%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP154^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 17.84s 5.22s
% Output : Refutation 18.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 263
% Syntax : Number of formulae : 528 ( 222 unt; 0 typ; 0 def)
% Number of atoms : 1616 ( 376 equ; 12 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 4634 ( 182 ~; 26 |; 144 &;3572 @)
% ( 0 <=>; 710 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 25 ( 24 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 10 con; 0-3 aty)
% Number of variables : 1360 ( 82 ^;1256 !; 22 ?;1360 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1295299783od_a_a_type,type,
set_Pr1295299783od_a_a: $tType ).
thf(produc1990712039od_a_a_type,type,
produc1990712039od_a_a: $tType ).
thf(produc398359056_set_a_type,type,
produc398359056_set_a: $tType ).
thf(produc1299534078_set_a_type,type,
produc1299534078_set_a: $tType ).
thf(set_Pr1948701895od_a_a_type,type,
set_Pr1948701895od_a_a: $tType ).
thf(produc304417648_set_a_type,type,
produc304417648_set_a: $tType ).
thf(produc270245360od_a_a_type,type,
produc270245360od_a_a: $tType ).
thf(produc386552094_set_a_type,type,
produc386552094_set_a: $tType ).
thf(produc1472671646_set_a_type,type,
produc1472671646_set_a: $tType ).
thf(produc1572603623od_a_a_type,type,
produc1572603623od_a_a: $tType ).
thf(produc376942416od_a_a_type,type,
produc376942416od_a_a: $tType ).
thf(produc275558334_set_a_type,type,
produc275558334_set_a: $tType ).
thf(produc407913767_set_a_type,type,
produc407913767_set_a: $tType ).
thf(set_Pr2045688071_set_a_type,type,
set_Pr2045688071_set_a: $tType ).
thf(produc1083127431_set_a_type,type,
produc1083127431_set_a: $tType ).
thf(produc522143687_set_a_type,type,
produc522143687_set_a: $tType ).
thf(set_se1596668135od_a_a_type,type,
set_se1596668135od_a_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(set_set_set_a_type,type,
set_set_set_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(finite179568208od_a_a_decl,type,
finite179568208od_a_a: set_Product_prod_a_a > $o ).
thf(finite_finite_set_a_decl,type,
finite_finite_set_a: set_set_a > $o ).
thf(finite_finite_a_decl,type,
finite_finite_a: set_a > $o ).
thf(inf_in920712437od_a_a_decl,type,
inf_in920712437od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(inf_inf_set_a_decl,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(sup_su615935707od_a_a_decl,type,
sup_su615935707od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(sup_sup_set_a_decl,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(lattic1600076923_set_a_decl,type,
lattic1600076923_set_a: set_set_a > set_a ).
thf(lattic501550101_set_a_decl,type,
lattic501550101_set_a: set_set_a > set_a ).
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_bo1293121322_a_a_o_decl,type,
bot_bo1293121322_a_a_o: product_prod_a_a > $o ).
thf(bot_bot_a_o_decl,type,
bot_bot_a_o: a > $o ).
thf(bot_bo1519632275_set_a_decl,type,
bot_bo1519632275_set_a: produc1691597095_set_a ).
thf(bot_bo2131659635od_a_a_decl,type,
bot_bo2131659635od_a_a: set_Product_prod_a_a ).
thf(bot_bot_set_set_a_decl,type,
bot_bot_set_set_a: set_set_a ).
thf(bot_bot_set_a_decl,type,
bot_bot_set_a: set_a ).
thf(ord_le2039441566_set_a_decl,type,
ord_le2039441566_set_a: produc1299534078_set_a > produc1299534078_set_a > $o ).
thf(ord_le1729087294_set_a_decl,type,
ord_le1729087294_set_a: produc1472671646_set_a > produc1472671646_set_a > $o ).
thf(ord_le642967742_set_a_decl,type,
ord_le642967742_set_a: produc386552094_set_a > produc386552094_set_a > $o ).
thf(ord_le2095302494_set_a_decl,type,
ord_le2095302494_set_a: produc275558334_set_a > produc275558334_set_a > $o ).
thf(ord_le1138266544_set_a_decl,type,
ord_le1138266544_set_a: produc398359056_set_a > produc398359056_set_a > $o ).
thf(ord_le526661008od_a_a_decl,type,
ord_le526661008od_a_a: produc270245360od_a_a > produc270245360od_a_a > $o ).
thf(ord_le723713223_set_a_decl,type,
ord_le723713223_set_a: produc407913767_set_a > produc407913767_set_a > $o ).
thf(ord_le1201700711_set_a_decl,type,
ord_le1201700711_set_a: produc522143687_set_a > produc522143687_set_a > $o ).
thf(ord_le560833296_set_a_decl,type,
ord_le560833296_set_a: produc304417648_set_a > produc304417648_set_a > $o ).
thf(ord_le49202928od_a_a_decl,type,
ord_le49202928od_a_a: produc376942416od_a_a > produc376942416od_a_a > $o ).
thf(ord_le1762684455_set_a_decl,type,
ord_le1762684455_set_a: produc1083127431_set_a > produc1083127431_set_a > $o ).
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_le318720350_set_a_decl,type,
ord_le318720350_set_a: set_set_a > set_set_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(produc759028718_set_a_decl,type,
produc759028718_set_a: produc1691597095_set_a > set_set_a > produc1299534078_set_a ).
thf(produc1719072398_set_a_decl,type,
produc1719072398_set_a: produc1691597095_set_a > set_a > produc1472671646_set_a ).
thf(produc1599887374_set_a_decl,type,
produc1599887374_set_a: set_Product_prod_a_a > set_set_a > produc386552094_set_a ).
thf(produc194376366_set_a_decl,type,
produc194376366_set_a: set_Product_prod_a_a > set_a > produc275558334_set_a ).
thf(produc760262016_set_a_decl,type,
produc760262016_set_a: set_set_a > produc1691597095_set_a > produc398359056_set_a ).
thf(produc1618062688od_a_a_decl,type,
produc1618062688od_a_a: set_set_a > set_Product_prod_a_a > produc270245360od_a_a ).
thf(produc2102896407_set_a_decl,type,
produc2102896407_set_a: set_set_a > set_set_a > produc407913767_set_a ).
thf(produc32105911_set_a_decl,type,
produc32105911_set_a: set_set_a > set_a > produc522143687_set_a ).
thf(produc272677600_set_a_decl,type,
produc272677600_set_a: set_a > produc1691597095_set_a > produc304417648_set_a ).
thf(produc1397177024od_a_a_decl,type,
produc1397177024od_a_a: set_a > set_Product_prod_a_a > produc376942416od_a_a ).
thf(produc1560024183_set_a_decl,type,
produc1560024183_set_a: set_a > set_set_a > produc1083127431_set_a ).
thf(produc1928581911_set_a_decl,type,
produc1928581911_set_a: set_a > set_a > produc1691597095_set_a ).
thf(product_Pair_a_a_decl,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(id_on_a_decl,type,
id_on_a: set_a > set_Product_prod_a_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_set_a_decl,type,
collect_set_a: ( set_a > $o ) > set_set_a ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(is_empty_a_decl,type,
is_empty_a: set_a > $o ).
thf(member449909584od_a_a_decl,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member_set_a_decl,type,
member_set_a: set_a > set_set_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(x_decl,type,
x: a ).
thf(y_decl,type,
y: a ).
thf(223,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_Int__subset__iff) ).
thf(1024,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(34,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ~ ( ( ord_le1824328871od_a_a @ A @ B )
=> ~ ( ord_le1824328871od_a_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_equalityE) ).
thf(365,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ~ ( ( ord_le1824328871od_a_a @ A @ B )
=> ~ ( ord_le1824328871od_a_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',fact_151_at__lst__asgd__ge) ).
thf(347,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)],[28]) ).
thf(175,axiom,
! [A: set_set_a,B: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( A != bot_bot_set_set_a )
=> ( ( finite_finite_set_a @ B )
=> ( ord_less_eq_set_a @ ( lattic501550101_set_a @ A ) @ ( lattic501550101_set_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_Sup__fin_Osubset__imp) ).
thf(846,plain,
! [A: set_set_a,B: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( A != bot_bot_set_set_a )
=> ( ( finite_finite_set_a @ B )
=> ( ord_less_eq_set_a @ ( lattic501550101_set_a @ A ) @ ( lattic501550101_set_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',fact_18_strict__trans) ).
