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ C @ D )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_a] :
( ( B
= ( insert_a @ C @ E ) )
& ~ ( member_a @ C @ E )
& ( D
= ( insert_a @ A @ E ) )
& ~ ( member_a @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_insert__eq__iff) ).
thf(880,plain,
! [A: a,B: set_a,C: a,D: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ C @ D )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_a] :
( ( B
= ( insert_a @ C @ E ) )
& ~ ( member_a @ C @ E )
& ( D
= ( insert_a @ A @ E ) )
& ~ ( member_a @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(67,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_order__class_Oorder_Oantisym) ).
thf(434,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(51,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_subset__antisym) ).
thf(387,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(82,axiom,
( is_singleton_a
= ( ^ [A: set_a] :
( A
= ( insert_a @ ( the_elem_a @ A ) @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_is__singleton__the__elem) ).
thf(494,plain,
( is_singleton_a
= ( ^ [A: set_a] :
( A
= ( insert_a @ ( the_elem_a @ A ) @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(165,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ A @ ( prefer161218362good_a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_pref__in__at__least__as) ).
thf(758,plain,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ A @ ( prefer161218362good_a @ B @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(39,axiom,
! [A: set_Product_prod_a_a] :
( ( ? [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= ( A != bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_ex__in__conv) ).
thf(345,plain,
! [A: set_Product_prod_a_a] :
( ( ? [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= ( A != bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(33,axiom,
! [A: product_prod_a_a] : ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ A @ bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_singletonI) ).
thf(323,plain,
! [A: product_prod_a_a] : ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ A @ bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(89,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_empty__subsetI) ).
thf(520,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(227,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ( member_a @ C @ A )
& ( member_a @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_refl__on__domain) ).
thf(964,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ( member_a @ C @ A )
& ( member_a @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(211,axiom,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_ex__in__conv) ).
thf(915,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(221,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_subset__iff) ).
thf(943,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(5,axiom,
trans_a @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_transitivity) ).
thf(240,plain,
trans_a @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ A @ B )
=> ( A = C ) )
=> ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_insertCI) ).
thf(251,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ A @ B )
=> ( A = C ) )
=> ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(75,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_antisym) ).
thf(462,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(217,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_singletonD) ).
thf(932,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(210,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_refl__onD1) ).
thf(912,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(232,axiom,
! [A: a,B: a,C: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier )
& ( member_a @ C @ carrier ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_strict__is__neg__transitive) ).
thf(983,plain,
! [A: a,B: a,C: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier )
& ( member_a @ C @ carrier ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(170,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_empty__iff) ).
thf(768,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(119,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_prod_Oinject) ).
thf(608,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(25,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ~ ! [C: set_Product_prod_a_a] :
( ( B
= ( insert1116662519od_a_a @ A @ C ) )
=> ( member449909584od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_Set_Oset__insert) ).
thf(299,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ~ ! [C: set_Product_prod_a_a] :
( ( B
= ( insert1116662519od_a_a @ A @ C ) )
=> ( member449909584od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(193,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ~ ! [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_Set_Oset__insert) ).
thf(851,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ~ ! [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(66,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_dual__order_Otrans) ).
thf(431,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(18,axiom,
! [A: a] : ( trans_a @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ A ) @ bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_trans__singleton) ).
thf(278,plain,
! [A: a] : ( trans_a @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ A ) @ bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(198,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_subsetI) ).
thf(868,plain,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(6,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ bot_bo2131659635od_a_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_empty__subsetI) ).
thf(241,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ bot_bo2131659635od_a_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(132,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_rational__preference_Oaxioms_I2_J) ).
thf(653,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(151,axiom,
! [A: a,B: set_a] :
( ~ ( member_a @ A @ B )
=> ( member_a @ A @ ( uminus_uminus_set_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_ComplI) ).
thf(722,plain,
! [A: a,B: set_a] :
( ~ ( member_a @ A @ B )
=> ( member_a @ A @ ( uminus_uminus_set_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(64,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_Collect__empty__eq) ).
thf(426,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(130,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( total_on_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_rational__preference__axioms_Ointro) ).
