%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP155^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:59 AM UTC 2026
% Result : Theorem 20.51s 5.06s
% Output : Refutation 21.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 276
% Syntax : Number of formulae : 554 ( 172 unt; 0 typ; 0 def)
% Number of atoms : 1919 ( 346 equ; 14 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 5861 ( 172 ~; 33 |; 192 &;4402 @)
% ( 0 <=>;1062 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 120 ( 120 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 12 con; 0-3 aty)
% Number of variables : 1604 ( 74 ^;1456 !; 74 ?;1604 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1948701895od_a_a_type,type,
set_Pr1948701895od_a_a: $tType ).
thf(produc1572603623od_a_a_type,type,
produc1572603623od_a_a: $tType ).
thf(produc1691597095_set_a_type,type,
produc1691597095_set_a: $tType ).
thf(set_Pr1986765409at_nat_type,type,
set_Pr1986765409at_nat: $tType ).
thf(produc1404140509_a_nat_type,type,
produc1404140509_a_nat: $tType ).
thf(produc1463940355_set_a_type,type,
produc1463940355_set_a: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $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_nat_type,type,
set_nat: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(finite_card_nat_decl,type,
finite_card_nat: set_nat > nat ).
thf(finite1481642319od_a_a_decl,type,
finite1481642319od_a_a: set_Product_prod_a_a > nat ).
thf(finite_card_a_decl,type,
finite_card_a: set_a > nat ).
thf(finite_finite_nat_decl,type,
finite_finite_nat: set_nat > $o ).
thf(finite1664988688od_a_a_decl,type,
finite1664988688od_a_a: set_Pr1948701895od_a_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(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(order_preorder_on_a_decl,type,
order_preorder_on_a: set_a > set_Product_prod_a_a > $o ).
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_bot_nat_decl,type,
bot_bot_nat: nat ).
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_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_le841160035_set_a_decl,type,
ord_le841160035_set_a: produc1463940355_set_a > produc1463940355_set_a > $o ).
thf(ord_le781360189_a_nat_decl,type,
ord_le781360189_a_nat: produc1404140509_a_nat > produc1404140509_a_nat > $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_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
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(prefer1498087410od_a_a_decl,type,
prefer1498087410od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_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(prefer697821563od_a_a_decl,type,
prefer697821563od_a_a: set_Product_prod_a_a > set_Pr1948701895od_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(produc1450889781_set_a_decl,type,
produc1450889781_set_a: nat > set_a > produc1463940355_set_a ).
thf(produc515611863_a_nat_decl,type,
produc515611863_a_nat: set_a > nat > produc1404140509_a_nat ).
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(refl_on_a_decl,type,
refl_on_a: set_a > set_Product_prod_a_a > $o ).
thf(total_on_a_decl,type,
total_on_a: set_a > set_Product_prod_a_a > $o ).
thf(trans_a_decl,type,
trans_a: set_Product_prod_a_a > $o ).
thf(collec645855634od_a_a_decl,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(is_empty_a_decl,type,
is_empty_a: set_a > $o ).
thf(member_nat_decl,type,
member_nat: nat > set_nat > $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(129,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Collect__empty__eq) ).
thf(809,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(50,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( refl_on_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_refl__onD) ).
thf(479,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)],[50]) ).
thf(138,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 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rational__preference_Oindifferent__imp__weak__pref_I2_J) ).
thf(846,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 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(82,axiom,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_all__not__in__conv) ).
thf(628,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(146,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_old_Oprod_Oinject) ).
thf(893,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)],[146]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',fact_192_infinite__super) ).
thf(1315,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)],[265]) ).
thf(20,axiom,
! [A: set_Product_prod_a_a] :
( ( ? [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= ( A != bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ex__in__conv) ).
thf(352,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)],[20]) ).
thf(195,axiom,
! [A: nat,B: set_a,C: nat,D: set_a] :
( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ A @ B ) @ ( produc1450889781_set_a @ C @ D ) )
= ( ( ord_less_eq_nat @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Pair__le) ).
thf(1083,plain,
! [A: nat,B: set_a,C: nat,D: set_a] :
( ( ord_le841160035_set_a @ ( produc1450889781_set_a @ A @ B ) @ ( produc1450889781_set_a @ C @ D ) )
= ( ( ord_less_eq_nat @ A @ C )
& ( ord_less_eq_set_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',fact_159_rational__preference_Osame__at__least__as__equal) ).
thf(962,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)],[161]) ).
thf(121,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_Pair__inject) ).
thf(777,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)],[121]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_dual__order_Oantisym) ).
thf(555,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(92,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_refl__onD2) ).
thf(666,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)],[92]) ).
thf(257,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( ord_less_eq_set_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_subset__emptyI) ).
thf(1295,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)],[257]) ).
thf(31,axiom,
! [A: nat,B: set_Product_prod_a_a] :
( ( ord_less_eq_nat @ A @ ( finite1481642319od_a_a @ B ) )
=> ~ ! [C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ C @ B )
=> ( ( ( finite1481642319od_a_a @ C )
= A )
=> ~ ( finite179568208od_a_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_obtain__subset__with__card__n) ).
thf(408,plain,
! [A: nat,B: set_Product_prod_a_a] :
( ( ord_less_eq_nat @ A @ ( finite1481642319od_a_a @ B ) )
=> ~ ! [C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ C @ B )
=> ( ( ( finite1481642319od_a_a @ C )
= A )
=> ~ ( finite179568208od_a_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(218,axiom,
member_a @ x @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(1158,plain,
member_a @ x @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(173,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_eq__iff) ).
thf(1005,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)],[173]) ).
thf(95,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 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_rational__preference_Oindifferent__imp__weak__pref_I1_J) ).
thf(683,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 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(110,axiom,
! [A: set_Product_prod_a_a,B: set_a,C: a > product_prod_a_a > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [D: a] :
( ( member_a @ D @ B )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: a,E: a,F: product_prod_a_a] :
( ( member_a @ D @ B )
=> ( ( member_a @ E @ B )
=> ( ( member449909584od_a_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite1481642319od_a_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_card__le__if__inj__on__rel) ).
thf(730,plain,
! [A: set_Product_prod_a_a,B: set_a,C: a > product_prod_a_a > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [D: a] :
( ( member_a @ D @ B )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: a,E: a,F: product_prod_a_a] :
( ( member_a @ D @ B )
=> ( ( member_a @ E @ B )
=> ( ( member449909584od_a_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite1481642319od_a_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(43,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_bot__nat__0_Oextremum__unique) ).
thf(449,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(141,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_ord__eq__le__subst) ).
thf(861,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(224,axiom,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( member_a @ A @ ( prefer1676310729than_a @ B @ carrier @ relation ) )
| ( member_a @ B @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_xy__in__eachothers__nbt) ).
thf(1173,plain,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( member_a @ A @ ( prefer1676310729than_a @ B @ carrier @ relation ) )
| ( member_a @ B @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(40,axiom,
! [A: set_Product_prod_a_a] :
( ( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A ) )
= ( A = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_all__not__in__conv) ).
thf(440,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)],[40]) ).
thf(60,axiom,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_equals0D) ).
thf(511,plain,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(193,axiom,
! [A: a,B: a,C: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier )
& ( member_a @ C @ carrier ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_weak__is__transitive) ).
thf(1078,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)],[193]) ).
thf(212,axiom,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ B @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_no__better__thansubset__rel) ).
thf(1137,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)],[212]) ).
thf(262,axiom,
member_a @ y @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).
thf(1310,plain,
member_a @ y @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(240,axiom,
! [A: set_a,B: set_a,C: set_a > nat,D: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_order__subst2) ).
thf(1233,plain,
! [A: set_a,B: set_a,C: set_a > nat,D: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(101,axiom,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_ex__in__conv) ).
thf(698,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_le__cases) ).
thf(538,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(112,axiom,
( trans_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_trans__def) ).
