%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP153^2 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:58 AM UTC 2026
% Result : Theorem 165.54s 139.95s
% Output : Refutation 166.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 254
% Syntax : Number of formulae : 510 ( 173 unt; 0 typ; 0 def)
% Number of atoms : 2133 ( 396 equ; 4 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 8727 ( 178 ~; 30 |; 147 &;7800 @)
% ( 0 <=>; 572 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 108 ( 108 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 8 con; 0-5 aty)
% Number of variables : 1898 ( 60 ^;1816 !; 22 ?;1898 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(order_bot_decl,type,
order_bot:
!>[TA: $tType] : $o ).
thf(bNF_Ca1785829860lChain_decl,type,
bNF_Ca1785829860lChain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(order_1409979114der_on_decl,type,
order_1409979114der_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(order_preorder_on_decl,type,
order_preorder_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(order_under_decl,type,
order_under:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > TA > ( set @ TA ) ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(prefer951318096ood_as_decl,type,
prefer951318096ood_as:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(prefer310429814s_good_decl,type,
prefer310429814s_good:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(prefer1532642881r_than_decl,type,
prefer1532642881r_than:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(prefer199794634erence_decl,type,
prefer199794634erence:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(prefer1997167224erence_decl,type,
prefer1997167224erence:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(prefer1801827867axioms_decl,type,
prefer1801827867axioms:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(produc2004651681e_prod_decl,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_fst_decl,type,
product_fst:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TB ) ).
thf(product_snd_decl,type,
product_snd:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TA ) ).
thf(domain_decl,type,
domain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ TB ) ) ).
thf(id_on_decl,type,
id_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(range_decl,type,
range:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ TA ) ) ).
thf(refl_on_decl,type,
refl_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(total_on_decl,type,
total_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(trans_decl,type,
trans:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_decl,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(is_singleton_decl,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(the_elem_decl,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(carrier_decl,type,
carrier: set @ a ).
thf(relation_decl,type,
relation: set @ ( product_prod @ a @ a ) ).
thf(y_decl,type,
y: a ).
thf(z_decl,type,
z: a ).
thf(129,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_subset__insertI) ).
thf(629,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(172,axiom,
! [A: a,B: a,C: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier )
& ( member @ a @ C @ carrier ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
=> ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_weak__is__transitive) ).
thf(760,plain,
! [A: a,B: a,C: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier )
& ( member @ a @ C @ carrier ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
=> ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_prod_Oexpand) ).
thf(347,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_insert__eq__iff) ).
thf(846,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(216,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ ( prefer310429814s_good @ TA @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_rational__preference_Opref__in__at__least__as) ).
thf(893,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ ( prefer310429814s_good @ TA @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(71,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_is__singleton__def) ).
thf(468,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(232,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rational__preference_Ono__better__thansubset__rel) ).
thf(941,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(136,axiom,
! [TA: $tType] : ( trans @ TA @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_trans__empty) ).
thf(645,plain,
! [TA: $tType] : ( trans @ TA @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(215,axiom,
prefer199794634erence @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_preference__axioms) ).
thf(892,plain,
prefer199794634erence @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(75,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Collect__mono__iff) ).
thf(481,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_snd__eqD) ).
thf(352,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(244,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) )
=> ( ( ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rational__preference_Ostrict__not__refl__weak) ).
thf(977,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) )
=> ( ( ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(253,axiom,
! [TA: $tType] :
( ( trans @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_trans__def) ).
thf(1005,plain,
! [TA: $tType] :
( ( trans @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(165,axiom,
refl_on @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_reflexivity) ).
thf(741,plain,
refl_on @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(86,axiom,
! [TA: $tType] :
( ( order_preorder_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
& ( trans @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_preorder__on__def) ).
thf(511,plain,
! [TA: $tType] :
( ( order_preorder_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
& ( trans @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_surjective__pairing) ).
thf(269,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(116,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_subset__insertI2) ).
thf(597,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(206,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( A = B )
=> ( ( member @ TA @ A @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Id__on__eqI) ).
thf(861,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( A = B )
=> ( ( member @ TA @ A @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(109,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_is__singleton__the__elem) ).
thf(582,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(173,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_equals0I) ).
thf(762,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_subrelI) ).
thf(873,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_le__funE) ).