thf(893,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)],[188]) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',fact_261_antisym__conv) ).
thf(1083,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)],[243]) ).
thf(90,axiom,
( ord_le318720350_set_a
= ( ^ [A: set_set_a,B: set_set_a] :
! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_subset__eq) ).
thf(555,plain,
( ord_le318720350_set_a
= ( ^ [A: set_set_a,B: set_set_a] :
! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(123,axiom,
! [A: set_set_a,B: set_set_a,C: set_set_a,D: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le318720350_set_a @ C @ D )
=> ( ord_le723713223_set_a @ ( produc2102896407_set_a @ A @ C ) @ ( produc2102896407_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_Pair__mono) ).
thf(666,plain,
! [A: set_set_a,B: set_set_a,C: set_set_a,D: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le318720350_set_a @ C @ D )
=> ( ord_le723713223_set_a @ ( produc2102896407_set_a @ A @ C ) @ ( produc2102896407_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',fact_41_preference_Oindiff__trans) ).
thf(352,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)],[30]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',fact_222_rational__preference_Oas__good__asIff) ).
thf(479,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)],[70]) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',fact_204_set__eq__subset) ).
thf(1105,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)],[252]) ).
thf(191,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/sandbox2/benchmark/theBenchmark.p',fact_182_subset__eq) ).
thf(909,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)],[191]) ).
thf(112,axiom,
! [A: set_a,B: set_a] :
( ( ( sup_sup_set_a @ A @ B )
= bot_bot_set_a )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_Un__empty) ).
thf(628,plain,
! [A: set_a,B: set_a] :
( ( ( sup_sup_set_a @ A @ B )
= bot_bot_set_a )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(226,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ B @ C ) )
=> ( ord_less_eq_set_a @ B @ ( lattic1600076923_set_a @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_Inf__fin_OboundedI) ).
thf(1031,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ B @ C ) )
=> ( ord_less_eq_set_a @ B @ ( lattic1600076923_set_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',fact_158_equals0I) ).
thf(276,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)],[4]) ).
thf(238,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( member_set_a @ B @ A )
=> ( ord_less_eq_set_a @ B @ ( lattic501550101_set_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Sup__fin_OcoboundedI) ).
thf(1068,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( member_set_a @ B @ A )
=> ( ord_less_eq_set_a @ B @ ( lattic501550101_set_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',fact_154_ex__in__conv) ).
thf(308,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)],[15]) ).
thf(37,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( total_on_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_rational__preference_Ototal) ).
thf(379,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)],[37]) ).
thf(103,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o,D: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1824328871od_a_a @ ( inf_in920712437od_a_a @ A @ ( collec645855634od_a_a @ C ) ) @ ( inf_in920712437od_a_a @ B @ ( collec645855634od_a_a @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_Int__Collect__mono) ).
thf(597,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o,D: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1824328871od_a_a @ ( inf_in920712437od_a_a @ A @ ( collec645855634od_a_a @ C ) ) @ ( inf_in920712437od_a_a @ B @ ( collec645855634od_a_a @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',fact_44_rational__preference_Ocompl) ).
thf(523,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)],[84]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',fact_305_transI) ).
thf(582,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)],[99]) ).
thf(152,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: set_a,D: set_Product_prod_a_a] :
( ( refl_on_a @ A @ B )
=> ( ( refl_on_a @ C @ D )
=> ( refl_on_a @ ( sup_sup_set_a @ A @ C ) @ ( sup_su615935707od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_refl__on__Un) ).
thf(762,plain,
! [A: set_a,B: set_Product_prod_a_a,C: set_a,D: set_Product_prod_a_a] :
( ( refl_on_a @ A @ B )
=> ( ( refl_on_a @ C @ D )
=> ( refl_on_a @ ( sup_sup_set_a @ A @ C ) @ ( sup_su615935707od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',fact_83_rational__preference_Onbt__nest) ).
thf(878,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)],[183]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',fact_303_transD) ).
thf(440,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)],[57]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_53_rational__preference_Ostrict__trans) ).
thf(614,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)],[108]) ).
thf(127,axiom,
! [A: set_Product_prod_a_a] : ( total_on_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_total__on__empty) ).
thf(677,plain,
! [A: set_Product_prod_a_a] : ( total_on_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',fact_198_Collect__mono) ).
thf(1041,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)],[228]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_77_rational__preference_Ono__better__thansubset__rel) ).
thf(861,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(39,axiom,
( ( (=) @ set_set_a )
= ( ^ [A: set_set_a,B: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
& ( ord_le318720350_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_set__eq__subset) ).
thf(385,plain,
( ( (=) @ set_set_a )
= ( ^ [A: set_set_a,B: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
& ( ord_le318720350_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',fact_319_Id__onE) ).
thf(550,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)],[89]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',fact_16_strict__is__neg__transitive) ).
thf(814,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)],[167]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',fact_247_total__onI) ).
thf(698,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)],[134]) ).
thf(236,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/sandbox2/benchmark/theBenchmark.p',fact_69_rational__preference_Oworse__in__no__better) ).
thf(1063,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)],[236]) ).
thf(87,axiom,
! [A: set_a,B: a > a > $o] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
~ ( B @ C @ C )
=> ( ! [C: a,D: a,E: a] :
( ( B @ C @ D )
=> ( ( B @ D @ E )
=> ( B @ C @ E ) ) )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ? [D: a] :
( ( member_a @ D @ A )
& ( B @ C @ D ) ) )
=> ( A = bot_bot_set_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_finite__transitivity__chain) ).
thf(538,plain,
! [A: set_a,B: a > a > $o] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
~ ( B @ C @ C )
=> ( ! [C: a,D: a,E: a] :
( ( B @ C @ D )
=> ( ( B @ D @ E )
=> ( B @ C @ E ) ) )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ? [D: a] :
( ( member_a @ D @ A )
& ( B @ C @ D ) ) )
=> ( A = bot_bot_set_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(44,axiom,
( bot_bo1519632275_set_a
= ( produc1928581911_set_a @ bot_bot_set_a @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_bot__prod__def) ).
thf(404,plain,
( bot_bo1519632275_set_a
= ( produc1928581911_set_a @ bot_bot_set_a @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',fact_14_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)],[189]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',fact_253_dual__order_Oeq__iff) ).
thf(782,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)],[161]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',fact_304_transE) ).
thf(417,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)],[49]) ).
thf(211,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( member_set_a @ B @ A )
=> ? [C: set_a] :
( ( member_set_a @ C @ A )
& ( ord_less_eq_set_a @ B @ C )
& ! [D: set_a] :
( ( member_set_a @ D @ A )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_finite__has__maximal2) ).
thf(973,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( member_set_a @ B @ A )
=> ? [C: set_a] :
( ( member_set_a @ C @ A )
& ( ord_less_eq_set_a @ B @ C )
& ! [D: set_a] :
( ( member_set_a @ D @ A )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(8,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_emptyE) ).
thf(288,plain,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(118,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( trans_a @ A )
=> ( ( trans_a @ B )
=> ( trans_a @ ( inf_in920712437od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_trans__Int) ).
thf(651,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( trans_a @ A )
=> ( ( trans_a @ B )
=> ( trans_a @ ( inf_in920712437od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(138,axiom,
refl_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_refl__on__empty) ).
thf(719,plain,
refl_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',fact_287_refl__on__domain) ).
thf(504,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)],[78]) ).
thf(109,axiom,
! [A: set_a] :
~ ( member_set_a @ A @ bot_bot_set_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_empty__iff) ).
thf(619,plain,
! [A: set_a] :
~ ( member_set_a @ A @ bot_bot_set_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(27,axiom,
! [A: set_set_a,B: set_set_a,C: set_set_a,D: set_set_a] :
( ( ord_le723713223_set_a @ ( produc2102896407_set_a @ A @ B ) @ ( produc2102896407_set_a @ C @ D ) )
= ( ( ord_le318720350_set_a @ A @ C )
& ( ord_le318720350_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Pair__le) ).
thf(344,plain,
! [A: set_set_a,B: set_set_a,C: set_set_a,D: set_set_a] :
( ( ord_le723713223_set_a @ ( produc2102896407_set_a @ A @ B ) @ ( produc2102896407_set_a @ C @ D ) )
= ( ( ord_le318720350_set_a @ A @ C )
& ( ord_le318720350_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(31,axiom,
! [A: set_set_a] :
( ( ? [B: set_a] : ( member_set_a @ B @ A ) )
= ( A != bot_bot_set_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_ex__in__conv) ).