thf(747,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)],[112]) ).
thf(150,axiom,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_old_Oprod_Oexhaust) ).
thf(913,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)],[150]) ).
thf(165,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ D @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_rational__preference_Ono__better__subset__pref) ).
thf(973,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)],[165]) ).
thf(136,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( total_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_rational__preference_Ototal) ).
thf(841,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)],[136]) ).
thf(33,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_le0) ).
thf(417,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',fact_95_same__at__least__as__equal) ).
thf(1055,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)],[186]) ).
thf(258,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ C @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_rational__preference_Onbt__subset__carrier) ).
thf(1298,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ C @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_eq__refl) ).
thf(917,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(16,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ~ ( finite179568208od_a_a @ A )
=> ~ ( finite179568208od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_infinite__super) ).
thf(344,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ~ ( finite179568208od_a_a @ A )
=> ~ ( finite179568208od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(264,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 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_indifferent__imp__weak__pref_I2_J) ).
thf(1313,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 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(230,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_subset__trans) ).
thf(1191,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)],[230]) ).
thf(267,axiom,
! [A: nat,B: nat,C: nat > set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_order__subst2) ).
thf(1323,plain,
! [A: nat,B: nat,C: nat > set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ 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)],[267]) ).
thf(135,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_bot_Oextremum__uniqueI) ).
thf(838,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
=> ( A = bot_bot_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(188,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_bot_Oextremum__uniqueI) ).
thf(1059,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)],[188]) ).
thf(211,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_order__subst2) ).
thf(1132,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)],[211]) ).
thf(215,axiom,
order_preorder_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_trans__refl) ).
thf(1147,plain,
order_preorder_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(142,axiom,
finite_finite_a @ bot_bot_set_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_finite_OemptyI) ).
thf(870,plain,
finite_finite_a @ bot_bot_set_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(176,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_eq__refl) ).
thf(1013,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(204,axiom,
! [A: nat,B: set_a > nat,C: set_a,D: set_a] :
( ( ord_less_eq_nat @ 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_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_order__subst1) ).
thf(1115,plain,
! [A: nat,B: set_a > nat,C: set_a,D: set_a] :
( ( ord_less_eq_nat @ 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_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(275,axiom,
! [A: set_a,B: set_a,C: nat,D: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ A @ C ) @ ( produc515611863_a_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Pair__mono) ).
thf(1362,plain,
! [A: set_a,B: set_a,C: nat,D: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ A @ C ) @ ( produc515611863_a_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(78,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( order_preorder_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_preference_Otrans__refl) ).
thf(606,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)],[78]) ).
thf(271,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_subset__refl) ).
thf(1347,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(49,axiom,
! [A: set_a] :
( ~ ( finite_finite_a @ A )
=> ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_infinite__imp__nonempty) ).
thf(475,plain,
! [A: set_a] :
( ~ ( finite_finite_a @ A )
=> ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(114,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mem__Collect__eq) ).
thf(756,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(41,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_emptyE) ).
thf(443,plain,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(269,axiom,
! [A: nat,B: set_a > nat,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_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_ord__eq__le__subst) ).
thf(1334,plain,
! [A: nat,B: set_a > nat,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_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(156,axiom,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Collect__mem__eq) ).
thf(937,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)],[156]) ).
thf(128,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_prod_Oinject) ).
thf(806,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)],[128]) ).
thf(162,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( total_on_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_rational__preference__axioms_Ointro) ).
thf(966,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)],[162]) ).
thf(227,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ D @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_rational__preference_Ono__better__thansubset__rel) ).
thf(1183,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)],[227]) ).
thf(178,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_dual__order_Otrans) ).
thf(1020,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)],[178]) ).
thf(18,axiom,
( bot_bo1293121322_a_a_o
= ( ^ [A: product_prod_a_a] : ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_bot__empty__eq) ).
thf(348,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)],[18]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',fact_198_finite__has__maximal) ).
thf(1215,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)],[236]) ).
thf(120,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A )
& ( member_a @ E @ A ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rational__preference_Oweak__is__transitive) ).
thf(774,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)],[120]) ).
thf(233,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_order__refl) ).
thf(1201,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(59,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rational__preference_OcompleteD) ).
thf(507,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)],[59]) ).
thf(10,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( ( member449909584od_a_a @ D @ A )
=> ( ( member449909584od_a_a @ C @ ( prefer1498087410od_a_a @ D @ A @ B ) )
| ( member449909584od_a_a @ D @ ( prefer1498087410od_a_a @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_rational__preference_Oxy__in__eachothers__nbt) ).
thf(312,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( ( member449909584od_a_a @ D @ A )
=> ( ( member449909584od_a_a @ C @ ( prefer1498087410od_a_a @ D @ A @ B ) )
| ( member449909584od_a_a @ D @ ( prefer1498087410od_a_a @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(201,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_equalityD1) ).
thf(1104,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(243,axiom,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_card__mono) ).
thf(1242,plain,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(139,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Collect__mem__eq) ).
thf(849,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(90,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_empty__iff) ).
thf(661,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(116,axiom,
prefer580340847ioms_a = total_on_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_rational__preference__axioms__def) ).
thf(761,plain,
prefer580340847ioms_a = total_on_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(25,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_bot__nat__0_Oextremum) ).
thf(381,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(263,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ A @ ( prefer161218362good_a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_pref__in__at__least__as) ).
thf(1311,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)],[263]) ).
thf(191,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_equalityE) ).
thf(1067,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)],[191]) ).
thf(235,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_ord__eq__le__subst) ).
thf(1206,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)],[235]) ).
thf(44,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( ( ( finite1481642319od_a_a @ B )
= ( finite1481642319od_a_a @ A ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_card__subset__eq) ).
thf(452,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( ( ( finite1481642319od_a_a @ B )
= ( finite1481642319od_a_a @ A ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(149,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_le__trans) ).
thf(910,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(238,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( finite_finite_a @ A )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ C @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ C @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_rational__preference_Onbt__subset) ).
thf(1223,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( finite_finite_a @ A )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ C @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(270,axiom,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( ( ( finite_card_a @ B )
= ( finite_card_a @ A ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_card__subset__eq) ).
thf(1343,plain,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( ( ( finite_card_a @ B )
= ( finite_card_a @ A ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(207,axiom,
( ( finite_finite_a @ carrier )
=> ( finite179568208od_a_a @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_fnt__carrier__fnt__rel) ).
thf(1123,plain,
( ( finite_finite_a @ carrier )
=> ( finite179568208od_a_a @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(68,axiom,
order_preorder_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_preorder__on__empty) ).
thf(561,plain,
order_preorder_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(123,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_le__refl) ).
thf(788,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(241,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_subset__iff) ).
thf(1238,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)],[241]) ).
thf(246,axiom,
! [A: set_a,B: nat,C: set_a,D: nat] :
( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ A @ B ) @ ( produc515611863_a_nat @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_Pair__le) ).
thf(1255,plain,
! [A: set_a,B: nat,C: set_a,D: nat] :
( ( ord_le781360189_a_nat @ ( produc515611863_a_nat @ A @ B ) @ ( produc515611863_a_nat @ C @ D ) )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(8,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( ord_le1824328871od_a_a @ ( prefer1498087410od_a_a @ C @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_rational__preference_Onbt__subset__carrier) ).
thf(302,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( ord_le1824328871od_a_a @ ( prefer1498087410od_a_a @ C @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(276,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_subset__empty) ).
thf(1365,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)],[276]) ).
thf(140,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_ord__le__eq__subst) ).
thf(852,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(219,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ C @ A @ B ) @ ( prefer1676310729than_a @ D @ A @ B ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ D @ A @ B ) @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rational__preference_Onbt__nest) ).
thf(1159,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)],[219]) ).
thf(55,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_rational__preference_Ostrict__trans) ).
thf(493,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)],[55]) ).