thf(449,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_old_Oprod_Oinject) ).
thf(533,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(157,axiom,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ A @ carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_not__outside) ).
thf(715,plain,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ A @ carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(151,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_singleton__insert__inj__eq_H) ).
thf(698,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(94,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_4) ).
thf(538,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(168,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_emptyE) ).
thf(747,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(223,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_total__onI) ).
thf(913,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(196,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ ( prefer1532642881r_than @ TA @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_rational__preference_Oworse__in__no__better) ).
thf(829,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ ( prefer1532642881r_than @ TA @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(251,axiom,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_no__better__subset__pref) ).
thf(1001,plain,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(52,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Set_Ois__empty__def) ).
thf(417,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Pair__inject) ).
thf(565,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(436,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Pair__mono) ).
thf(389,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(159,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_insert__iff) ).
thf(719,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(228,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_refl__onD2) ).
thf(934,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(111,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_7) ).
thf(587,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(200,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_empty__iff) ).
thf(838,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(187,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Set_Oset__insert) ).
thf(802,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_prod_Ocollapse) ).
thf(344,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(219,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_bot__empty__eq) ).
thf(902,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_singleton__inject) ).
thf(559,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(119,axiom,
! [TA: $tType,A: set @ TA] : ( refl_on @ TA @ A @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_refl__on__Id__on) ).
thf(606,plain,
! [TA: $tType,A: set @ TA] : ( refl_on @ TA @ A @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(255,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_subset__emptyI) ).
thf(1013,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(212,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ C @ B ) )
=> ( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ D @ B ) )
=> ( ( order_preorder_on @ TA @ B @ A )
=> ( prefer199794634erence @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_preference_Ointro) ).
thf(881,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ C @ B ) )
=> ( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ D @ B ) )
=> ( ( order_preorder_on @ TA @ B @ A )
=> ( prefer199794634erence @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_conjI__realizer) ).
thf(325,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: TB,C: TA] :
( ( A
= ( product_Pair @ TB @ TA @ B @ C ) )
=> ( ( product_snd @ TB @ TA @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_sndI) ).
thf(289,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: TB,C: TA] :
( ( A
= ( product_Pair @ TB @ TA @ B @ C ) )
=> ( ( product_snd @ TB @ TA @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(182,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rational__preference_Ostrict__trans) ).
thf(789,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(113,axiom,
! [TA: $tType] : ( order_1409979114der_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_lnear__order__on__empty) ).
thf(591,plain,
! [TA: $tType] : ( order_1409979114der_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(87,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_bot__set__def) ).
thf(514,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(240,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_subsetI) ).
thf(966,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(220,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( prefer951318096ood_as @ TA @ D @ A @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rational__preference_Oas__good__as__sameIff) ).
thf(905,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( prefer951318096ood_as @ TA @ D @ A @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_prod__cases3) ).
thf(475,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(225,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_refl__on__domain) ).
thf(924,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_prod__induct6) ).
thf(602,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(45,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_insert__absorb2) ).
thf(397,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType] :
( ( domain @ TA @ TB @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Domain__empty) ).
thf(634,plain,
! [TA: $tType,TB: $tType] :
( ( domain @ TA @ TB @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(210,axiom,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ A @ ( prefer310429814s_good @ a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_pref__in__at__least__as) ).
thf(877,plain,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ A @ ( prefer310429814s_good @ a @ B @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_bot__fun__def) ).
thf(293,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(140,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_ord__eq__le__trans) ).
thf(660,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_insert__not__empty) ).
thf(428,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_fst__conv) ).
thf(312,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(6,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_eq__refl) ).
thf(265,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(203,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_is__singletonI_H) ).
thf(849,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(189,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_rational__preference_OcompleteD) ).
thf(810,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(39,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_le__cases) ).
thf(381,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(185,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A )
& ( member @ TA @ E @ A ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rational__preference_Oweak__is__transitive) ).
thf(798,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A )
& ( member @ TA @ E @ A ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(97,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_doubleton__eq__iff) ).
thf(546,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(183,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_subset__eq) ).
thf(793,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(237,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_equals0D) ).
thf(957,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(178,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_ComplI) ).
thf(778,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(235,axiom,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_total__on__def) ).
thf(952,plain,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( ( preorder @ TB )
& ( preorder @ TA ) )
=> ( preorder @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Opreorder_12) ).