thf(357,plain,
! [A: set_set_a] :
( ( ? [B: set_a] : ( member_set_a @ B @ A ) )
= ( A != bot_bot_set_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(64,axiom,
! [A: set_set_a,B: set_set_a,C: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le318720350_set_a @ B @ C )
=> ( ord_le318720350_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_subset__trans) ).
thf(460,plain,
! [A: set_set_a,B: set_set_a,C: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le318720350_set_a @ B @ C )
=> ( ord_le318720350_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(190,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) )
=> ( ord_less_eq_set_a @ ( lattic501550101_set_a @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_Sup__fin_OboundedI) ).
thf(902,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) )
=> ( ord_less_eq_set_a @ ( lattic501550101_set_a @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(245,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/sandbox2/benchmark/theBenchmark.p',fact_256_order__trans) ).
thf(1087,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)],[245]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',fact_254_dual__order_Otrans) ).
thf(1147,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)],[264]) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',fact_306_trans__def) ).
thf(606,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)],[105]) ).
thf(221,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_order__refl) ).
thf(1013,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(184,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/sandbox2/benchmark/theBenchmark.p',fact_192_subset__iff) ).
thf(881,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)],[184]) ).
thf(60,axiom,
! [A: set_a] : ( trans_a @ ( id_on_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_trans__Id__on) ).
thf(448,plain,
! [A: set_a] : ( trans_a @ ( id_on_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(17,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_empty__iff) ).
thf(316,plain,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(255,axiom,
! [A: produc1691597095_set_a,B: set_a,C: produc1691597095_set_a,D: set_a] :
( ( ord_le1729087294_set_a @ ( produc1719072398_set_a @ A @ B ) @ ( produc1719072398_set_a @ C @ D ) )
= ( ( ord_le486764743_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Pair__le) ).
thf(1115,plain,
! [A: produc1691597095_set_a,B: set_a,C: produc1691597095_set_a,D: set_a] :
( ( ord_le1729087294_set_a @ ( produc1719072398_set_a @ A @ B ) @ ( produc1719072398_set_a @ C @ D ) )
= ( ( ord_le486764743_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(20,axiom,
! [A: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ bot_bo2131659635od_a_a )
= ( A = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_subset__empty) ).
thf(325,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)],[20]) ).
thf(195,axiom,
! [A: set_set_a,B: set_set_a,C: set_a,D: set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_le1201700711_set_a @ ( produc32105911_set_a @ A @ C ) @ ( produc32105911_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_Pair__mono) ).
thf(924,plain,
! [A: set_set_a,B: set_set_a,C: set_a,D: set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_le1201700711_set_a @ ( produc32105911_set_a @ A @ C ) @ ( produc32105911_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(150,axiom,
! [A: set_a > $o] :
( ( bot_bot_set_set_a
= ( collect_set_a @ A ) )
= ( ! [B: set_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_empty__Collect__eq) ).
thf(756,plain,
! [A: set_a > $o] :
( ( bot_bot_set_set_a
= ( collect_set_a @ A ) )
= ( ! [B: set_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(101,axiom,
( ord_le318720350_set_a
= ( ^ [A: set_set_a,B: set_set_a] :
! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_subset__iff) ).
thf(591,plain,
( ord_le318720350_set_a
= ( ^ [A: set_set_a,B: set_set_a] :
! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(58,axiom,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_ex__in__conv) ).
thf(443,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(36,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: set_a,D: set_Product_prod_a_a] :
( ( refl_on_a @ A @ B )
=> ( ( refl_on_a @ C @ D )
=> ( refl_on_a @ ( inf_inf_set_a @ A @ C ) @ ( inf_in920712437od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_refl__on__Int) ).
thf(376,plain,
! [A: set_a,B: set_Product_prod_a_a,C: set_a,D: set_Product_prod_a_a] :
( ( refl_on_a @ A @ B )
=> ( ( refl_on_a @ C @ D )
=> ( refl_on_a @ ( inf_inf_set_a @ A @ C ) @ ( inf_in920712437od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(116,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_set__eq__subset) ).
thf(646,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(232,axiom,
! [A: set_set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ? [B: set_a] :
( ( member_set_a @ B @ A )
& ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_finite__has__maximal) ).
thf(1051,plain,
! [A: set_set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ? [B: set_a] :
( ( member_set_a @ B @ A )
& ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(72,axiom,
! [A: set_set_a] :
( ! [B: set_a] :
~ ( member_set_a @ B @ A )
=> ( A = bot_bot_set_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_equals0I) ).
thf(485,plain,
! [A: set_set_a] :
( ! [B: set_a] :
~ ( member_set_a @ B @ A )
=> ( A = bot_bot_set_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(172,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/sandbox2/benchmark/theBenchmark.p',fact_258_ord__le__eq__trans) ).
thf(834,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)],[172]) ).
thf(154,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_Int__lower1) ).
thf(766,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',fact_285_refl__onD2) ).
thf(687,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)],[131]) ).
thf(5,axiom,
! [A: set_a,B: set_a > $o] :
( ( member_set_a @ A @ ( collect_set_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_mem__Collect__eq) ).
thf(280,plain,
! [A: set_a,B: set_a > $o] :
( ( member_set_a @ A @ ( collect_set_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(217,axiom,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ ( collect_a @ C ) ) @ ( inf_inf_set_a @ B @ ( collect_a @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_Int__Collect__mono) ).
thf(998,plain,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ ( collect_a @ C ) ) @ ( inf_inf_set_a @ B @ ( collect_a @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(47,axiom,
! [A: set_set_a,B: set_set_a] :
( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) )
=> ( ord_le318720350_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_subsetI) ).
thf(411,plain,
! [A: set_set_a,B: set_set_a] :
( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) )
=> ( ord_le318720350_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',fact_13_compl) ).
thf(988,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)],[213]) ).
thf(1,conjecture,
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(265,plain,
~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(176,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/sandbox2/benchmark/theBenchmark.p',fact_143_subset__antisym) ).
thf(849,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)],[176]) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',fact_171_in__mono) ).
thf(1074,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)],[240]) ).
thf(122,axiom,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_equals0D) ).
thf(661,plain,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(38,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_equalityD1) ).
thf(381,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(80,axiom,
order_preorder_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_preorder__on__empty) ).
thf(512,plain,
order_preorder_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',fact_17_weak__is__transitive) ).
thf(942,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)],[201]) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',fact_175_subsetD) ).
thf(1047,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)],[230]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',fact_322_GreatestI2__order) ).
thf(798,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)],[166]) ).
thf(233,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_Int__absorb1) ).
thf(1057,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(247,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/sandbox2/benchmark/theBenchmark.p',fact_260_order__class_Oorder_Oeq__iff) ).
thf(1091,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)],[247]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',fact_3_nbt__nest) ).
thf(778,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)],[159]) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',fact_114_as__good__asIff) ).
thf(952,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)],[205]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_170_in__mono) ).
thf(349,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)],[29]) ).
thf(168,axiom,
! [A: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ A @ carrier )
=> ( ( prefer1676310729than_a @ A @ carrier @ relation )
!= bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_no__better__than__nonepty) ).
thf(820,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)],[168]) ).
thf(42,axiom,
! [A: set_set_a,B: set_set_a] :
( ( A = B )
=> ~ ( ( ord_le318720350_set_a @ A @ B )
=> ~ ( ord_le318720350_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_equalityE) ).
thf(392,plain,
! [A: set_set_a,B: set_set_a] :
( ( A = B )
=> ~ ( ( ord_le318720350_set_a @ A @ B )
=> ~ ( ord_le318720350_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(11,axiom,
! [A: product_prod_a_a > $o] :
( ( ( collec645855634od_a_a @ A )
= bot_bo2131659635od_a_a )
= ( ! [B: product_prod_a_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Collect__empty__eq) ).
thf(297,plain,
! [A: product_prod_a_a > $o] :
( ( ( collec645855634od_a_a @ A )
= bot_bo2131659635od_a_a )
= ( ! [B: product_prod_a_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(163,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ( ord_less_eq_set_a @ B @ ( lattic1600076923_set_a @ A ) )
=> ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_Inf__fin_OboundedE) ).
thf(788,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ( ord_less_eq_set_a @ B @ ( lattic1600076923_set_a @ A ) )
=> ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',fact_65_rational__preference_Ostrict__is__neg__transitive) ).