thf(209,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_dual__order_Oantisym) ).
thf(1128,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)],[209]) ).
thf(45,axiom,
finite179568208od_a_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_finite_OemptyI) ).
thf(456,plain,
finite179568208od_a_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(12,axiom,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ B @ C )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_finite__has__maximal2) ).
thf(324,plain,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ B @ C )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(71,axiom,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_transE) ).
thf(566,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)],[71]) ).
thf(52,axiom,
! [A: set_a] :
( ( finite_finite_a @ A )
=> ( ( ( finite_card_a @ A )
= zero_zero_nat )
= ( A = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_card__0__eq) ).
thf(484,plain,
! [A: set_a] :
( ( finite_finite_a @ A )
=> ( ( ( finite_card_a @ A )
= zero_zero_nat )
= ( A = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(274,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_bot_Oextremum) ).
thf(1360,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_ord__le__eq__trans) ).
thf(742,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(177,axiom,
! [A: a,B: a] :
( ( finite_finite_a @ carrier )
=> ( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_nbt__subset) ).
thf(1017,plain,
! [A: a,B: a] :
( ( finite_finite_a @ carrier )
=> ( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(268,axiom,
! [A: nat,B: set_a] :
( ( ord_less_eq_nat @ A @ ( finite_card_a @ B ) )
=> ~ ! [C: set_a] :
( ( ord_less_eq_set_a @ C @ B )
=> ( ( ( finite_card_a @ C )
= A )
=> ~ ( finite_finite_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_obtain__subset__with__card__n) ).
thf(1328,plain,
! [A: nat,B: set_a] :
( ( ord_less_eq_nat @ A @ ( finite_card_a @ B ) )
=> ~ ! [C: set_a] :
( ( ord_less_eq_set_a @ C @ B )
=> ( ( ( finite_card_a @ C )
= A )
=> ~ ( finite_finite_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(203,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 )
=> ( ( ( member_a @ C @ ( prefer1676310729than_a @ D @ A @ B ) )
& ( member_a @ D @ ( prefer1676310729than_a @ C @ A @ B ) ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_rational__preference_Osame__nbt__same__pref) ).
thf(1111,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 )
=> ( ( ( member_a @ C @ ( prefer1676310729than_a @ D @ A @ B ) )
& ( member_a @ D @ ( prefer1676310729than_a @ C @ 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)],[203]) ).
thf(108,axiom,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_surj__pair) ).
thf(725,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)],[108]) ).
thf(167,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( A != bot_bot_set_a )
=> ( ( member_a @ C @ A )
=> ( ( prefer1676310729than_a @ C @ A @ B )
!= bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_rational__preference_Ono__better__than__nonepty) ).
thf(980,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)],[167]) ).
thf(48,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_subrelI) ).
thf(471,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)],[48]) ).
thf(14,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_le__0__eq) ).
thf(339,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(256,axiom,
! [A: nat,B: nat,C: set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_le841160035_set_a @ ( produc1450889781_set_a @ A @ C ) @ ( produc1450889781_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Pair__mono) ).
thf(1292,plain,
! [A: nat,B: nat,C: set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_le841160035_set_a @ ( produc1450889781_set_a @ A @ C ) @ ( produc1450889781_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(93,axiom,
! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_bot_Oextremum) ).
thf(669,plain,
! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(85,axiom,
! [A: set_Product_prod_a_a] : ( total_on_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_total__on__empty) ).
thf(637,plain,
! [A: set_Product_prod_a_a] : ( total_on_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(76,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_order__refl) ).
thf(590,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_order__class_Oorder_Oantisym) ).
thf(970,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(148,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > nat > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ? [D: nat] : ( B @ C @ D ) )
=> ? [C: nat] :
! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ? [E: nat] :
( ( ord_less_eq_nat @ E @ C )
& ( B @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_finite__indexed__bound) ).
thf(901,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > nat > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ? [D: nat] : ( B @ C @ D ) )
=> ? [C: nat] :
! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ? [E: nat] :
( ( ord_less_eq_nat @ E @ C )
& ( B @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_antisym) ).
thf(686,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(192,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_bot_Oextremum__unique) ).
thf(1075,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)],[192]) ).
thf(248,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( prefer436369274d_as_a @ B @ carrier @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_as__good__asIff) ).
thf(1263,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)],[248]) ).
thf(199,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_subset__antisym) ).
thf(1099,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)],[199]) ).
thf(102,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_emptyE) ).
thf(701,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(249,axiom,
! [A: a,B: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) @ ( prefer1676310729than_a @ B @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ B @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_nbt__nest) ).
thf(1266,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)],[249]) ).
thf(210,axiom,
prefer719835986ence_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_rational__preference__axioms) ).
thf(1131,plain,
prefer719835986ence_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(46,axiom,
! [A: set_nat,B: set_Product_prod_a_a,C: product_prod_a_a > nat > $o] :
( ( finite_finite_nat @ A )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ? [E: nat] :
( ( member_nat @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: product_prod_a_a,E: product_prod_a_a,F: nat] :
( ( member449909584od_a_a @ D @ B )
=> ( ( member449909584od_a_a @ E @ B )
=> ( ( member_nat @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ B ) @ ( finite_card_nat @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_card__le__if__inj__on__rel) ).
thf(457,plain,
! [A: set_nat,B: set_Product_prod_a_a,C: product_prod_a_a > nat > $o] :
( ( finite_finite_nat @ A )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ? [E: nat] :
( ( member_nat @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: product_prod_a_a,E: product_prod_a_a,F: nat] :
( ( member449909584od_a_a @ D @ B )
=> ( ( member449909584od_a_a @ E @ B )
=> ( ( member_nat @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ B ) @ ( finite_card_nat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(168,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_dual__order_Orefl) ).
thf(984,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(72,axiom,
( bot_bo1519632275_set_a
= ( produc1928581911_set_a @ bot_bot_set_a @ bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_bot__prod__def) ).
thf(569,plain,
( bot_bo1519632275_set_a
= ( produc1928581911_set_a @ bot_bot_set_a @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(57,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( finite_finite_a @ A )
=> ( finite179568208od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rational__preference_Ofnt__carrier__fnt__rel) ).
thf(503,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( finite_finite_a @ A )
=> ( finite179568208od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(196,axiom,
! [A: a] :
( ( member_a @ A @ carrier )
=> ! [B: a] :
( ( member_a @ B @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_compl) ).
thf(1086,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)],[196]) ).
thf(84,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ ( prefer436369274d_as_a @ D @ A @ B ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_rational__preference_Oas__good__as__sameIff) ).
thf(633,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)],[84]) ).
thf(152,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) )
=> ( trans_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_transI) ).
thf(921,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)],[152]) ).
thf(118,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( A != bot_bot_set_a )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ~ ( member_a @ C @ ( prefer161218362good_a @ D @ A @ B ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_rational__preference_Oat__lst__asgd__not__ge) ).
thf(765,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)],[118]) ).
thf(182,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( prefer436369274d_as_a @ B @ carrier @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_as__good__as__sameIff) ).
thf(1035,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)],[182]) ).
thf(67,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_preference_Onot__outside) ).
thf(558,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)],[67]) ).
thf(62,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ( member_a @ C @ A )
& ( member_a @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_refl__on__domain) ).
thf(530,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)],[62]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat > set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_ord__le__eq__subst) ).
thf(1026,plain,
! [A: nat,B: nat,C: nat > set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ 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)],[181]) ).
thf(222,axiom,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( ( member_a @ A @ ( prefer1676310729than_a @ B @ carrier @ relation ) )
& ( member_a @ B @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_same__nbt__same__pref) ).
thf(1167,plain,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( ( member_a @ A @ ( prefer1676310729than_a @ B @ carrier @ relation ) )
& ( member_a @ B @ ( prefer1676310729than_a @ A @ 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)],[222]) ).
thf(6,axiom,
( finite_finite_nat
= ( ^ [A: set_nat] :
? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_finite__nat__set__iff__bounded__le) ).