thf(648,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( total_on_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(162,axiom,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_equals0D) ).
thf(749,plain,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(122,axiom,
! [A: a] :
( ( the_elem_a @ ( insert_a @ A @ bot_bot_set_a ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_the__elem__eq) ).
thf(617,plain,
! [A: a] :
( ( the_elem_a @ ( insert_a @ A @ bot_bot_set_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(163,axiom,
total_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_total) ).
thf(754,plain,
total_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(185,axiom,
! [A: a,B: set_Product_prod_a_a] :
( ( member_a @ A @ ( range_a_a @ B ) )
= ( ? [C: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_Range__iff) ).
thf(823,plain,
! [A: a,B: set_Product_prod_a_a] :
( ( member_a @ A @ ( range_a_a @ B ) )
= ( ? [C: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(173,axiom,
! [A: set_Product_prod_a_a,B: set_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ C @ B ) )
=> ( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ D @ B ) )
=> ( ( order_preorder_on_a @ B @ A )
=> ( prefer1292084992ence_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_preference_Ointro) ).
thf(776,plain,
! [A: set_Product_prod_a_a,B: set_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ C @ B ) )
=> ( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ D @ B ) )
=> ( ( order_preorder_on_a @ B @ A )
=> ( prefer1292084992ence_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(91,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_order__subst1) ).
thf(525,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(24,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A )
=> ( A = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_equals0I) ).
thf(295,plain,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A )
=> ( A = bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(199,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ A @ carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_not__outside) ).
thf(872,plain,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ A @ carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(148,axiom,
! [A: a,B: set_a,C: a] :
( ( ~ ( member_a @ A @ B )
=> ( A = C ) )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_insertCI) ).
thf(707,plain,
! [A: a,B: set_a,C: a] :
( ( ~ ( member_a @ A @ B )
=> ( A = C ) )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(61,axiom,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( range_a_a @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ B ) @ C ) )
= ( insert_a @ B @ ( range_a_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_Range__insert) ).
thf(414,plain,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( range_a_a @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ B ) @ C ) )
= ( insert_a @ B @ ( range_a_a @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(224,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_rational__preference_Ocompl) ).
thf(954,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(140,axiom,
! [A: product_prod_a_a,B: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_mem__Collect__eq) ).
thf(673,plain,
! [A: product_prod_a_a,B: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(37,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A )
=> ( ord_le1824328871od_a_a @ A @ bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_subset__emptyI) ).
thf(338,plain,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A )
=> ( ord_le1824328871od_a_a @ A @ bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(78,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Pair__inject) ).
thf(470,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(182,axiom,
! [A: set_a] :
( ( A != bot_bot_set_a )
=> ( ! [B: a,C: a] :
( ( member_a @ B @ A )
=> ( ( member_a @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_is__singletonI_H) ).
thf(808,plain,
! [A: set_a] :
( ( A != bot_bot_set_a )
=> ( ! [B: a,C: a] :
( ( member_a @ B @ A )
=> ( ( member_a @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(96,axiom,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_transE) ).
thf(544,plain,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(115,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_order_Otrans) ).
thf(600,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(153,axiom,
( total_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_total__on__def) ).
thf(727,plain,
( total_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(230,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_subset__eq) ).
thf(978,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(30,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ B @ bot_bo2131659635od_a_a ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_singletonD) ).
thf(314,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( insert1116662519od_a_a @ B @ bot_bo2131659635od_a_a ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(71,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_equalityE) ).
thf(446,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(76,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( insert_a @ C @ A ) @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_insert__mono) ).
thf(465,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( insert_a @ C @ A ) @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(100,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ C @ A @ B ) @ ( prefer1676310729than_a @ D @ A @ B ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ D @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_rational__preference_Onbt__nest) ).
thf(556,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ C @ A @ B ) @ ( prefer1676310729than_a @ D @ A @ B ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ D @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(95,axiom,
! [A: a,B: a,C: set_Product_prod_a_a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_ssubst__Pair__rhs) ).