thf(302,plain,
! [TA: $tType,TB: $tType] :
( ( ( preorder @ TB )
& ( preorder @ TA ) )
=> ( preorder @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_bot__apply) ).
thf(260,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(192,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_rational__preference_Ono__better__subset__pref) ).
thf(820,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_prod__induct3) ).
thf(424,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(9,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_1) ).
thf(275,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_subset__empty) ).
thf(407,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(149,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( refl_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_preference_Oreflexivity) ).
thf(693,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( refl_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_prod__cases4) ).
thf(484,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(127,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( prefer1801827867axioms @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_rational__preference_Oaxioms_I2_J) ).
thf(625,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( prefer1801827867axioms @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(211,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_singletonI) ).
thf(879,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(142,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_ord__eq__le__subst) ).
thf(665,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Range__iff) ).
thf(889,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_prod__induct4) ).
thf(493,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(171,axiom,
! [TA: $tType] :
( ( prefer199794634erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) )
& ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) )
& ( order_preorder_on @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_preference__def) ).
thf(757,plain,
! [TA: $tType] :
( ( prefer199794634erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) )
& ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) )
& ( order_preorder_on @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(146,axiom,
! [TA: $tType,A: set @ TA] :
( ( range @ TA @ TA @ ( id_on @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Range__Id__on) ).
thf(682,plain,
! [TA: $tType,A: set @ TA] :
( ( range @ TA @ TA @ ( id_on @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(155,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(710,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(243,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_insertE) ).
thf(974,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(166,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id_on @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Id__onI) ).
thf(742,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id_on @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(138,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( total_on @ TA @ A @ B )
=> ( prefer1801827867axioms @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_rational__preference__axioms_Ointro) ).
thf(650,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( total_on @ TA @ A @ B )
=> ( prefer1801827867axioms @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(123,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_empty__subsetI) ).
thf(615,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(245,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_insertCI) ).
thf(980,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_exI__realizer) ).
thf(356,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ord_less_eq @ ( product_prod @ TA @ TB ) @ A @ B )
=> ( ord_less_eq @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_fst__mono) ).
thf(593,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ord_less_eq @ ( product_prod @ TA @ TB ) @ A @ B )
=> ( ord_less_eq @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(81,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( prefer1801827867axioms @ TA @ A @ B )
=> ( prefer1997167224erence @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_rational__preference_Ointro) ).
thf(499,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( prefer1801827867axioms @ TA @ A @ B )
=> ( prefer1997167224erence @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(247,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ C @ A )
=> ( ( prefer1532642881r_than @ TA @ C @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_rational__preference_Ono__better__than__nonepty) ).
thf(989,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ C @ A )
=> ( ( prefer1532642881r_than @ TA @ C @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(204,axiom,
! [A: a] :
( ( member @ a @ A @ carrier )
=> ! [B: a] :
( ( member @ a @ B @ carrier )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
| ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_compl) ).
thf(857,plain,
! [A: a] :
( ( member @ a @ A @ carrier )
=> ! [B: a] :
( ( member @ a @ B @ carrier )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
| ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(180,axiom,
order_preorder_on @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_trans__refl) ).
thf(783,plain,
order_preorder_on @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_internal__case__prod__conv) ).
thf(420,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order_bot @ TB )
& ( order_bot @ TA ) )
=> ( order_bot @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oorder__bot_11) ).
thf(339,plain,
! [TA: $tType,TB: $tType] :
( ( ( order_bot @ TB )
& ( order_bot @ TA ) )
=> ( order_bot @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(132,axiom,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_refl__on__empty) ).
thf(637,plain,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(72,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Collect__mono) ).
thf(471,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1,conjecture,
( ( member @ a @ z @ carrier )
& ( member @ a @ y @ carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( member @ a @ z @ carrier )
& ( member @ a @ y @ carrier ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(256,plain,
~ ( ( member @ a @ z @ carrier )
& ( member @ a @ y @ carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(145,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(679,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(241,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_transE) ).
thf(970,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType] :
( ( range @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_Range__empty) ).
thf(622,plain,
! [TA: $tType,TB: $tType] :
( ( range @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( ord @ TA ) )
=> ( ord @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oord_14) ).