thf(298,plain,
( finite_finite_nat
= ( ^ [A: set_nat] :
? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(132,axiom,
( bot_bot_set_a
= ( collect_a @ bot_bot_a_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_bot__set__def) ).
thf(824,plain,
( bot_bot_set_a
= ( collect_a @ bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(3,axiom,
! [A: set_nat] :
( ( ~ ( finite_finite_nat @ A ) )
= ( ! [B: nat] :
? [C: nat] :
( ( ord_less_eq_nat @ B @ C )
& ( member_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_infinite__nat__iff__unbounded__le) ).
thf(279,plain,
! [A: set_nat] :
( ( ~ ( finite_finite_nat @ A ) )
= ( ! [B: nat] :
? [C: nat] :
( ( ord_less_eq_nat @ B @ C )
& ( member_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(259,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( finite_finite_a @ A )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ( finite_finite_a @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_rational__preference_Ofnt__carrier__fnt__nbt) ).
thf(1301,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( finite_finite_a @ A )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ( finite_finite_a @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(97,axiom,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_bot__empty__eq) ).
thf(689,plain,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_nat__le__linear) ).
thf(562,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(35,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_in__mono) ).
thf(423,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)],[35]) ).
thf(174,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_antisym__conv) ).
thf(1007,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)],[174]) ).
thf(29,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A )
=> ( ord_le1824328871od_a_a @ A @ bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_subset__emptyI) ).
thf(402,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)],[29]) ).
thf(160,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rational__preference_Ostrict__not__refl__weak) ).
thf(958,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)],[160]) ).
thf(239,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/sandbox/benchmark/theBenchmark.p',fact_176_finite__has__maximal2) ).
thf(1226,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)],[239]) ).
thf(137,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ ( prefer161218362good_a @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_rational__preference_Opref__in__at__least__as) ).
thf(843,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)],[137]) ).
thf(208,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ A @ carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_not__outside) ).
thf(1125,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)],[208]) ).
thf(144,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_Nat_Oex__has__greatest__nat) ).
thf(875,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(133,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_old_Oprod_Oinducts) ).
thf(826,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)],[133]) ).
thf(105,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) )
=> ( total_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_total__onI) ).
thf(711,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)],[105]) ).
thf(87,axiom,
! [A: product_prod_a_a,B: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_mem__Collect__eq) ).
thf(641,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)],[87]) ).
thf(251,axiom,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_indiff__trans) ).
thf(1271,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)],[251]) ).
thf(122,axiom,
trans_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_trans__empty) ).
thf(787,plain,
trans_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(56,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_ord__eq__le__trans) ).
thf(498,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(187,axiom,
ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062) ).
thf(1058,plain,
ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',fact_178_finite__has__minimal2) ).
thf(1092,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)],[198]) ).
thf(19,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_subset__eq) ).
thf(350,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)],[19]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_le__cases3) ).
thf(540,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(247,axiom,
! [A: nat,B: set_a] :
( ( ord_less_eq_nat @ A @ ( finite_card_a @ B ) )
=> ? [C: set_a] :
( ( ord_less_eq_set_a @ C @ B )
& ( ( finite_card_a @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_ex__card) ).
thf(1258,plain,
! [A: nat,B: set_a] :
( ( ord_less_eq_nat @ A @ ( finite_card_a @ B ) )
=> ? [C: set_a] :
( ( ord_less_eq_set_a @ C @ B )
& ( ( finite_card_a @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(103,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_equals0I) ).
thf(704,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(231,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_equalityD2) ).
thf(1194,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(134,axiom,
! [A: set_Product_prod_a_a,B: set_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ C @ B ) )
=> ( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ D @ B ) )
=> ( ( order_preorder_on_a @ B @ A )
=> ( prefer1292084992ence_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_preference_Ointro) ).
thf(831,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)],[134]) ).
thf(34,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A )
=> ( A = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_equals0I) ).
thf(419,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)],[34]) ).
thf(185,axiom,
! [A: set_a,B: nat] :
( ~ ( finite_finite_a @ A )
=> ? [C: set_a] :
( ( finite_finite_a @ C )
& ( ( finite_card_a @ C )
= B )
& ( ord_less_eq_set_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_infinite__arbitrarily__large) ).
thf(1048,plain,
! [A: set_a,B: nat] :
( ~ ( finite_finite_a @ A )
=> ? [C: set_a] :
( ( finite_finite_a @ C )
& ( ( finite_card_a @ C )
= B )
& ( ord_less_eq_set_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(272,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_ord__le__eq__subst) ).
thf(1349,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)],[272]) ).
thf(23,axiom,
! [A: set_Product_prod_a_a,B: nat] :
( ~ ( finite179568208od_a_a @ A )
=> ? [C: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ C )
& ( ( finite1481642319od_a_a @ C )
= B )
& ( ord_le1824328871od_a_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_infinite__arbitrarily__large) ).
thf(362,plain,
! [A: set_Product_prod_a_a,B: nat] :
( ~ ( finite179568208od_a_a @ A )
=> ? [C: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ C )
& ( ( finite1481642319od_a_a @ C )
= B )
& ( ord_le1824328871od_a_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(214,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_Collect__mono__iff) ).
thf(1144,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)],[214]) ).
thf(184,axiom,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_strict__trans) ).
thf(1043,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)],[184]) ).
thf(81,axiom,
! [A: set_a,B: set_nat,C: nat > a > $o] :
( ( finite_finite_a @ A )
=> ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ? [E: a] :
( ( member_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: nat,E: nat,F: a] :
( ( member_nat @ D @ B )
=> ( ( member_nat @ E @ B )
=> ( ( member_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_card__le__if__inj__on__rel) ).
thf(616,plain,
! [A: set_a,B: set_nat,C: nat > a > $o] :
( ( finite_finite_a @ A )
=> ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ? [E: a] :
( ( member_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: nat,E: nat,F: a] :
( ( member_nat @ D @ B )
=> ( ( member_nat @ E @ B )
=> ( ( member_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(206,axiom,
total_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_total) ).
thf(1122,plain,
total_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(27,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_empty__iff) ).
thf(387,plain,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(194,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_antisym) ).
thf(1080,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)],[194]) ).
thf(83,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_dual__order_Orefl) ).
thf(631,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(63,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_refl__onD1) ).
thf(535,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)],[63]) ).
thf(119,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_prod__cases) ).
thf(769,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)],[119]) ).
thf(158,axiom,
! [A: set_a,B: set_a,C: a > a > $o] :
( ( finite_finite_a @ A )
=> ( ! [D: a] :
( ( member_a @ D @ B )
=> ? [E: a] :
( ( member_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: a,E: a,F: a] :
( ( member_a @ D @ B )
=> ( ( member_a @ E @ B )
=> ( ( member_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_card__le__if__inj__on__rel) ).
thf(943,plain,
! [A: set_a,B: set_a,C: a > a > $o] :
( ( finite_finite_a @ A )
=> ( ! [D: a] :
( ( member_a @ D @ B )
=> ? [E: a] :
( ( member_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: a,E: a,F: a] :
( ( member_a @ D @ B )
=> ( ( member_a @ E @ B )
=> ( ( member_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(155,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_preference_Oindiff__trans) ).
thf(932,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)],[155]) ).
thf(125,axiom,
( prefer719835986ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
& ( prefer580340847ioms_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_rational__preference__def) ).
thf(799,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)],[125]) ).
thf(220,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Collect__mono) ).
thf(1162,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)],[220]) ).
thf(223,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ B @ ( prefer1676310729than_a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_worse__in__no__better) ).
thf(1171,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)],[223]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fact_99_Pair__le) ).
thf(1198,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)],[232]) ).
thf(1,conjecture,
ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(278,plain,
~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(169,axiom,
! [A: a,B: a,C: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier )
& ( member_a @ C @ carrier ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_strict__is__neg__transitive) ).