thf(539,plain,
! [A: a,B: a,C: set_Product_prod_a_a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(191,axiom,
! [A: a,B: a,C: set_a] :
( ( A = B )
=> ( ( member_a @ A @ C )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( id_on_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_Id__on__eqI) ).
thf(844,plain,
! [A: a,B: a,C: set_a] :
( ( A = B )
=> ( ( member_a @ A @ C )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( id_on_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(171,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Collect__mem__eq) ).
thf(771,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(88,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_doubleton__eq__iff) ).
thf(517,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(26,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ ( insert1116662519od_a_a @ A @ B ) @ C )
= ( ( member449909584od_a_a @ A @ C )
& ( ord_le1824328871od_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_insert__subset) ).
thf(304,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ ( insert1116662519od_a_a @ A @ B ) @ C )
= ( ( member449909584od_a_a @ A @ C )
& ( ord_le1824328871od_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(41,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( prefer580340847ioms_a @ A @ B )
=> ( prefer719835986ence_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_rational__preference_Ointro) ).
thf(351,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( prefer580340847ioms_a @ A @ B )
=> ( prefer719835986ence_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(52,axiom,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_surj__pair) ).
thf(390,plain,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(56,axiom,
prefer580340847ioms_a = total_on_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_rational__preference__axioms__def) ).
thf(401,plain,
prefer580340847ioms_a = total_on_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(111,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_subset__insertI2) ).
thf(588,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(145,axiom,
( is_singleton_a
= ( ^ [A: set_a] :
? [B: a] :
( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_is__singleton__def) ).
thf(699,plain,
( is_singleton_a
= ( ^ [A: set_a] :
? [B: a] :
( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(155,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( refl_on_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_refl__onD) ).
thf(731,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( refl_on_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(175,axiom,
! [A: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ A @ carrier )
=> ( ( prefer1676310729than_a @ A @ carrier @ relation )
!= bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_no__better__than__nonepty) ).
thf(786,plain,
! [A: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ A @ carrier )
=> ( ( prefer1676310729than_a @ A @ carrier @ relation )
!= bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(104,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_eq__iff) ).
thf(568,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(138,axiom,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( domain_a_a @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ B ) @ C ) )
= ( insert_a @ A @ ( domain_a_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_Domain__insert) ).
thf(667,plain,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( domain_a_a @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ B ) @ C ) )
= ( insert_a @ A @ ( domain_a_a @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(216,axiom,
! [A: a,B: set_a,C: a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_insertI2) ).
thf(929,plain,
! [A: a,B: set_a,C: a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(168,axiom,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ ( insert_a @ A @ C ) )
= ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_subset__insert) ).
thf(763,plain,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ ( insert_a @ A @ C ) )
= ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(188,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_mem__Collect__eq) ).
thf(832,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(179,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A )
& ( member_a @ E @ A ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rational__preference_Oweak__is__transitive) ).
thf(800,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A )
& ( member_a @ E @ A ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(123,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_subrelI) ).
thf(620,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(58,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_dual__order_Oantisym) ).
thf(405,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(176,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_equals0I) ).
thf(790,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(16,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_subset__eq) ).
thf(273,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(197,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_emptyE) ).
thf(865,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(116,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_dual__order_Oeq__iff) ).
thf(603,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(157,axiom,
! [A: a,B: a,C: set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( id_on_a @ C ) )
= ( ( A = B )
& ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Id__on__iff) ).
thf(735,plain,
! [A: a,B: a,C: set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( id_on_a @ C ) )
= ( ( A = B )
& ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(223,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ ( prefer436369274d_as_a @ D @ A @ B ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rational__preference_Oas__good__as__sameIff) ).
thf(950,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ ( prefer436369274d_as_a @ D @ A @ B ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(189,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A )
& ( member_a @ E @ A ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_rational__preference_Ostrict__is__neg__transitive) ).
thf(835,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A )
& ( member_a @ E @ A ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(212,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_insert__absorb) ).