thf(729,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)],[142]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',fact_61_rational__preference_Ostrict__not__refl__weak) ).
thf(361,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)],[33]) ).
thf(111,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_empty__iff) ).
thf(625,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',fact_267_ord__eq__le__subst) ).
thf(852,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)],[177]) ).
thf(22,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ bot_bo2131659635od_a_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_empty__subsetI) ).
thf(329,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ bot_bo2131659635od_a_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(171,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_equalityD2) ).
thf(830,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(74,axiom,
! [A: set_set_a] : ( ord_le318720350_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_subset__refl) ).
thf(493,plain,
! [A: set_set_a] : ( ord_le318720350_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(224,axiom,
! [A: a,B: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( prefer161218362good_a @ A @ carrier @ relation )
= ( prefer161218362good_a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_same__at__least__as__equal) ).
thf(1027,plain,
! [A: a,B: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( prefer161218362good_a @ A @ carrier @ relation )
= ( prefer161218362good_a @ B @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',fact_312_Id__onI) ).
thf(682,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)],[129]) ).
thf(136,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer1292084992ence_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_rational__preference_Oaxioms_I1_J) ).
thf(710,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)],[136]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',fact_226_rational__preference_Oat__lst__asgd__not__ge) ).
thf(456,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)],[63]) ).
thf(174,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_equalityD1) ).
thf(842,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(181,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ~ ( finite_finite_a @ A )
=> ~ ( finite_finite_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_infinite__super) ).
thf(874,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ~ ( finite_finite_a @ A )
=> ~ ( finite_finite_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',fact_178_equalityE) ).
thf(980,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)],[212]) ).
thf(249,axiom,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( finite_finite_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_rev__finite__subset) ).
thf(1096,plain,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( finite_finite_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(219,axiom,
! [A: set_a,B: set_set_a,C: set_a,D: set_set_a] :
( ( ord_le1762684455_set_a @ ( produc1560024183_set_a @ A @ B ) @ ( produc1560024183_set_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_le318720350_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Pair__le) ).
thf(1006,plain,
! [A: set_a,B: set_set_a,C: set_a,D: set_set_a] :
( ( ord_le1762684455_set_a @ ( produc1560024183_set_a @ A @ B ) @ ( produc1560024183_set_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_le318720350_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(261,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ A @ carrier ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_not__outside) ).
thf(1138,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)],[261]) ).
thf(102,axiom,
! [A: set_set_a,B: set_set_a] :
( ( A = B )
=> ( ord_le318720350_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_equalityD1) ).
thf(593,plain,
! [A: set_set_a,B: set_set_a] :
( ( A = B )
=> ( ord_le318720350_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',fact_269_order__subst1) ).
thf(869,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)],[180]) ).
thf(83,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_equalityD2) ).
thf(519,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(145,axiom,
! [A: set_set_a,B: set_set_a,C: produc1691597095_set_a,D: produc1691597095_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le486764743_set_a @ C @ D )
=> ( ord_le1138266544_set_a @ ( produc760262016_set_a @ A @ C ) @ ( produc760262016_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Pair__mono) ).
thf(742,plain,
! [A: set_set_a,B: set_set_a,C: produc1691597095_set_a,D: produc1691597095_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le486764743_set_a @ C @ D )
=> ( ord_le1138266544_set_a @ ( produc760262016_set_a @ A @ C ) @ ( produc760262016_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(50,axiom,
! [A: set_Product_prod_a_a,B: set_set_a,C: set_Product_prod_a_a,D: set_set_a] :
( ( ord_le642967742_set_a @ ( produc1599887374_set_a @ A @ B ) @ ( produc1599887374_set_a @ C @ D ) )
= ( ( ord_le1824328871od_a_a @ A @ C )
& ( ord_le318720350_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Pair__le) ).
thf(420,plain,
! [A: set_Product_prod_a_a,B: set_set_a,C: set_Product_prod_a_a,D: set_set_a] :
( ( ord_le642967742_set_a @ ( produc1599887374_set_a @ A @ B ) @ ( produc1599887374_set_a @ C @ D ) )
= ( ( ord_le1824328871od_a_a @ A @ C )
& ( ord_le318720350_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',fact_84_at__lst__asgd__not__ge) ).
thf(1118,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)],[256]) ).
thf(21,axiom,
trans_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_trans__empty) ).
thf(328,plain,
trans_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(124,axiom,
( prefer719835986ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
& ( prefer580340847ioms_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_rational__preference__def) ).
thf(669,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)],[124]) ).
thf(69,axiom,
! [A: produc1691597095_set_a,B: produc1691597095_set_a,C: set_set_a,D: set_set_a] :
( ( ord_le486764743_set_a @ A @ B )
=> ( ( ord_le318720350_set_a @ C @ D )
=> ( ord_le2039441566_set_a @ ( produc759028718_set_a @ A @ C ) @ ( produc759028718_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_Pair__mono) ).
thf(476,plain,
! [A: produc1691597095_set_a,B: produc1691597095_set_a,C: set_set_a,D: set_set_a] :
( ( ord_le486764743_set_a @ A @ B )
=> ( ( ord_le318720350_set_a @ C @ D )
=> ( ord_le2039441566_set_a @ ( produc759028718_set_a @ A @ C ) @ ( produc759028718_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(73,axiom,
! [A: set_a] :
( ~ ( finite_finite_a @ A )
=> ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_infinite__imp__nonempty) ).
thf(489,plain,
! [A: set_a] :
( ~ ( finite_finite_a @ A )
=> ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(128,axiom,
! [A: set_a] :
~ ( member_set_a @ A @ bot_bot_set_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_emptyE) ).
thf(679,plain,
! [A: set_a] :
~ ( member_set_a @ A @ bot_bot_set_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(210,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ C ) @ ( inf_inf_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_Int__mono) ).
thf(970,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ C ) @ ( inf_inf_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',fact_174_subsetD) ).
thf(622,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)],[110]) ).
thf(250,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_finite__subset) ).
thf(1099,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',fact_257_order__class_Oorder_Oantisym) ).
thf(911,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)],[192]) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',fact_140_subsetI) ).
thf(1131,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)],[259]) ).
thf(119,axiom,
! [A: set_a] : ( refl_on_a @ A @ ( id_on_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_refl__on__Id__on) ).
thf(654,plain,
! [A: set_a] : ( refl_on_a @ A @ ( id_on_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(234,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/sandbox2/benchmark/theBenchmark.p',fact_86_pref__in__at__least__as) ).
thf(1060,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)],[234]) ).
thf(231,axiom,
total_on_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_total) ).
thf(1050,plain,
total_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',fact_310_under__incr) ).
thf(792,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)],[164]) ).
thf(244,axiom,
finite_finite_a @ carrier,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).
thf(1086,plain,
finite_finite_a @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(3,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > product_prod_a_a > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [C: product_prod_a_a] :
~ ( B @ C @ C )
=> ( ! [C: product_prod_a_a,D: product_prod_a_a,E: product_prod_a_a] :
( ( B @ C @ D )
=> ( ( B @ D @ E )
=> ( B @ C @ E ) ) )
=> ( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ? [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
& ( B @ C @ D ) ) )
=> ( A = bot_bo2131659635od_a_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_finite__transitivity__chain) ).
thf(266,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > product_prod_a_a > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [C: product_prod_a_a] :
~ ( B @ C @ C )
=> ( ! [C: product_prod_a_a,D: product_prod_a_a,E: product_prod_a_a] :
( ( B @ C @ D )
=> ( ( B @ D @ E )
=> ( B @ C @ E ) ) )
=> ( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ? [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
& ( B @ C @ D ) ) )
=> ( A = bot_bo2131659635od_a_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
finite_finite_a @ bot_bot_set_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_finite_OemptyI) ).
thf(360,plain,
finite_finite_a @ bot_bot_set_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',fact_162_equals0D) ).
thf(311,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)],[16]) ).
thf(194,axiom,
! [A: set_set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ord_less_eq_set_a @ ( lattic1600076923_set_a @ A ) @ ( lattic501550101_set_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_Inf__fin__le__Sup__fin) ).
thf(921,plain,
! [A: set_set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ord_less_eq_set_a @ ( lattic1600076923_set_a @ A ) @ ( lattic501550101_set_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(153,axiom,
trans_a @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_transitivity) ).
thf(765,plain,
trans_a @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(239,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A @ B ) @ ( produc1928581911_set_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Pair__le) ).