thf(986,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)],[169]) ).
thf(171,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_subsetD) ).
thf(1000,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)],[171]) ).
thf(245,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_order__subst1) ).
thf(1250,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)],[245]) ).
thf(200,axiom,
! [A: a] :
( ( member_a @ A @ carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_fnt__carrier__fnt__nbt) ).
thf(1102,plain,
! [A: a] :
( ( member_a @ A @ carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(58,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( prefer580340847ioms_a @ A @ B )
=> ( prefer719835986ence_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_rational__preference_Ointro) ).
thf(505,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)],[58]) ).
thf(37,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_subset__iff) ).
thf(431,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)],[37]) ).
thf(99,axiom,
refl_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_refl__on__empty) ).
thf(695,plain,
refl_on_a @ bot_bot_set_a @ bot_bo2131659635od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(244,axiom,
! [A: set_a,B: nat > set_a,C: nat,D: nat] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_order__subst1) ).
thf(1245,plain,
! [A: set_a,B: nat > set_a,C: nat,D: nat] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ 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)],[244]) ).
thf(225,axiom,
! [A: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ A @ carrier )
=> ( ( prefer1676310729than_a @ A @ carrier @ relation )
!= bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_no__better__than__nonepty) ).
thf(1176,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)],[225]) ).
thf(79,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_order__subst2) ).
thf(608,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(54,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( A = bot_bot_a_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_Collect__empty__eq__bot) ).
thf(490,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( A = bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(234,axiom,
! [A: a,B: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_strict__not__refl__weak) ).
thf(1203,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)],[234]) ).
thf(153,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ A )
=> ( finite1664988688od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_rational__preference_Ofnt__carrier__fnt__rel) ).
thf(927,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ A )
=> ( finite1664988688od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_order__trans) ).
thf(487,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',fact_318_finite__transitivity__chain) ).
thf(812,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)],[130]) ).
thf(113,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A )
& ( member_a @ E @ A ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_rational__preference_Ostrict__is__neg__transitive) ).
thf(749,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)],[113]) ).
thf(61,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_ex__least__nat__le) ).
thf(516,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(15,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ B )
=> ( finite179568208od_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_finite__subset) ).
thf(342,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ B )
=> ( finite179568208od_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( finite179568208od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_rev__finite__subset) ).
thf(355,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( finite179568208od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(163,axiom,
( prefer1292084992ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) )
& ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) )
& ( order_preorder_on_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_preference__def) ).
thf(968,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)],[163]) ).
thf(36,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( A = bot_bo2131659635od_a_a )
=> ~ ( member449909584od_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_equals0D) ).
thf(426,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( A = bot_bo2131659635od_a_a )
=> ~ ( member449909584od_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(221,axiom,
prefer1292084992ence_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_preference__axioms) ).
thf(1166,plain,
prefer1292084992ence_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(172,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_dual__order_Oeq__iff) ).
thf(1003,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)],[172]) ).
thf(180,axiom,
trans_a @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_transitivity) ).
thf(1025,plain,
trans_a @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(4,axiom,
! [A: set_nat,B: set_nat,C: nat > nat > $o] :
( ( finite_finite_nat @ A )
=> ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ? [E: nat] :
( ( member_nat @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( member_nat @ D @ B )
=> ( ( member_nat @ E @ B )
=> ( ( member_nat @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_card__le__if__inj__on__rel) ).
thf(282,plain,
! [A: set_nat,B: set_nat,C: nat > nat > $o] :
( ( finite_finite_nat @ A )
=> ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ? [E: nat] :
( ( member_nat @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( member_nat @ D @ B )
=> ( ( member_nat @ E @ B )
=> ( ( member_nat @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ B ) @ ( finite1481642319od_a_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_card__mono) ).
thf(414,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ B ) @ ( finite1481642319od_a_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(277,axiom,
! [A: a,B: a] :
( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ( A != B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_completeD) ).
thf(1368,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)],[277]) ).
thf(183,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_ord__eq__le__trans) ).
thf(1038,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)],[183]) ).
thf(266,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/sandbox/benchmark/theBenchmark.p',fact_196_finite__has__minimal) ).
thf(1317,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)],[266]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',fact_172_Pair__mono) ).
thf(1285,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)],[253]) ).
thf(13,axiom,
! [A: set_Product_prod_a_a,B: nat] :
( ! [C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ C @ A )
=> ( ( finite179568208od_a_a @ C )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ C ) @ B ) ) )
=> ( ( finite179568208od_a_a @ A )
& ( ord_less_eq_nat @ ( finite1481642319od_a_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_finite__if__finite__subsets__card__bdd) ).
thf(331,plain,
! [A: set_Product_prod_a_a,B: nat] :
( ! [C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ C @ A )
=> ( ( finite179568208od_a_a @ C )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ C ) @ B ) ) )
=> ( ( finite179568208od_a_a @ A )
& ( ord_less_eq_nat @ ( finite1481642319od_a_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(228,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( member_a @ C @ ( prefer1676310729than_a @ D @ A @ B ) )
| ( member_a @ D @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_rational__preference_Oxy__in__eachothers__nbt) ).
thf(1186,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 )
=> ( ( member_a @ C @ ( prefer1676310729than_a @ D @ A @ B ) )
| ( member_a @ D @ ( prefer1676310729than_a @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(273,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_subset__eq) ).
thf(1358,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)],[273]) ).
thf(80,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
= ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_bot_Oextremum__unique) ).
thf(613,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
= ( A = bot_bot_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(237,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_empty__subsetI) ).
thf(1221,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(213,axiom,
! [A: a,B: a] :
( ( carrier != bot_bot_set_a )
=> ( ( member_a @ A @ carrier )
=> ( ( member_a @ B @ carrier )
=> ( ~ ( member_a @ A @ ( prefer161218362good_a @ B @ carrier @ relation ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_at__lst__asgd__not__ge) ).
thf(1140,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)],[213]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',fact_189_finite__subset) ).
thf(1240,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)],[242]) ).
thf(89,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_order__subst1) ).
thf(656,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(179,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 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_indifferent__imp__weak__pref_I1_J) ).
thf(1023,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 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(42,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_bot__nat__0_Oextremum__uniqueI) ).
thf(446,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',fact_316_finite__transitivity__chain) ).
thf(571,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)],[73]) ).
thf(226,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_order__trans) ).
thf(1180,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)],[226]) ).
thf(51,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer1292084992ence_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rational__preference_Oaxioms_I1_J) ).
thf(482,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)],[51]) ).
thf(94,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: product_prod_a_a > a > $o] :
( ( finite_finite_a @ A )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ? [E: a] :
( ( member_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: product_prod_a_a,E: product_prod_a_a,F: a] :
( ( member449909584od_a_a @ D @ B )
=> ( ( member449909584od_a_a @ E @ B )
=> ( ( member_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ B ) @ ( finite_card_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_card__le__if__inj__on__rel) ).
thf(671,plain,
! [A: set_a,B: set_Product_prod_a_a,C: product_prod_a_a > a > $o] :
( ( finite_finite_a @ A )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ? [E: a] :
( ( member_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: product_prod_a_a,E: product_prod_a_a,F: a] :
( ( member449909584od_a_a @ D @ B )
=> ( ( member449909584od_a_a @ E @ B )
=> ( ( member_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ B ) @ ( finite_card_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(217,axiom,
refl_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_reflexivity) ).
thf(1157,plain,
refl_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(166,axiom,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_card__seteq) ).
thf(976,plain,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(74,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_linorder__wlog) ).
thf(581,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(115,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_dual__order_Oeq__iff) ).
thf(759,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(145,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_rational__preference_Oaxioms_I2_J) ).
thf(891,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)],[145]) ).
thf(229,axiom,
! [A: a] :
( ( member_a @ A @ carrier )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) @ carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_nbt__subset__carrier) ).