thf(918,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(38,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ A @ B )
=> ( ~ ( member449909584od_a_a @ C @ D )
=> ( ( ( insert1116662519od_a_a @ A @ B )
= ( insert1116662519od_a_a @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Product_prod_a_a] :
( ( B
= ( insert1116662519od_a_a @ C @ E ) )
& ~ ( member449909584od_a_a @ C @ E )
& ( D
= ( insert1116662519od_a_a @ A @ E ) )
& ~ ( member449909584od_a_a @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_insert__eq__iff) ).
thf(341,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ A @ B )
=> ( ~ ( member449909584od_a_a @ C @ D )
=> ( ( ( insert1116662519od_a_a @ A @ B )
= ( insert1116662519od_a_a @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Product_prod_a_a] :
( ( B
= ( insert1116662519od_a_a @ C @ E ) )
& ~ ( member449909584od_a_a @ C @ E )
& ( D
= ( insert1116662519od_a_a @ A @ E ) )
& ~ ( member449909584od_a_a @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_dual__order_Orefl) ).
thf(358,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(68,axiom,
! [A: a,B: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_swap__simp) ).
thf(437,plain,
! [A: a,B: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(169,axiom,
refl_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_reflexivity) ).
thf(767,plain,
refl_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(137,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_subset__trans) ).
thf(664,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(93,axiom,
( order_preorder_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( refl_on_a @ A @ B )
& ( trans_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_preorder__on__def) ).
thf(532,plain,
( order_preorder_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( refl_on_a @ A @ B )
& ( trans_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(20,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec645855634od_a_a @ A )
= ( collec645855634od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Collect__cong) ).
thf(283,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec645855634od_a_a @ A )
= ( collec645855634od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(86,axiom,
( ord_le486764743_set_a
= ( ^ [A: produc1691597095_set_a,B: produc1691597095_set_a] :
( ( ord_less_eq_set_a @ ( produc1926412547_set_a @ A ) @ ( produc1926412547_set_a @ B ) )
& ( ord_less_eq_set_a @ ( produc918972485_set_a @ A ) @ ( produc918972485_set_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_less__eq__prod__def) ).
thf(506,plain,
( ord_le486764743_set_a
= ( ^ [A: produc1691597095_set_a,B: produc1691597095_set_a] :
( ( ord_less_eq_set_a @ ( produc1926412547_set_a @ A ) @ ( produc1926412547_set_a @ B ) )
& ( ord_less_eq_set_a @ ( produc918972485_set_a @ A ) @ ( produc918972485_set_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(14,axiom,
! [A: a] : ( order_653178931r_on_a @ ( insert_a @ A @ bot_bot_set_a ) @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ A ) @ bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_linear__order__on__singleton) ).
thf(268,plain,
! [A: a] : ( order_653178931r_on_a @ ( insert_a @ A @ bot_bot_set_a ) @ ( insert1116662519od_a_a @ ( product_Pair_a_a @ A @ A ) @ bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(226,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( A != bot_bot_set_a )
=> ( ( member_a @ C @ A )
=> ( ( prefer1676310729than_a @ C @ A @ B )
!= bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_rational__preference_Ono__better__than__nonepty) ).
thf(960,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( A != bot_bot_set_a )
=> ( ( member_a @ C @ A )
=> ( ( prefer1676310729than_a @ C @ A @ B )
!= bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(126,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ A @ B )
=> ( member449909584od_a_a @ A @ ( uminus1440301054od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_ComplI) ).
thf(635,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ A @ B )
=> ( member449909584od_a_a @ A @ ( uminus1440301054od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(124,axiom,
! [A: set_a > $o,B: set_a] :
( ( A @ B )
=> ( ! [C: set_a] :
( ( A @ C )
=> ( ord_less_eq_set_a @ C @ B ) )
=> ( ( order_Greatest_set_a @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_Greatest__equality) ).
thf(624,plain,
! [A: set_a > $o,B: set_a] :
( ( A @ B )
=> ( ! [C: set_a] :
( ( A @ C )
=> ( ord_less_eq_set_a @ C @ B ) )
=> ( ( order_Greatest_set_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(107,axiom,
! [A: a,B: set_a] :
( ( insert_a @ A @ B )
!= bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_insert__not__empty) ).