thf(1071,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A @ B ) @ ( produc1928581911_set_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',fact_259_ord__eq__le__trans) ).
thf(888,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)],[187]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',fact_252_dual__order_Oantisym) ).
thf(1135,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)],[260]) ).
thf(147,axiom,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_bot__empty__eq) ).
thf(750,plain,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(52,axiom,
prefer580340847ioms_a = total_on_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_rational__preference__axioms__def) ).
thf(425,plain,
prefer580340847ioms_a = total_on_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(169,axiom,
! [A: set_set_a,B: set_a,C: set_set_a,D: set_a] :
( ( ord_le1201700711_set_a @ ( produc32105911_set_a @ A @ B ) @ ( produc32105911_set_a @ C @ D ) )
= ( ( ord_le318720350_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Pair__le) ).
thf(824,plain,
! [A: set_set_a,B: set_a,C: set_set_a,D: set_a] :
( ( ord_le1201700711_set_a @ ( produc32105911_set_a @ A @ B ) @ ( produc32105911_set_a @ C @ D ) )
= ( ( ord_le318720350_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',fact_274_old_Oprod_Oinducts) ).
thf(745,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)],[146]) ).
thf(81,axiom,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_surj__pair) ).
thf(513,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)],[81]) ).
thf(54,axiom,
! [A: set_set_a,B: set_set_a] :
( ( A = B )
=> ( ord_le318720350_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_equalityD2) ).
thf(430,plain,
! [A: set_set_a,B: set_set_a] :
( ( A = B )
=> ( ord_le318720350_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(51,axiom,
( bot_bot_set_a
= ( collect_a @ bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_bot__set__def) ).
thf(423,plain,
( bot_bot_set_a
= ( collect_a @ bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(133,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_equals0I) ).
thf(694,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(258,axiom,
! [A: set_set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ? [B: set_a] :
( ( member_set_a @ B @ A )
& ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_finite__has__minimal) ).
thf(1125,plain,
! [A: set_set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ? [B: set_a] :
( ( member_set_a @ B @ A )
& ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(157,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A @ C ) @ ( produc1928581911_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Pair__mono) ).
thf(772,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_le486764743_set_a @ ( produc1928581911_set_a @ A @ C ) @ ( produc1928581911_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(7,axiom,
( bot_bo1293121322_a_a_o
= ( ^ [A: product_prod_a_a] : ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_bot__empty__eq) ).
thf(286,plain,
( bot_bo1293121322_a_a_o
= ( ^ [A: product_prod_a_a] : ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',fact_26_preference__def) ).
thf(577,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)],[97]) ).
thf(207,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/sandbox2/benchmark/theBenchmark.p',fact_321_Greatest__equality) ).
thf(958,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)],[207]) ).
thf(98,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/sandbox2/benchmark/theBenchmark.p',fact_292_subset__emptyI) ).
thf(579,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)],[98]) ).
thf(9,axiom,
! [A: set_set_a] :
( ( collect_set_a
@ ^ [B: set_a] : ( member_set_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Collect__mem__eq) ).
thf(291,plain,
! [A: set_set_a] :
( ( collect_set_a
@ ^ [B: set_a] : ( member_set_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',fact_317_Id__on__eqI) ).
thf(641,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)],[115]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',fact_242_prod_Oinject) ).
thf(572,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)],[95]) ).
thf(107,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_subset__antisym) ).
thf(611,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',fact_281_refl__onD) ).
thf(498,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)],[76]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',fact_19_indiff__trans) ).
thf(1107,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)],[253]) ).
thf(24,axiom,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_empty__Collect__eq) ).
thf(335,plain,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(246,axiom,
prefer1292084992ence_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_preference__axioms) ).
thf(1090,plain,
prefer1292084992ence_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(203,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: set_a,D: set_Product_prod_a_a] :
( ( ord_le49202928od_a_a @ ( produc1397177024od_a_a @ A @ B ) @ ( produc1397177024od_a_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_le1824328871od_a_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_Pair__le) ).
thf(947,plain,
! [A: set_a,B: set_Product_prod_a_a,C: set_a,D: set_Product_prod_a_a] :
( ( ord_le49202928od_a_a @ ( produc1397177024od_a_a @ A @ B ) @ ( produc1397177024od_a_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_le1824328871od_a_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(45,axiom,
! [A: set_set_a,B: set_set_a,C: set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_in__mono) ).
thf(406,plain,
! [A: set_set_a,B: set_set_a,C: set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(162,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ( ord_less_eq_set_a @ ( lattic501550101_set_a @ A ) @ B )
=> ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_Sup__fin_OboundedE) ).
thf(784,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ( ord_less_eq_set_a @ ( lattic501550101_set_a @ A ) @ B )
=> ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(143,axiom,
! [A: set_set_a,B: set_set_a,C: set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_subsetD) ).
thf(736,plain,
! [A: set_set_a,B: set_set_a,C: set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( member_set_a @ C @ A )
=> ( member_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',fact_7_no__better__subset__pref) ).
thf(990,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)],[214]) ).
thf(263,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_bot_Oextremum__uniqueI) ).
thf(1144,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)],[263]) ).
thf(79,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_mem__Collect__eq) ).
thf(509,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(55,axiom,
! [A: set_a,B: set_a] :
( ( ( finite_finite_a @ A )
| ( finite_finite_a @ B ) )
=> ( finite_finite_a @ ( inf_inf_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_finite__Int) ).
thf(434,plain,
! [A: set_a,B: set_a] :
( ( ( finite_finite_a @ A )
| ( finite_finite_a @ B ) )
=> ( finite_finite_a @ ( inf_inf_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(13,axiom,
( ( id_on_a @ bot_bot_set_a )
= bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_Id__on__empty) ).
thf(303,plain,
( ( id_on_a @ bot_bot_set_a )
= bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(257,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_Un__subset__iff) ).
thf(1122,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(40,axiom,
! [A: set_a > $o,B: set_a > $o] :
( ( ord_le318720350_set_a @ ( collect_set_a @ A ) @ ( collect_set_a @ B ) )
= ( ! [C: set_a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Collect__mono__iff) ).
thf(387,plain,
! [A: set_a > $o,B: set_a > $o] :
( ( ord_le318720350_set_a @ ( collect_set_a @ A ) @ ( collect_set_a @ B ) )
= ( ! [C: set_a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(242,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/sandbox2/benchmark/theBenchmark.p',fact_8_no__better__thansubset__rel) ).
thf(1080,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)],[242]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',fact_271_prod__cases) ).
thf(631,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)],[113]) ).
thf(141,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_subset__trans) ).
thf(726,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(71,axiom,
( is_empty_a
= ( ^ [A: set_a] : ( A = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_Set_Ois__empty__def) ).
thf(483,plain,
( is_empty_a
= ( ^ [A: set_a] : ( A = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(198,axiom,
! [A: set_set_a,B: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( A != bot_bot_set_set_a )
=> ( ( finite_finite_set_a @ B )
=> ( ord_less_eq_set_a @ ( lattic1600076923_set_a @ B ) @ ( lattic1600076923_set_a @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_Inf__fin_Osubset__imp) ).
thf(932,plain,
! [A: set_set_a,B: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( A != bot_bot_set_set_a )
=> ( ( finite_finite_set_a @ B )
=> ( ord_less_eq_set_a @ ( lattic1600076923_set_a @ B ) @ ( lattic1600076923_set_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(254,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( member_set_a @ B @ A )
=> ( ord_less_eq_set_a @ ( lattic1600076923_set_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Inf__fin_OcoboundedI) ).
thf(1112,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( member_set_a @ B @ A )
=> ( ord_less_eq_set_a @ ( lattic1600076923_set_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',fact_294_ssubst__Pair__rhs) ).
thf(636,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)],[114]) ).
thf(237,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_subset__refl) ).
thf(1066,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(160,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_bot_Oextremum) ).
thf(780,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(185,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_Int__absorb2) ).
thf(883,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',fact_266_ord__le__eq__subst) ).
thf(1015,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)],[222]) ).
thf(106,axiom,
! [A: set_set_a] :
( ( ! [B: set_a] :
~ ( member_set_a @ B @ A ) )
= ( A = bot_bot_set_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_all__not__in__conv) ).