thf(1189,plain,
! [A: a] :
( ( member_a @ A @ carrier )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ A @ carrier @ relation ) @ carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(175,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_in__mono) ).
thf(1010,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)],[175]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',fact_195_rev__finite__subset) ).
thf(1289,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)],[255]) ).
thf(202,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_order_Otrans) ).
thf(1108,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)],[202]) ).
thf(252,axiom,
! [A: set_a,B: nat > set_a,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_ord__eq__le__subst) ).
thf(1276,plain,
! [A: set_a,B: nat > set_a,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ 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)],[252]) ).
thf(75,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( refl_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_preference_Oreflexivity) ).
thf(588,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)],[75]) ).
thf(147,axiom,
! [A: a,B: a,C: set_Product_prod_a_a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_ssubst__Pair__rhs) ).
thf(896,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)],[147]) ).
thf(189,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_order__class_Oorder_Oantisym) ).
thf(1062,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)],[189]) ).
thf(28,axiom,
! [A: set_nat,B: set_a,C: a > nat > $o] :
( ( finite_finite_nat @ A )
=> ( ! [D: a] :
( ( member_a @ D @ B )
=> ? [E: nat] :
( ( member_nat @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: a,E: a,F: nat] :
( ( member_a @ D @ B )
=> ( ( member_a @ E @ B )
=> ( ( member_nat @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_nat @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_card__le__if__inj__on__rel) ).
thf(390,plain,
! [A: set_nat,B: set_a,C: a > nat > $o] :
( ( finite_finite_nat @ A )
=> ( ! [D: a] :
( ( member_a @ D @ B )
=> ? [E: nat] :
( ( member_nat @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: a,E: a,F: nat] :
( ( member_a @ D @ B )
=> ( ( member_a @ E @ B )
=> ( ( member_nat @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_nat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(38,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_subsetI) ).
thf(433,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)],[38]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_le__antisym) ).
thf(929,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(261,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ B @ carrier @ relation ) @ ( prefer1676310729than_a @ A @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_no__better__subset__pref) ).
thf(1308,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)],[261]) ).
thf(117,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_rational__preference_Ocompl) ).
thf(763,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)],[117]) ).
thf(26,axiom,
! [A: set_Product_prod_a_a] :
( ~ ( finite179568208od_a_a @ A )
=> ( A != bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_infinite__imp__nonempty) ).
thf(383,plain,
! [A: set_Product_prod_a_a] :
( ~ ( finite179568208od_a_a @ A )
=> ( A != bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(17,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_less__eq__nat_Osimps_I1_J) ).
thf(346,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ A )
=> ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( finite179568208od_a_a @ ( prefer1498087410od_a_a @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_rational__preference_Ofnt__carrier__fnt__nbt) ).
thf(300,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ A )
=> ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( finite179568208od_a_a @ ( prefer1498087410od_a_a @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: set_nat,B: nat > nat > $o] :
( ( finite_finite_nat @ A )
=> ( ! [C: nat] :
( ( member_nat @ C @ A )
=> ? [D: nat] : ( B @ C @ D ) )
=> ? [C: nat] :
! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: nat] :
( ( ord_less_eq_nat @ E @ C )
& ( B @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_finite__indexed__bound) ).
thf(315,plain,
! [A: set_nat,B: nat > nat > $o] :
( ( finite_finite_nat @ A )
=> ( ! [C: nat] :
( ( member_nat @ C @ A )
=> ? [D: nat] : ( B @ C @ D ) )
=> ? [C: nat] :
! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: nat] :
( ( ord_less_eq_nat @ E @ C )
& ( B @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_subsetD) ).
thf(405,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)],[30]) ).
thf(260,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_ord__le__eq__trans) ).
thf(1303,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)],[260]) ).
thf(216,axiom,
! [A: set_a,B: set_a,C: set_a > nat,D: nat] :
( ( 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_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_ord__le__eq__subst) ).
thf(1148,plain,
! [A: set_a,B: set_a,C: set_a > nat,D: nat] :
( ( 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_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(124,axiom,
! [A: set_a,B: a > nat > $o] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ? [D: nat] : ( B @ C @ D ) )
=> ? [C: nat] :
! [D: a] :
( ( member_a @ D @ A )
=> ? [E: nat] :
( ( ord_less_eq_nat @ E @ C )
& ( B @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_finite__indexed__bound) ).
thf(790,plain,
! [A: set_a,B: a > nat > $o] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ? [D: nat] : ( B @ C @ D ) )
=> ? [C: nat] :
! [D: a] :
( ( member_a @ D @ A )
=> ? [E: nat] :
( ( ord_less_eq_nat @ E @ C )
& ( B @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(70,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_order__class_Oorder_Oeq__iff) ).
thf(564,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(9,axiom,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_finite__has__minimal2) ).
thf(305,plain,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite1481642319od_a_a @ A ) @ ( finite1481642319od_a_a @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_card__seteq) ).
thf(358,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite1481642319od_a_a @ A ) @ ( finite1481642319od_a_a @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(39,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ A )
=> ( ( member449909584od_a_a @ C @ A )
=> ( ( member449909584od_a_a @ D @ A )
=> ( ( ord_le1824328871od_a_a @ ( prefer1498087410od_a_a @ C @ A @ B ) @ ( prefer1498087410od_a_a @ C @ A @ B ) )
| ( ord_le1824328871od_a_a @ ( prefer1498087410od_a_a @ C @ A @ B ) @ ( prefer1498087410od_a_a @ C @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_rational__preference_Onbt__subset) ).
thf(437,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ A )
=> ( ( member449909584od_a_a @ C @ A )
=> ( ( member449909584od_a_a @ D @ A )
=> ( ord_le1824328871od_a_a @ ( prefer1498087410od_a_a @ C @ A @ B ) @ ( prefer1498087410od_a_a @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(91,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( trans_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_preference_Otransitivity) ).
thf(664,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)],[91]) ).
thf(254,axiom,
finite_finite_a @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__092_060open_062finite_Acarrier_092_060close_062) ).
thf(1288,plain,
finite_finite_a @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(190,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_order__class_Oorder_Oeq__iff) ).
thf(1065,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)],[190]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_linear) ).
thf(696,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(106,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_order_Otrans) ).
thf(720,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(159,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_dual__order_Otrans) ).
thf(955,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(5,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( A != bot_bo2131659635od_a_a )
=> ( ( member449909584od_a_a @ C @ A )
=> ( ( prefer1498087410od_a_a @ C @ A @ B )
!= bot_bo2131659635od_a_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_rational__preference_Ono__better__than__nonepty) ).
thf(294,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( A != bot_bo2131659635od_a_a )
=> ( ( member449909584od_a_a @ C @ A )
=> ( ( prefer1498087410od_a_a @ C @ A @ B )
!= bot_bo2131659635od_a_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(126,axiom,
( is_empty_a
= ( ^ [A: set_a] : ( A = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_Set_Ois__empty__def) ).
thf(801,plain,
( is_empty_a
= ( ^ [A: set_a] : ( A = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(109,axiom,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_at__least__as__goodD) ).
thf(728,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)],[109]) ).
thf(250,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ ( prefer1676310729than_a @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rational__preference_Oworse__in__no__better) ).
thf(1268,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)],[250]) ).
thf(88,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > product_prod_a_a > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: product_prod_a_a,E: product_prod_a_a,F: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ( ( member449909584od_a_a @ E @ B )
=> ( ( member449909584od_a_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ B ) @ ( finite1481642319od_a_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_card__le__if__inj__on__rel) ).
thf(644,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > product_prod_a_a > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: product_prod_a_a,E: product_prod_a_a,F: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ( ( member449909584od_a_a @ E @ B )
=> ( ( member449909584od_a_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite1481642319od_a_a @ B ) @ ( finite1481642319od_a_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(170,axiom,
! [A: set_a,B: nat] :
( ! [C: set_a] :
( ( ord_less_eq_set_a @ C @ A )
=> ( ( finite_finite_a @ C )
=> ( ord_less_eq_nat @ ( finite_card_a @ C ) @ B ) ) )
=> ( ( finite_finite_a @ A )
& ( ord_less_eq_nat @ ( finite_card_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_finite__if__finite__subsets__card__bdd) ).