thf(575,plain,
! [A: a,B: set_a] :
( ( insert_a @ A @ B )
!= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(195,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_preference_Onot__outside) ).
thf(860,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(114,axiom,
! [A: set_a] :
( ( is_singleton_a @ A )
=> ~ ! [B: a] :
( A
!= ( insert_a @ B @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_is__singletonE) ).
thf(596,plain,
! [A: set_a] :
( ( is_singleton_a @ A )
=> ~ ! [B: a] :
( A
!= ( insert_a @ B @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(74,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_bot_Oextremum__unique) ).
thf(459,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(84,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_order__trans) ).
thf(501,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(47,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( trans_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_preference_Otransitivity) ).
thf(369,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( trans_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(118,axiom,
order_preorder_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_preorder__on__empty) ).
thf(607,plain,
order_preorder_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(180,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( insert_a @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_insert__subsetI) ).
thf(803,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( insert_a @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(218,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ ( prefer161218362good_a @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_rational__preference_Opref__in__at__least__as) ).
thf(935,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ ( prefer161218362good_a @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(135,axiom,
( prefer719835986ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
& ( prefer580340847ioms_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_rational__preference__def) ).
thf(659,plain,
( prefer719835986ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
& ( prefer580340847ioms_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(46,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_preference_Oindiff__trans) ).
thf(364,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(164,axiom,
! [A: a,B: set_Product_prod_a_a] :
( ( member_a @ A @ ( range_a_a @ B ) )
= ( ? [C: a,D: a] :
( ( A = D )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_Range_Osimps) ).
thf(755,plain,
! [A: a,B: set_Product_prod_a_a] :
( ( member_a @ A @ ( range_a_a @ B ) )
= ( ? [C: a,D: a] :
( ( A = D )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(141,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_antisym__conv) ).
thf(676,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(83,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_prod__cases) ).
thf(496,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(72,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Collect__cong) ).
thf(454,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1009,plain,
$false,
inference(e,[status(thm)],[760,468,234,941,909,333,408,762,683,308,741,440,655,384,797,715,945,670,898,417,973,257,320,565,724,570,504,559,969,325,289,261,817,902,924,591,646,348,806,353,480,280,877,734,956,774,396,411,243,849,307,292,248,380,270,661,534,746,820,429,275,729,484,329,889,551,842,522,830,317,650,593,989,980,403,783,420,884,554,637,489,679,547,393,701,738,457,371,605,237,938,266,508,311,921,657,398,530,888,926,633,360,794,586,906,856,444,584,562,286,743,579,875,826,641,572,611,713,236,704,681,362,245,616,863,880,434,387,494,758,345,323,520,964,915,943,240,251,462,932,912,983,768,608,299,851,431,278,868,241,653,722,426,648,749,617,754,823,776,525,295,872,707,414,954,673,338,470,808,544,600,727,978,314,446,465,556,539,844,771,517,304,351,390,401,588,699,731,786,568,667,929,763,832,800,620,405,790,273,865,603,735,950,835,918,341,358,437,767,664,532,283,506,268,960,635,624,575,860,596,459,501,369,607,803,935,659,364,755,676,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP153^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:05:48 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.15/1.20 % [INFO] Parsing done (408ms).
% 2.48/1.21 % [INFO] Running in sequential loop mode.
% 3.76/1.62 % [INFO] eprover registered as external prover.
% 3.76/1.62 % [INFO] Scanning for conjecture ...
% 3.95/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ...
% 4.44/1.91 % [INFO] Axiom selection finished. Selected 231 axioms (removed 124 axioms).
% 5.13/2.14 % [INFO] Problem is higher-order (TPTP THF).
% 5.13/2.16 % [INFO] Type checking passed.
% 5.13/2.17 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 16.50/5.34 % External prover 'e' found a proof!
% 16.50/5.34 % [INFO] Killing All external provers ...