thf(701,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( ord @ TA ) )
=> ( ord @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(164,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_Compl__iff) ).
thf(738,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(222,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_insert__subsetI) ).
thf(911,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( bot_bot @ ( product_prod @ TB @ TA ) )
= ( product_Pair @ TB @ TA @ ( bot_bot @ TB ) @ ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_bot__prod__def) ).
thf(503,plain,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( bot_bot @ ( product_prod @ TB @ TA ) )
= ( product_Pair @ TB @ TA @ ( bot_bot @ TB ) @ ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(137,axiom,
! [TA: $tType] :
( ( prefer1801827867axioms @ TA )
= ( total_on @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_rational__preference__axioms__def) ).
thf(647,plain,
! [TA: $tType] :
( ( prefer1801827867axioms @ TA )
= ( total_on @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(250,axiom,
! [A: a] :
( ( carrier
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( member @ a @ A @ carrier )
=> ( ( prefer1532642881r_than @ a @ A @ carrier @ relation )
!= ( bot_bot @ ( set @ a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_no__better__than__nonepty) ).
thf(997,plain,
! [A: a] :
( ( carrier
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( member @ a @ A @ carrier )
=> ( ( prefer1532642881r_than @ a @ A @ carrier @ relation )
!= ( bot_bot @ ( set @ a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(230,axiom,
prefer1997167224erence @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_rational__preference__axioms) ).
thf(938,plain,
prefer1997167224erence @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_snd__conv) ).
thf(360,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(224,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_subset__insert) ).
thf(921,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_relChain__def) ).
thf(765,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(158,axiom,
trans @ a @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_transitivity) ).
thf(718,plain,
trans @ a @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(239,axiom,
total_on @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_total) ).
thf(965,plain,
total_on @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(194,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ~ ( member @ TA @ C @ ( prefer310429814s_good @ TA @ D @ A @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rational__preference_Oat__lst__asgd__not__ge) ).
thf(824,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ~ ( member @ TA @ C @ ( prefer310429814s_good @ TA @ D @ A @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_le__funD) ).
thf(573,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_prod__induct5) ).
thf(689,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_prod__eq__iff) ).
thf(296,plain,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_le__fun__def) ).
thf(562,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(54,axiom,
order_bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_6) ).
thf(423,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_prod__cases5) ).
thf(402,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(176,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) )
= ( ( A = B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Id__on__iff) ).
thf(772,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) )
= ( ( A = B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_prod_Oexhaust__sel) ).
thf(286,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( ( range @ TA @ TB @ A )
= ( bot_bot @ ( set @ TB ) ) )
= ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_Range__empty__iff) ).
thf(577,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( ( range @ TA @ TB @ A )
= ( bot_bot @ ( set @ TB ) ) )
= ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(281,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ( ( ord_less_eq @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ord_less_eq @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) )
& ( ord_less_eq @ TB @ ( product_snd @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_less__eq__prod__def) ).
thf(391,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ( ( ord_less_eq @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ord_less_eq @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) )
& ( ord_less_eq @ TB @ ( product_snd @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(121,axiom,
! [TA: $tType,A: TA] : ( refl_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_refl__on__singleton) ).
thf(611,plain,
! [TA: $tType,A: TA] : ( refl_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ TB @ B @ ( range @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Range_Ointros) ).
thf(713,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ TB @ B @ ( range @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(335,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(32,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_linear) ).
thf(350,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(95,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_is__singletonE) ).
thf(540,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_le__funI) ).
thf(445,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(229,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
=> ~ ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Range_Ocases) ).
thf(936,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
=> ~ ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(197,axiom,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ B @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_worse__in__no__better) ).
thf(831,plain,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ B @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(181,axiom,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id_on @ TA @ B ) )
=> ~ ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( A
!= ( product_Pair @ TA @ TA @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_Id__onE) ).
thf(784,plain,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id_on @ TA @ B ) )
=> ~ ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( A
!= ( product_Pair @ TA @ TA @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(65,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Compl__subset__Compl__iff) ).
thf(451,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( range @ TA @ TB @ ( insert @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C ) )
= ( insert @ TB @ B @ ( range @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_Range__insert) ).
thf(599,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( range @ TA @ TB @ ( insert @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C ) )
= ( insert @ TB @ B @ ( range @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(85,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( total_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_total__on__empty) ).