thf(992,plain,
! [A: set_a,B: nat] :
( ! [C: set_a] :
( ( ord_less_eq_set_a @ C @ A )
=> ( ( finite_finite_a @ C )
=> ( ord_less_eq_nat @ ( finite_card_a @ C ) @ B ) ) )
=> ( ( finite_finite_a @ A )
& ( ord_less_eq_nat @ ( finite_card_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(107,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_eq__iff) ).
thf(723,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(131,axiom,
( order_preorder_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( refl_on_a @ A @ B )
& ( trans_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_preorder__on__def) ).
thf(822,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)],[131]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_eq__imp__le) ).
thf(691,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(143,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( member_a @ C @ ( prefer436369274d_as_a @ D @ A @ B ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_rational__preference_Oas__good__asIff) ).
thf(871,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)],[143]) ).
thf(205,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_set__eq__subset) ).
thf(1120,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)],[205]) ).
thf(24,axiom,
! [A: set_Product_prod_a_a,B: set_nat,C: nat > product_prod_a_a > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: nat,E: nat,F: product_prod_a_a] :
( ( member_nat @ D @ B )
=> ( ( member_nat @ E @ B )
=> ( ( member449909584od_a_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite1481642319od_a_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_card__le__if__inj__on__rel) ).
thf(369,plain,
! [A: set_Product_prod_a_a,B: set_nat,C: nat > product_prod_a_a > $o] :
( ( finite179568208od_a_a @ A )
=> ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: nat,E: nat,F: product_prod_a_a] :
( ( member_nat @ D @ B )
=> ( ( member_nat @ E @ B )
=> ( ( member449909584od_a_a @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite1481642319od_a_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(127,axiom,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_empty__Collect__eq) ).
thf(803,plain,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(86,axiom,
( total_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_total__on__def) ).
thf(639,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)],[86]) ).
thf(197,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_subsetI) ).
thf(1088,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)],[197]) ).
thf(77,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_bounded__Max__nat) ).
thf(592,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(104,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_antisym__conv) ).
thf(708,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(47,axiom,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_at__lst__asgd__ge) ).
thf(469,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)],[47]) ).
thf(157,axiom,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_transD) ).
thf(940,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)],[157]) ).
thf(1588,plain,
$false,
inference(e,[status(thm)],[809,479,846,628,893,1315,352,1083,962,777,555,666,1295,408,1158,1005,683,730,449,861,1173,440,511,1078,1137,1310,1233,698,538,747,913,973,841,417,1055,1298,917,344,1313,1191,1323,838,1059,1132,1147,870,1013,1115,1362,606,1347,475,756,443,1334,937,806,966,1183,1020,348,1215,774,1201,507,312,1104,1242,849,661,761,381,1311,1067,1206,452,910,1223,1343,1123,561,788,1238,1255,302,1365,852,1159,493,1128,456,324,566,484,1360,742,1017,1328,1111,725,980,471,339,1292,669,637,590,970,901,686,1075,1263,1099,701,1266,1131,457,984,569,503,1086,633,921,765,1035,558,530,1026,1167,298,824,279,1301,689,562,423,1007,402,958,1226,843,1125,875,826,711,641,1271,787,498,1058,1092,350,540,1258,704,1194,831,419,1048,1349,362,1144,1043,616,1122,387,1080,631,535,769,943,932,799,1162,1171,1198,278,986,1000,1250,1102,505,431,695,1245,1176,608,490,1203,927,487,812,749,516,342,355,968,426,1166,1003,1025,282,414,1368,1038,1317,1285,331,1186,1358,613,1221,1140,1240,656,1023,446,571,1180,482,671,1157,976,581,759,891,1189,1010,1289,1108,1276,588,896,1062,390,433,929,1308,763,383,346,300,315,405,1303,1148,790,564,305,358,437,664,1288,1065,696,720,955,294,801,728,1268,644,992,723,822,691,871,1120,369,803,639,1088,592,708,469,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP155^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n015.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 20:06:03 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.65/0.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/0.79 % [INFO] Parsing done (291ms).
% 1.96/0.80 % [INFO] Running in sequential loop mode.
% 2.94/1.06 % [INFO] eprover registered as external prover.
% 2.94/1.06 % [INFO] Scanning for conjecture ...
% 3.46/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 354 axioms. Running axiom selection ...
% 4.07/1.45 % [INFO] Axiom selection finished. Selected 275 axioms (removed 79 axioms).
% 5.16/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 5.16/1.79 % [INFO] Type checking passed.
% 5.16/1.79 % [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 ...
% 20.51/5.05 % External prover 'e' found a proof!
% 20.51/5.06 % [INFO] Killing All external provers ...
% 20.51/5.06 % Time passed: 4760ms (effective reasoning time: 4252ms)
% 20.51/5.06 % 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)>
% 20.51/5.06 % Axioms used in derivation (275): fact_229_bot__set__def, fact_241_order__class_Oorder_Oantisym, fact_300_refl__on__empty, fact_200_card__subset__eq, fact_151_subset__iff, fact_303_refl__on__domain, fact_15_fnt__carrier__fnt__nbt, fact_135_equals0D, fact_289_bot_Oextremum, fact_347_le__trans, fact_93_rational__preference_Onbt__nest, fact_249_antisym__conv, fact_192_infinite__super, fact_114_empty__iff, fact_187_finite__subset, fact_251_le__cases3, fact_352_bot__nat__0_Oextremum__uniqueI, fact_31_rational__preference_Oindifferent__imp__weak__pref_I1_J, fact_0_assms_I2_J, fact_350_le__0__eq, fact_314_Collect__empty__eq__bot, fact_321_subset__emptyI, fact_312_refl__onD, fact_2_xy__in__eachothers__nbt, fact_244_ord__le__eq__trans, fact_203_infinite__arbitrarily__large, fact_24_indifferent__imp__weak__pref_I2_J, fact_231_dual__order_Oantisym, fact_179_finite__has__minimal2, fact_156_subset__trans, fact_29_rational__preference_Oaxioms_I1_J, fact_326_rational__preference_Oaxioms_I2_J, fact_148_subset__eq, fact_272_order__subst2, fact_184_finite_OemptyI, fact_126_at__lst__asgd__ge, fact_108_card__mono, fact_329_finite__indexed__bound, fact_271_order__subst2, fact_223_card__le__if__inj__on__rel, fact_196_finite__has__minimal, fact_95_same__at__least__as__equal, fact_45_rational__preference_Ototal, fact_18_reflexivity, fact_12_no__better__thansubset__rel, fact_186_finite_OemptyI, fact_344_nat__le__linear, fact_327_rational__preference_Ointro, fact_117_subsetI, fact_23_indifferent__imp__weak__pref_I1_J, fact_106_card__mono, fact_87_rational__preference_Oxy__in__eachothers__nbt, fact_274_order