% 16.50/5.34 % Time passed: 5000ms (effective reasoning time: 4123ms)
% 16.50/5.34 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 16.50/5.35 % Axioms used in derivation (231): fact_276_singleton__insert__inj__eq, fact_337_Range__insert, fact_16_rational__preference_Oaxioms_I1_J, fact_223_order__subst1, fact_354_subset__Compl__self__eq, fact_90_refl__onD2, fact_210_in__mono, fact_2_preference__axioms, fact_1_rational__preference__axioms, fact_157_rational__preference__axioms__def, fact_207_equalityE, fact_299_insert__absorb, fact_261_Id__onE, fact_307_insertI1, fact_250_preorder__on__def, fact_38_rational__preference_Ocompl, fact_324_is__singletonI, fact_274_insert__subset, fact_78_total__on__def, fact_198_subset__trans, fact_270_insertCI, fact_241_ssubst__Pair__rhs, fact_14_pref__in__at__least__as, fact_272_singletonI, fact_234_ord__le__eq__trans, fact_323_the__elem__eq, fact_220_bot__set__def, fact_199_Collect__mono, fact_94_refl__on__domain, fact_32_preference_Oreflexivity, fact_255_Id__onI, fact_159_rational__preference__axioms_Ointro, fact_229_eq__refl, fact_233_ord__eq__le__trans, fact_287_singletonD, fact_179_subsetI, fact_61_as__good__as__sameIff, fact_280_insert__subsetI, fact_217_bot_Oextremum__uniqueI, fact_204_equalityD1, fact_110_mem__Collect__eq, fact_332_lnear__order__on__empty, fact_247_trans__def, fact_224_order__subst2, fact_111_mem__Collect__eq, fact_51_rational__preference_Oweak__is__transitive, fact_349_Compl__iff, fact_26_preference_Otrans__refl, fact_341_Range_Ocases, fact_186_Collect__empty__eq, fact_228_antisym, fact_5_reflexivity, fact_243_Set_Ois__empty__def, fact_59_rational__preference_Ostrict__is__neg__transitive, fact_308_insertE, fact_152_rational__preference_Onbt__nest, fact_195_emptyE, fact_281_less__eq__prod__def, fact_13_strict__trans, fact_176_empty__subsetI, fact_127_surj__pair, fact_343_Range_Ointros, fact_225_ord__eq__le__subst, fact_232_order__class_Oorder_Oeq__iff, fact_102_at__lst__asgd__ge, fact_215_subset__emptyI, fact_269_insert__iff, fact_164_rational__preference_Ono__better__subset__pref, fact_35_preference_Oindiff__trans, fact_227_eq__iff, fact_293_insert__mono, fact_268_insert__iff, fact_285_singleton__iff, fact_181_empty__iff, fact_319_subset__singleton__iff, fact_139_no__better__than__nonepty, fact_30_preference_Onot__outside, fact_339_RangeE, fact_205_subset__eq, fact_135_rational__preference_Opref__in__at__least__as, fact_328_is__singletonE, fact_193_equals0D, fact_304_insertI2, fact_226_ord__le__eq__subst, fact_115_Collect__cong, fact_237_dual__order_Orefl, fact_148_preorder__on__empty, fact_284_doubleton__eq__iff, fact_248_trans__empty, fact_196_Collect__mono__iff, fact_282_singleton__inject, fact_200_subset__refl, fact_208_subsetD, fact_239_dual__order_Oeq__iff, fact_140_nbt__nest, fact_190_equals0I, fact_305_insertI2, fact_235_order__class_Oorder_Oantisym, fact_47_rational__preference_Ostrict__trans, fact_262_trans__Id__on, fact_114_Collect__mem__eq, fact_263_refl__on__Id__on, fact_347_subset__Compl__singleton, fact_350_ComplI, fact_7_completeD, fact_173_subset__empty, fact_246_transI, fact_273_singletonI, fact_182_empty__iff, fact_203_equalityD2, fact_338_swap__simp, fact_316_refl__on__singleton, fact_249_preference_Otransitivity, fact_300_insert__ident, fact_244_transD, fact_116_Collect__cong, fact_11_strict__not__refl__weak, fact_277_singleton__insert