thf(608,plain,
! [A: set_set_a] :
( ( ! [B: set_a] :
~ ( member_set_a @ B @ A ) )
= ( A = bot_bot_set_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(93,axiom,
! [A: set_set_a,B: set_a] :
( ( A = bot_bot_set_set_a )
=> ~ ( member_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_equals0D) ).
thf(563,plain,
! [A: set_set_a,B: set_a] :
( ( A = bot_bot_set_set_a )
=> ~ ( member_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(56,axiom,
! [A: set_set_a] : ( ord_le318720350_set_a @ bot_bot_set_set_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_empty__subsetI) ).
thf(438,plain,
! [A: set_set_a] : ( ord_le318720350_set_a @ bot_bot_set_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',fact_36_preference_Onot__outside) ).
thf(658,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)],[121]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',fact_262_order_Otrans) ).
thf(768,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)],[155]) ).
thf(170,axiom,
! [A: set_Product_prod_a_a,B: set_a,C: set_Product_prod_a_a,D: set_a] :
( ( ord_le2095302494_set_a @ ( produc194376366_set_a @ A @ B ) @ ( produc194376366_set_a @ C @ D ) )
= ( ( ord_le1824328871od_a_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_Pair__le) ).
thf(827,plain,
! [A: set_Product_prod_a_a,B: set_a,C: set_Product_prod_a_a,D: set_a] :
( ( ord_le2095302494_set_a @ ( produc194376366_set_a @ A @ B ) @ ( produc194376366_set_a @ C @ D ) )
= ( ( ord_le1824328871od_a_a @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(68,axiom,
! [A: set_a,B: set_a] :
( ( ~ ( finite_finite_a @ ( sup_sup_set_a @ A @ B ) ) )
= ( ~ ( finite_finite_a @ A )
| ~ ( finite_finite_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_infinite__Un) ).
thf(473,plain,
! [A: set_a,B: set_a] :
( ( ~ ( finite_finite_a @ ( sup_sup_set_a @ A @ B ) ) )
= ( ~ ( finite_finite_a @ A )
| ~ ( finite_finite_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',fact_20_strict__not__refl__weak) ).
thf(944,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)],[202]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',fact_201_subset__trans) ).
thf(795,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)],[165]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',fact_191_subset__iff) ).
thf(548,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)],[88]) ).
thf(196,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ( ord_less_eq_set_a @ B @ ( lattic1600076923_set_a @ A ) )
= ( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_Inf__fin_Obounded__iff) ).
thf(927,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ( ord_less_eq_set_a @ B @ ( lattic1600076923_set_a @ A ) )
= ( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(117,axiom,
! [A: set_a,B: set_a] :
( ~ ( finite_finite_a @ A )
=> ~ ( finite_finite_a @ ( sup_sup_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_Un__infinite) ).
thf(648,plain,
! [A: set_a,B: set_a] :
( ~ ( finite_finite_a @ A )
=> ~ ( finite_finite_a @ ( sup_sup_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(82,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Collect__empty__eq) ).
thf(516,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',fact_207_Collect__mono__iff) ).
thf(939,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)],[200]) ).
thf(149,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( order_preorder_on_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_preference_Otrans__refl) ).
thf(754,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)],[149]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',fact_265_eq__iff) ).
thf(968,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)],[209]) ).
thf(85,axiom,
! [A: set_set_a,B: set_Product_prod_a_a,C: set_set_a,D: set_Product_prod_a_a] :
( ( ord_le526661008od_a_a @ ( produc1618062688od_a_a @ A @ B ) @ ( produc1618062688od_a_a @ C @ D ) )
= ( ( ord_le318720350_set_a @ A @ C )
& ( ord_le1824328871od_a_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Pair__le) ).
thf(525,plain,
! [A: set_set_a,B: set_Product_prod_a_a,C: set_set_a,D: set_Product_prod_a_a] :
( ( ord_le526661008od_a_a @ ( produc1618062688od_a_a @ A @ B ) @ ( produc1618062688od_a_a @ C @ D ) )
= ( ( ord_le318720350_set_a @ A @ C )
& ( ord_le1824328871od_a_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',fact_218_rational__preference_Oas__good__as__sameIff) ).
thf(690,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)],[132]) ).
thf(135,axiom,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ ( sup_sup_set_a @ A @ B ) )
= ( ( finite_finite_a @ A )
& ( finite_finite_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_finite__Un) ).
thf(707,plain,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ ( sup_sup_set_a @ A @ B ) )
= ( ( finite_finite_a @ A )
& ( finite_finite_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(144,axiom,
! [A: set_set_a,B: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le318720350_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_subset__antisym) ).
thf(739,plain,
! [A: set_set_a,B: set_set_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le318720350_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(46,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_subset__refl) ).
thf(409,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',fact_30_preference_Ointro) ).
thf(712,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)],[137]) ).
thf(91,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Collect__mem__eq) ).
thf(557,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',fact_50_rational__preference_OcompleteD) ).
thf(673,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)],[126]) ).
thf(23,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ A ) @ ( collec645855634od_a_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_Collect__mono) ).
thf(331,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ A ) @ ( collec645855634od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(227,axiom,
! [A: set_a,B: produc1691597095_set_a,C: set_a,D: produc1691597095_set_a] :
( ( ord_le560833296_set_a @ ( produc272677600_set_a @ A @ B ) @ ( produc272677600_set_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_le486764743_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_Pair__le) ).
thf(1038,plain,
! [A: set_a,B: produc1691597095_set_a,C: set_a,D: produc1691597095_set_a] :
( ( ord_le560833296_set_a @ ( produc272677600_set_a @ A @ B ) @ ( produc272677600_set_a @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_le486764743_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(65,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( refl_on_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_preference_Oreflexivity) ).
thf(463,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)],[65]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',fact_283_refl__onD1) ).
thf(338,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)],[25]) ).
thf(262,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/sandbox2/benchmark/theBenchmark.p',fact_113_as__good__as__sameIff) ).
thf(1141,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)],[262]) ).
thf(120,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( total_on_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_rational__preference__axioms_Ointro) ).
thf(656,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)],[120]) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',fact_268_order__subst2) ).
thf(864,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)],[179]) ).
thf(59,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( trans_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_preference_Otransitivity) ).
thf(446,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)],[59]) ).
thf(182,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_Int__lower2) ).
thf(876,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',fact_275_subrelI) ).
thf(465,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)],[66]) ).
thf(61,axiom,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_old_Oprod_Oexhaust) ).
thf(450,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)],[61]) ).
thf(197,axiom,
prefer719835986ence_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_rational__preference__axioms) ).
thf(931,plain,
prefer719835986ence_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(125,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_rational__preference_Oaxioms_I2_J) ).
thf(671,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)],[125]) ).
thf(75,axiom,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ ( sup_sup_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_finite__UnI) ).
thf(495,plain,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ ( sup_sup_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(151,axiom,
! [A: set_a > $o] :
( ( ( collect_set_a @ A )
= bot_bot_set_set_a )
= ( ! [B: set_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Collect__empty__eq) ).
thf(759,plain,
! [A: set_a > $o] :
( ( ( collect_set_a @ A )
= bot_bot_set_set_a )
= ( ! [B: set_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(156,axiom,
member_a @ x @ carrier,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(771,plain,
member_a @ x @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(100,axiom,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_all__not__in__conv) ).
thf(588,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',fact_101_Collect__cong) ).
thf(319,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)],[18]) ).
thf(235,axiom,
refl_on_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_reflexivity) ).
thf(1062,plain,
refl_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(251,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_eq__refl) ).
thf(1101,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_289_rational__preference_Ointro) ).
thf(390,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(216,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_Int__greatest) ).
thf(995,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(225,axiom,
order_preorder_on_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_trans__refl) ).
thf(1030,plain,
order_preorder_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(94,axiom,
! [A: set_a > $o,B: set_a > $o] :
( ! [C: set_a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le318720350_set_a @ ( collect_set_a @ A ) @ ( collect_set_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Collect__mono) ).
thf(568,plain,
! [A: set_a > $o,B: set_a > $o] :
( ! [C: set_a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le318720350_set_a @ ( collect_set_a @ A ) @ ( collect_set_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(193,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( member_set_a @ B @ A )
=> ? [C: set_a] :
( ( member_set_a @ C @ A )
& ( ord_less_eq_set_a @ C @ B )
& ! [D: set_a] :
( ( member_set_a @ D @ A )
=> ( ( ord_less_eq_set_a @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_finite__has__minimal2) ).