thf(509,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( total_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(58,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) )
| ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_rational__preference_Onbt__nest) ).
thf(434,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) )
| ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(130,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_bot_Oextremum__unique) ).
thf(631,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_prod__cases) ).
thf(552,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(24,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order__trans) ).
thf(323,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(161,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) )
=> ( trans @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_transI) ).
thf(726,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) )
=> ( trans @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_ord__le__eq__subst) ).
thf(520,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(217,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_preference_Oindiff__trans) ).
thf(895,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(233,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) )
=> ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_no__better__thansubset__rel) ).
thf(943,plain,
! [A: a,B: a] :
( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) )
=> ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_surj__pair) ).
thf(462,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_old_Oprod_Oinducts) ).
thf(685,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_singleton__insert__inj__eq) ).
thf(695,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(179,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ~ ( member @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_subset__Compl__singleton) ).
thf(780,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ~ ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(67,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_empty__Collect__eq) ).
thf(455,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(120,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Collect__empty__eq) ).
thf(608,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TB @ TA] :
( ( A
= ( product_fst @ TB @ TA @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TB @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_eq__fst__iff) ).
thf(299,plain,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TB @ TA] :
( ( A
= ( product_fst @ TB @ TA @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TB @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_prod__induct7) ).
thf(438,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_old_Oprod_Orec) ).
thf(431,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(175,axiom,
! [A: a,B: a] :
( ( carrier
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ~ ( member @ a @ A @ ( prefer310429814s_good @ a @ B @ carrier @ relation ) )
=> ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_at__lst__asgd__not__ge) ).
thf(768,plain,
! [A: a,B: a] :
( ( carrier
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ~ ( member @ a @ A @ ( prefer310429814s_good @ a @ B @ carrier @ relation ) )
=> ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(195,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_refl__onD1) ).
thf(827,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(44,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_subset__singleton__iff) ).
thf(394,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(246,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_insert__subset) ).
thf(986,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(20,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_linorder__wlog) ).
thf(306,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_ssubst__Pair__rhs) ).
thf(722,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(91,axiom,
! [TA: $tType] : ( order_preorder_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_preorder__on__empty) ).
thf(531,plain,
! [TA: $tType] : ( order_preorder_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(77,axiom,
! [TA: $tType] :
( ( id_on @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Id__on__empty) ).
thf(487,plain,
! [TA: $tType] :
( ( id_on @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(169,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_singletonD) ).
thf(749,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_prod__cases6) ).
thf(617,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(231,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_in__mono) ).
thf(939,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(68,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_ord__le__eq__trans) ).
thf(458,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(199,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_insertI1) ).
thf(836,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(78,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_bot_Oextremum__uniqueI) ).
thf(490,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(144,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_less__by__empty) ).
thf(675,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(252,axiom,
! [A: a,B: a] :
( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) )
| ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_nbt__nest) ).
thf(1003,plain,
! [A: a,B: a] :
( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) )
| ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(108,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( prefer199794634erence @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_rational__preference_Oaxioms_I1_J) ).
thf(580,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( prefer199794634erence @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( ord_less_eq @ TB @ A @ C )
& ( ord_less_eq @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Pair__le) ).
thf(640,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( ord_less_eq @ TB @ A @ C )
& ( ord_less_eq @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_prod__cases7) ).
thf(707,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(213,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_subsetD) ).
thf(887,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(51,axiom,
! [TA: $tType] :
( ( prefer1997167224erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
& ( prefer1801827867axioms @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rational__preference__def) ).
thf(414,plain,
! [TA: $tType] :
( ( prefer1997167224erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
& ( prefer1801827867axioms @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TB )
& ( bot @ TA ) )
=> ( bot @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Obot_15) ).
thf(263,plain,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TB )
& ( bot @ TA ) )
=> ( bot @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(143,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( trans @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_preference_Otransitivity) ).
thf(673,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( trans @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(110,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( total_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rational__preference_Ototal) ).
thf(585,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( total_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(201,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A )
& ( member @ TA @ E @ A ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) )
| ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rational__preference_Ostrict__is__neg__transitive) ).
thf(840,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A )
& ( member @ TA @ E @ A ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) )
| ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(135,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( order_preorder_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_preference_Otrans__refl) ).