__inj__eq_H, fact_178_subsetI, fact_75_total__onI, fact_206_subset__eq, fact_327_is__singletonI_H, fact_71_rational__preference_Oas__good__as__sameIff, fact_346_subset__Compl__singleton, fact_240_dual__order_Oantisym, fact_303_Set_Oset__insert, fact_4_total, fact_297_insert__eq__iff, fact_209_subsetD, fact_180_subset__antisym, fact_330_linear__order__on__singleton, fact_317_total__on__singleton, fact_3_trans__refl, fact_137_no__better__subset__pref, fact_138_no__better__thansubset__rel, fact_318_subset__singletonD, fact_306_insertI1, fact_236_order__trans, fact_257_Id__on__iff, fact_6_compl, fact_216_subset__emptyI, fact_238_dual__order_Otrans, fact_197_set__eq__subset, fact_302_Set_Oset__insert, fact_8_not__outside, fact_201_subset__iff, fact_231_antisym__conv, fact_194_emptyE, fact_267_trans__singleton, fact_108_old_Oprod_Oexhaust, fact_67_old_Oprod_Oinject, fact_44_rational__preference_OcompleteD, fact_191_equals0I, fact_187_subrelI, fact_188_ex__in__conv, fact_342_Range_Osimps, fact_296_insert__eq__iff, fact_155_rational__preference_Ono__better__than__nonepty, fact_161_rational__preference_Oaxioms_I2_J, fact_24_preference_Ointro, fact_82_refl__onD, fact_86_refl__onD1, fact_251_Collect__empty__eq__bot, fact_150_total__on__empty, fact_295_mk__disjoint__insert, fact_259_Id__on__eqI, fact_289_subset__insertI2, fact_329_is__singleton__def, fact_266_Greatest__equality, fact_189_ex__in__conv, fact_64_prod_Oinject, fact_222_bot__empty__eq, fact_291_subset__insert, fact_252_relChain__def, fact_219_bot_Oextremum, fact_175_empty__subsetI, fact_60_worse__in__no__better, fact_264_under__incr, fact_40_rational__preference_Ototal, fact_214_order__refl, fact_168_rational__preference_Ono__better__thansubset__rel, fact_121_Pair__inject, fact_202_subset__iff, fact_279_insert__subsetI, fact_242_transitivity, fact_136_at__lst__asgd__not__ge, fact_245_transE, fact_10_weak__is__transitive, fact_294_mk__disjoint__insert, fact_144_rational__preference__def, fact_325_is__singleton__the__elem, fact_124_prod__cases, fact_55_rational__preference_Ostrict__not__refl__weak, fact_351_ComplI, fact_184_all__not__in__conv, fact_286_singleton__iff, fact_309_insertE, fact_353_Compl__subset__Compl__iff, fact_345_Domain__insert, fact_211_in__mono, fact_344_Range_Oinducts, fact_105_old_Oprod_Oinducts, fact_298_insert__absorb, fact_183_all__not__in__conv, fact_131_rational__preference_Oworse__in__no__better, fact_288_singletonD, fact_265_GreatestI2__order, fact_271_insertCI, fact_172_rational__preference_Oat__lst__asgd__not__ge, fact_0_assms, fact_292_subset__insert, fact_192_equals0D, fact_230_order_Otrans, fact_348_Compl__iff, fact_352_Compl__anti__mono, fact_301_insert__ident, fact_174_subset__empty, fact_340_Range__iff, fact_275_insert__subset, fact_9_strict__is__neg__transitive, fact_218_bot_Oextremum__unique, fact_290_subset__insertI, fact_185_empty__Collect__eq, fact_146_refl__on__empty, fact_142_rational__preference_Ointro, fact_283_insert__not__empty, fact_98_at__least__as__goodD, fact_20_preference__def, fact_113_Collect__mem__eq, fact_12_indiff__trans, fact_253_Id__on__empty
% 16.50/5.35 % No. of inferences in proof: 466
% 16.50/5.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5000 ms resp. 4123 ms w/o parsing
% 17.70/5.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.70/5.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------