thf(914,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( member_set_a @ B @ A )
=> ? [C: set_a] :
( ( member_set_a @ C @ A )
& ( ord_less_eq_set_a @ C @ B )
& ! [D: set_a] :
( ( member_set_a @ D @ A )
=> ( ( ord_less_eq_set_a @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(241,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_subset__empty) ).
thf(1077,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)],[241]) ).
thf(130,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_emptyE) ).
thf(684,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(229,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/sandbox2/benchmark/theBenchmark.p',fact_11_worse__in__no__better) ).
thf(1045,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)],[229]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',fact_96_mem__Collect__eq) ).
thf(300,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)],[12]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',fact_245_total__on__def) ).
thf(752,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)],[148]) ).
thf(208,axiom,
member_a @ y @ carrier,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).
thf(967,plain,
member_a @ y @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(204,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_dual__order_Orefl) ).
thf(950,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(35,axiom,
! [A: set_set_a] :
( ( ord_le318720350_set_a @ A @ bot_bot_set_set_a )
= ( A = bot_bot_set_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_subset__empty) ).
thf(373,plain,
! [A: set_set_a] :
( ( ord_le318720350_set_a @ A @ bot_bot_set_set_a )
= ( A = bot_bot_set_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(104,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( A = bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_Collect__empty__eq__bot) ).
thf(603,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( A = bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(14,axiom,
! [A: product_prod_a_a > $o] :
( ( bot_bo2131659635od_a_a
= ( collec645855634od_a_a @ A ) )
= ( ! [B: product_prod_a_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_empty__Collect__eq) ).
thf(305,plain,
! [A: product_prod_a_a > $o] :
( ( bot_bo2131659635od_a_a
= ( collec645855634od_a_a @ A ) )
= ( ! [B: product_prod_a_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ A ) @ ( collec645855634od_a_a @ B ) )
= ( ! [C: product_prod_a_a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_Collect__mono__iff) ).
thf(294,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ A ) @ ( collec645855634od_a_a @ B ) )
= ( ! [C: product_prod_a_a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',fact_57_rational__preference_Oweak__is__transitive) ).
thf(341,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)],[26]) ).
thf(43,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 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( prefer161218362good_a @ C @ A @ B )
= ( prefer161218362good_a @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_rational__preference_Osame__at__least__as__equal) ).
thf(400,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 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( prefer161218362good_a @ C @ A @ B )
= ( prefer161218362good_a @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',fact_315_Id__on__iff) ).
thf(720,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)],[139]) ).
thf(206,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( ord_less_eq_set_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_subset__emptyI) ).
thf(955,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)],[206]) ).
thf(6,axiom,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_Collect__mem__eq) ).
thf(283,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)],[6]) ).
thf(186,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_empty__subsetI) ).
thf(886,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',fact_307_preorder__on__def) ).
thf(415,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)],[48]) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',fact_181_subset__eq) ).
thf(575,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)],[96]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',fact_241_old_Oprod_Oinject) ).
thf(427,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)],[53]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',fact_272_Pair__inject) ).
thf(528,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)],[86]) ).
thf(215,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_bot_Oextremum__unique) ).
thf(992,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)],[215]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',fact_214_rational__preference_Opref__in__at__least__as) ).
thf(723,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)],[140]) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',fact_308_relChain__def) ).
thf(1004,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)],[218]) ).
thf(77,axiom,
! [A: set_set_a,B: set_set_a,C: set_Product_prod_a_a,D: set_Product_prod_a_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( ord_le526661008od_a_a @ ( produc1618062688od_a_a @ A @ C ) @ ( produc1618062688od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_Pair__mono) ).
thf(501,plain,
! [A: set_set_a,B: set_set_a,C: set_Product_prod_a_a,D: set_Product_prod_a_a] :
( ( ord_le318720350_set_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( ord_le526661008od_a_a @ ( produc1618062688od_a_a @ A @ C ) @ ( produc1618062688od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(248,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/sandbox2/benchmark/theBenchmark.p',fact_264_antisym) ).
thf(1093,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)],[248]) ).
thf(173,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ( sup_sup_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
= ( inf_inf_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) )
= ( ord_less_eq_set_a @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_Un__Int__assoc__eq) ).
thf(839,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ( sup_sup_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
= ( inf_inf_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) )
= ( ord_less_eq_set_a @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',fact_131_all__not__in__conv) ).
thf(322,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)],[19]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',fact_139_subsetI) ).
thf(469,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)],[67]) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',fact_147_at__least__as__goodD) ).
thf(454,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)],[62]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',fact_73_rational__preference_Ono__better__than__nonepty) ).
thf(935,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)],[199]) ).
thf(220,axiom,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ( ord_less_eq_set_a @ ( lattic501550101_set_a @ A ) @ B )
= ( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_Sup__fin_Obounded__iff) ).
thf(1009,plain,
! [A: set_set_a,B: set_a] :
( ( finite_finite_set_a @ A )
=> ( ( A != bot_bot_set_set_a )
=> ( ( ord_less_eq_set_a @ ( lattic501550101_set_a @ A ) @ B )
= ( ! [C: set_a] :
( ( member_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',fact_80_rational__preference_Ono__better__subset__pref) ).
thf(775,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)],[158]) ).
thf(92,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_Collect__cong) ).
thf(560,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)],[92]) ).
thf(1298,plain,
$false,
inference(e,[status(thm)],[1024,365,347,846,893,1083,555,666,352,479,1105,909,628,1031,276,1068,308,379,597,523,582,762,878,440,614,677,1041,861,385,550,814,698,1063,538,404,898,782,417,973,288,651,719,504,619,344,357,460,902,1087,1147,606,1013,881,448,316,1115,325,924,756,591,443,376,646,1051,485,834,766,687,280,998,411,988,265,849,1074,661,381,512,942,1047,798,1057,1091,778,952,349,820,392,297,788,729,361,625,852,329,830,493,1027,682,710,456,842,874,980,1096,1006,1138,593,869,519,742,420,1118,328,669,476,489,679,970,622,1099,911,1131,654,1060,1050,792,1086,266,360,311,921,765,1071,888,1135,750,425,824,745,513,430,423,694,1125,772,286,577,958,579,291,641,572,611,498,1107,335,1090,947,406,784,736,990,1144,509,434,303,1122,387,1080,631,726,483,932,1112,636,1066,780,883,1015,608,563,438,658,768,827,473,944,795,548,927,648,516,939,754,968,525,690,707,739,409,712,557,673,331,1038,463,338,1141,656,864,446,876,465,450,931,671,495,759,771,588,319,1062,1101,390,995,1030,568,914,1077,684,1045,300,752,967,950,373,603,305,294,341,400,720,955,283,886,415,575,427,528,992,723,1004,501,1093,839,322,469,454,935,1009,775,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP154^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n006.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 20:02:09 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.08/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.29/1.28 % [INFO] Parsing done (427ms).
% 2.29/1.29 % [INFO] Running in sequential loop mode.
% 3.53/1.69 % [INFO] eprover registered as external prover.
% 3.76/1.70 % [INFO] Scanning for conjecture ...
% 3.98/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 354 axioms. Running axiom selection ...
% 4.19/2.02 % [INFO] Axiom selection finished. Selected 262 axioms (removed 92 axioms).
% 5.23/2.27 % [INFO] Problem is higher-order (TPTP THF).
% 5.23/2.30 % [INFO] Type checking passed.
% 5.63/2.30 % [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 ...
% 17.84/5.21 % External prover 'e' found a proof!
% 17.84/5.21 % [INFO] Killing All external provers ...