__subst1, fact_341_bot__nat__0_Oextremum, fact_227_order__refl, fact_214_obtain__subset__with__card__n, fact_67_rational__preference_Ostrict__is__neg__transitive, fact_259_antisym, fact_155_Collect__mono, fact_247_order__class_Oorder_Oeq__iff, fact_337_preference_Otransitivity, fact_250_antisym__conv, fact_158_Collect__mono__iff, fact_42_preference_Oreflexivity, fact_90_rational__preference_Onbt__subset__carrier, fact_275_order__subst1, fact_342_le0, fact_165_rational__preference_Oas__good__as__sameIff, fact_193_rev__finite__subset, fact_89_rational__preference_Oxy__in__eachothers__nbt, fact_202_card__subset__eq, fact_37_preference_Ointro, fact_44_rational__preference_Ocompl, fact_1_assms_I1_J, fact_236_linorder__wlog, fact_239_order__trans, fact_144_subsetD, fact_340_card__0__eq, fact_43_preference_Oindiff__trans, fact_59_mem__Collect__eq, fact_345_le__antisym, fact_286_bot_Oextremum__uniqueI, fact_60_mem__Collect__eq, fact_324_rational__preference__axioms_Ointro, fact_10_nbt__subset, fact_20_completeD, fact_142_subsetD, fact_162_rational__preference_Opref__in__at__least__as, fact_105_fnt__carrier__fnt__rel, fact_323_ssubst__Pair__rhs, fact_180_bot__prod__def, fact_215_card__le__if__inj__on__rel, fact_113_all__not__in__conv, fact_77_rational__preference_Ono__better__than__nonepty, fact_273_order__subst2, fact_181_infinite__imp__nonempty, fact_237_dual__order_Orefl, fact_306_refl__onD2, fact_48_rational__preference_OcompleteD, fact_101_Pair__le, fact_63_Collect__mem__eq, fact_116_empty__iff, fact_270_order__subst2, fact_258_antisym, fact_183_infinite__imp__nonempty, fact_130_equals0I, fact_315_infinite__nat__iff__unbounded__le, fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062, fact_92_rational__preference_Onbt__subset__carrier, fact_34_preference__def, fact_351_bot__nat__0_Oextremum__unique, fact_8_preference__axioms, fact_318_finite__transitivity__chain, fact_234_dual__order_Otrans, fact_133_equals0D, fact_267_ord__eq__le__subst, fact_11_no__better__subset__pref, fact_299_subrelI, fact_226_prod_Oinject, fact_285_bot_Oextremum__uniqueI, fact_290_bot_Oextremum, fact_22_indiff__trans, fact_330_finite__indexed__bound, fact_284_finite__nat__set__iff__bounded__le, fact_248_order__class_Oorder_Oeq__iff, fact_261_eq__iff, fact_254_le__cases, fact_219_card__le__if__inj__on__rel, fact_129_ex__in__conv, fact_240_order__trans, fact_99_Pair__le, fact_41_preference_Onot__outside, fact_228_order__refl, fact_298_bot__empty__eq, fact_38_preference_Otrans__refl, fact_13_no__better__than__nonepty, fact_138_emptyE, fact_76_rational__preference_Ofnt__carrier__fnt__nbt, fact_319_subset__emptyI, fact_328_finite__indexed__bound, fact_336_trans__def, fact_339_Set_Ois__empty__def, fact_103_as__good__as__sameIff, fact_174_Pair__mono, fact_127_ex__in__conv, fact_30_rational__preference_Oindifferent__imp__weak__pref_I2_J, fact_281_old_Oprod_Oexhaust, fact_253_order_Otrans, fact_245_ord__eq__le__trans, fact_132_equals0I, fact_338_preorder__on__def, fact_25_weak__is__transitive, fact_233_dual__order_Oeq__iff, fact_70_rational__preference_Oworse__in__no__better, fact_5_nbt__subset__carrier, fact_296_bot__empty__eq, fact_82_rational__preference_Ono__better__thansubset__rel, fact_14_total, fact_178_finite__has__minimal2, fact_159_rational__preference_Osame__at__least__as__equal, fact_334_transE, fact_16_same__nbt__same__pref, fact_157_set__eq__subset, fact_53_rational__preference_Ofnt__carrier__fnt__rel, fact_146_subset__eq, fact_86_rational__preference_Onbt__subset, fact_195_rev__finite__subset, fact_6_rational__preference__axioms, fact_84_rational__preference_Onbt__subset, fact_4_nbt__nest, fact_238_dual__order_Orefl, fact_242_order__class_Oorder_Oantisym, fact_52_rational__preference_Oweak__is__transitive, fact_79_rational__preference_Ono__better__than__nonepty, fact_177_finite__has__maximal2, fact_349_less__eq__nat_Osimps_I1_J, fact_58_rational__preference_Ostrict__not__refl__weak, fact_141_in__mono, fact_313_total__on__empty, fact_262_ord__le__eq__subst, fact_348_le__refl, fact_278_surj__pair, fact_100_Pair__le, fact_216_card__le__if__inj__on__rel, fact_333_transD, fact_49_rational__preference_Ostrict__trans, fact_83_rational__preference_Ono__better__subset__pref, fact_168_rational__preference_Oas__good__asIff, fact_331_transitivity, fact_343_Nat_Oex__has__greatest__nat, fact_283_bounded__Max__nat, fact_153_subset__iff, fact_104_as__good__asIff, fact_232_dual__order_Oeq__iff, fact_7__092_060open_062finite_Acarrier_092_060close_062, fact_230_dual__order_Oantisym, fact_221_card__le__if__inj__on__rel, fact_172_Pair__mono, fact_27_not__outside, fact_322_rational__preference__def, fact_246_ord__eq__le__trans, fact_282_old_Oprod_Oinducts, fact_256_eq__refl, fact_280_Pair__inject, fact_269_ord__eq__le__subst, fact_28_strict__not__refl__weak, fact_255_eq__refl, fact_62_Collect__mem__eq, fact_96_pref__in__at__least__as, fact_288_bot_Oextremum__unique, fact_268_ord__eq__le__subst, fact_171_rational__preference_Oat__lst__asgd__not__ge, fact_212_obtain__subset__with__card__n, fact_243_ord__le__eq__trans, fact_265_ord__le__eq__subst, fact_154_subset__refl, fact_346_eq__imp__le, fact_208_finite__if__finite__subsets__card__bdd, fact_335_transI, fact_94_at__lst__asgd__not__ge, fact_136_emptyE, fact_109_empty__Collect__eq, fact_211_card__seteq, fact_257_linear, fact_225_old_Oprod_Oinject, fact_9_trans__refl, fact_294_total__onI, fact_291_preorder__on__empty, fact_206_finite__if__finite__subsets__card__bdd, fact_332_trans__empty, fact_150_equalityD2, fact_263_ord__le__eq__subst, fact_217_card__le__if__inj__on__rel, fact_209_card__seteq, fact_17_worse__in__no__better, fact_176_finite__has__maximal2, fact_149_equalityD1, fact_295_total__on__def, fact_98_subset__empty, fact_190_infinite__super, fact_173_Pair__mono, fact_198_finite__has__maximal, fact_220_card__le__if__inj__on__rel, fact_218_card__le__if__inj__on__rel, fact_119_subsetI, fact_111_all__not__in__conv, fact_309_refl__onD1, fact_73_rational__preference_Osame__nbt__same__pref, fact_266_ord__eq__le__subst, fact_264_ord__le__eq__subst, fact_189_finite__subset, fact_123_at__least__as__goodD, fact_277_order__subst1, fact_110_Collect__empty__eq, fact_19_compl, fact_26_strict__is__neg__transitive, fact_55_rational__preference_Ofnt__carrier__fnt__rel, fact_287_bot_Oextremum__unique, fact_145_equalityE, fact_279_prod__cases, fact_325_rational__preference__axioms__def, fact_353_ex__least__nat__le, fact_97_empty__subsetI, fact_224_ex__card, fact_74_rational__preference_Ofnt__carrier__fnt__nbt, fact_139_in__mono, fact_316_finite__transitivity__chain, fact_222_card__le__if__inj__on__rel, fact_235_dual__order_Otrans, fact_120_subset__antisym, fact_205_infinite__arbitrarily__large, fact_252_order_Otrans, fact_21_strict__trans, fact_276_order__subst1, fact_260_eq__iff
% 20.51/5.06 % No. of inferences in proof: 554
% 20.51/5.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4760 ms resp. 4252 ms w/o parsing
% 21.27/5.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.27/5.28 % [INFO] Killing All external provers ...
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