% 17.84/5.22 % Time passed: 4828ms (effective reasoning time: 3916ms)
% 17.84/5.22 % 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)>
% 17.84/5.22 % Axioms used in derivation (262): fact_351_Int__greatest, fact_269_order__subst1, fact_248_total__on__empty, fact_222_rational__preference_Oas__good__asIff, fact_94_mem__Collect__eq, fact_154_ex__in__conv, fact_277_bot_Oextremum__unique, fact_4_assms_I1_J, fact_293_subset__emptyI, fact_346_Int__mono, fact_237_finite_OemptyI, fact_130_all__not__in__conv, fact_41_preference_Oindiff__trans, fact_85_same__at__least__as__equal, fact_113_as__good__as__sameIff, fact_30_preference_Ointro, fact_203_set__eq__subset, fact_338_finite__Un, fact_157_equals0I, fact_46_rational__preference_Ototal, fact_291_finite__transitivity__chain, fact_15_not__outside, fact_88_empty__subsetI, fact_288_rational__preference__def, fact_253_dual__order_Oeq__iff, fact_87_empty__subsetI, fact_256_order__trans, fact_22_rational__preference_Oaxioms_I1_J, fact_155_ex__in__conv, fact_333_Sup__fin_Obounded__iff, fact_247_total__onI, fact_334_Un__empty, fact_296_rational__preference__axioms__def, fact_181_subset__eq, fact_308_relChain__def, fact_281_refl__onD, fact_255_dual__order_Orefl, fact_204_set__eq__subset, fact_14_completeD, fact_69_rational__preference_Oworse__in__no__better, fact_320_refl__on__Id__on, fact_283_refl__onD1, fact_336_Un__subset__iff, fact_328_Inf__fin_OboundedE, fact_274_old_Oprod_Oinducts, fact_171_in__mono, fact_185_equalityD1, fact_306_trans__def, fact_105_Pair__le, fact_0_assms_I3_J, fact_275_subrelI, fact_228_Pair__mono, fact_258_ord__le__eq__trans, fact_330_Sup__fin_OboundedE, fact_170_in__mono, fact_207_Collect__mono__iff, fact_205_Collect__mono__iff, fact_199_subset__trans, fact_178_equalityE, fact_112_Pair__le, fact_180_subset__eq, fact_36_preference_Onot__outside, fact_324_Sup__fin_Osubset__imp, fact_44_rational__preference_Ocompl, fact_163_equals0D, fact_337_finite__Int, fact_147_at__least__as__goodD, fact_206_Collect__mono__iff, fact_11_worse__in__no__better, fact_315_Id__on__iff, fact_17_weak__is__transitive, fact_38_preference_Oreflexivity, fact_10_total, fact_250_bot__empty__eq, fact_263_eq__refl, fact_298_Collect__empty__eq__bot, fact_345_Un__Int__assoc__eq, fact_302_trans__empty, fact_124_empty__Collect__eq, fact_254_dual__order_Otrans, fact_103_Pair__le, fact_135_empty__iff, fact_266_ord__le__eq__subst, fact_279_refl__on__empty, fact_106_Pair__le, fact_348_Int__lower2, fact_161_equals0D, fact_83_rational__preference_Onbt__nest, fact_260_order__class_Oorder_Oeq__iff, fact_86_pref__in__at__least__as, fact_332_Inf__fin_Obounded__iff, fact_92_subset__empty, fact_271_prod__cases, fact_2_rational__preference__axioms, fact_187_equalityD2, fact_289_rational__preference_Ointro, fact_111_Pair__le, fact_240_rev__finite__subset, fact_300_Set_Ois__empty__def, fact_125_empty__Collect__eq, fact_267_ord__eq__le__subst, fact_16_strict__is__neg__transitive, fact_235_bot__prod__def, fact_95_mem__Collect__eq, fact_270_surj__pair, fact_159_equals0I, fact_307_preorder__on__def, fact_245_total__on__def, fact_252_dual__order_Oantisym, fact_192_subset__iff, fact_273_old_Oprod_Oexhaust, fact_80_rational__preference_Ono__better__subset__pref, fact_294_ssubst__Pair__rhs, fact_190_subset__iff, fact_99_Collect__mem__eq, fact_264_antisym, fact_305_transI, fact_102_Collect__cong, fact_342_finite__UnI, fact_297_rational__preference_Oaxioms_I2_J, fact_249_bot__empty__eq, fact_331_Sup__fin_OboundedI, fact_243_order__refl, fact_122_finite__has__minimal, fact_344_infinite__Un, fact_138_subsetI, fact_139_subsetI, fact_126_Collect__empty__eq, fact_8_no__better__thansubset__rel, fact_9_no__better__than__nonepty, fact_323_Inf__fin_Osubset__imp, fact_20_strict__not__refl__weak, fact_134_empty__iff, fact_197_Collect__mono, fact_287_refl__on__domain, fact_118_finite__has__maximal, fact_339_trans__Int, fact_136_empty__iff, fact_313_trans__Id__on, fact_132_all__not__in__conv, fact_3_nbt__nest, fact_100_Collect__mem__eq, fact_165_emptyE, fact_109_Pair__le, fact_177_equalityE, fact_174_subsetD, fact_131_all__not__in__conv, fact_278_bot_Oextremum, fact_265_eq__iff, fact_353_Int__Collect__mono, fact_108_Pair__le, fact_32_preference_Otrans__refl, fact_50_rational__preference_OcompleteD, fact_169_in__mono, fact_234_finite__has__minimal2, fact_198_Collect__mono, fact_233_finite__has__maximal2, fact_1_assms_I2_J, fact_242_prod_Oinject, fact_241_old_Oprod_Oinject, fact_194_subset__refl, fact_227_Pair__mono, fact_12_reflexivity, fact_310_under__incr, fact_304_transE, fact_341_refl__on__Int, fact_176_equalityE, fact_26_preference__def, fact_167_emptyE, fact_340_refl__on__Un, fact_251_bot__set__def, fact_319_Id__onE, fact_322_GreatestI2__order, fact_226_rational__preference_Oat__lst__asgd__not__ge, fact_127_Collect__empty__eq, fact_232_Pair__mono, fact_188_equalityD2, fact_214_rational__preference_Opref__in__at__least__as, fact_166_emptyE, fact_96_mem__Collect__eq, fact_158_equals0I, fact_98_Collect__mem__eq, fact_183_equalityD1, fact_299_transitivity, fact_272_Pair__inject, fact_268_order__subst2, fact_141_subset__antisym, fact_295_rational__preference__axioms_Ointro, fact_77_rational__preference_Ono__better__thansubset__rel, fact_186_equalityD2, fact_343_Un__infinite, fact_202_set__eq__subset, fact_261_antisym__conv, fact_101_Collect__cong, fact_259_ord__eq__le__trans, fact_193_subset__refl, fact_191_subset__iff, fact_61_rational__preference_Ostrict__not__refl__weak, fact_19_indiff__trans, fact_285_refl__onD2, fact_13_compl, fact_162_equals0D, fact_107_Pair__le, fact_5_preference__axioms, fact_89_empty__subsetI, fact_110_Pair__le, fact_201_subset__trans, fact_312_Id__onI, fact_84_at__lst__asgd__not__ge, fact_218_rational__preference_Oas__good__as__sameIff, fact_18_strict__trans, fact_329_Inf__fin_OboundedI, fact_257_order__class_Oorder_Oantisym, fact_290_finite__transitivity__chain, fact_327_Inf__fin_OcoboundedI, fact_326_Sup__fin_OcoboundedI, fact_7_no__better__subset__pref, fact_140_subsetI, fact_53_rational__preference_Ostrict__trans, fact_182_subset__eq, fact_123_empty__Collect__eq, fact_104_Pair__le, fact_238_finite__subset, fact_57_rational__preference_Oweak__is__transitive, fact_309_Id__on__empty, fact_231_Pair__mono, fact_153_ex__in__conv, fact_65_rational__preference_Ostrict__is__neg__transitive, fact_229_Pair__mono, fact_173_subsetD, fact_349_Int__absorb1, fact_184_equalityD1, fact_143_subset__antisym, fact_276_bot_Oextremum__uniqueI, fact_200_subset__trans, fact_350_Int__absorb2, fact_317_Id__on__eqI, fact_301_preference_Otransitivity, fact_91_subset__empty, fact_6_trans__refl, fact_128_Collect__empty__eq, fact_347_Int__lower1, fact_236_infinite__imp__nonempty, fact_90_subset__empty, fact_230_Pair__mono, fact_244_preorder__on__empty, fact_195_subset__refl, fact_114_as__good__asIff, fact_73_rational__preference_Ono__better__than__nonepty, fact_210_rational__preference_Osame__at__least__as__equal, fact_142_subset__antisym, fact_335_Int__subset__iff, fact_151_at__lst__asgd__ge, fact_175_subsetD, fact_352_Int__Collect__mono, fact_292_subset__emptyI, fact_303_transD, fact_239_infinite__super, fact_321_Greatest__equality, fact_196_Collect__mono, fact_262_order_Otrans, fact_325_Inf__fin__le__Sup__fin
% 17.84/5.22 % No. of inferences in proof: 528
% 17.84/5.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4828 ms resp. 3916 ms w/o parsing
% 18.84/5.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.84/5.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------