thf(643,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( order_preorder_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(167,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( prefer951318096ood_as @ a @ B @ carrier @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_as__good__as__sameIff) ).
thf(744,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( prefer951318096ood_as @ a @ B @ carrier @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_equalityD2) ).
thf(703,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(122,axiom,
! [TA: $tType,A: TA] : ( order_1409979114der_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_linear__order__on__singleton) ).
thf(613,plain,
! [TA: $tType,A: TA] : ( order_1409979114der_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(41,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_Compl__eq__Compl__iff) ).
thf(386,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(254,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_mk__disjoint__insert) ).
thf(1008,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( range @ TA @ TB @ A ) @ ( range @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_Range__mono) ).
thf(571,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( range @ TA @ TB @ A ) @ ( range @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Compl__anti__mono) ).
thf(595,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ord_less_eq @ ( product_prod @ TA @ TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( product_snd @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_snd__mono) ).
thf(497,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ord_less_eq @ ( product_prod @ TA @ TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( product_snd @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(205,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_refl__onD) ).
thf(859,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_old_Oprod_Oexhaust) ).
thf(465,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(128,axiom,
! [TA: $tType,A: TA] : ( total_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_total__on__singleton) ).
thf(627,plain,
! [TA: $tType,A: TA] : ( total_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(227,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_ex__in__conv) ).
thf(931,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(37,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_le__cases3) ).
thf(363,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(100,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_subset__antisym) ).
thf(556,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(112,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_set__eq__subset) ).
thf(588,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(88,axiom,
! [TA: $tType,A: set @ TA] :
( ( domain @ TA @ TA @ ( id_on @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Domain__Id__on) ).
thf(517,plain,
! [TA: $tType,A: set @ TA] :
( ( domain @ TA @ TA @ ( id_on @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(319,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_2) ).
thf(304,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(139,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_equalityE) ).
thf(652,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(162,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ( A != B )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
| ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_completeD) ).
thf(731,plain,
! [A: a,B: a] :
( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ( A != B )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
| ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(249,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_insertI2) ).
thf(995,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(238,axiom,
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ z @ y ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ y @ z ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
thf(961,plain,
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ z @ y ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ y @ z ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(190,axiom,
! [A: a,B: a,C: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_indiff__trans) ).
thf(813,plain,
! [A: a,B: a,C: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(234,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TB @ TA ),C: TA > $o] :
( ( member @ TA @ A @ ( range @ TB @ TA @ B ) )
=> ( ! [D: TB,E: TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ D @ E ) @ B )
=> ( C @ E ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Range_Oinducts) ).
thf(946,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TB @ TA ),C: TA > $o] :
( ( member @ TA @ A @ ( range @ TB @ TA @ B ) )
=> ( ! [D: TB,E: TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ D @ E ) @ B )
=> ( C @ E ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(3,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_order__refl) ).
thf(258,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( product_fst @ TA @ TB @ ( bot_bot @ ( product_prod @ TA @ TB ) ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_fst__bot) ).
thf(378,plain,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( product_fst @ TA @ TB @ ( bot_bot @ ( product_prod @ TA @ TB ) ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(74,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_subset__Compl__self__eq) ).
thf(478,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TA @ TB] :
( ( A
= ( product_snd @ TA @ TB @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_eq__snd__iff) ).
thf(272,plain,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TA @ TB] :
( ( A
= ( product_snd @ TA @ TB @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prod_Oinject) ).
thf(383,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(218,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_insert__absorb) ).
thf(899,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(98,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Collect__empty__eq__bot) ).
thf(549,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(93,axiom,
! [TA: $tType,A: set @ TA] : ( trans @ TA @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_trans__Id__on) ).
thf(536,plain,
! [TA: $tType,A: set @ TA] : ( trans @ TA @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(186,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_at__lst__asgd__ge) ).
thf(800,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(125,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_insert__mono) ).
thf(620,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(170,axiom,
! [A: a,B: a,C: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_strict__trans) ).
thf(752,plain,
! [A: a,B: a,C: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(63,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_subset__refl) ).
thf(447,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA,C: TB] :
( ( A
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( ( product_fst @ TA @ TB @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_fstI) ).
thf(315,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA,C: TB] :
( ( A
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( ( product_fst @ TA @ TB @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(191,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_preference_Onot__outside) ).
thf(818,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(48,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_bot_Oextremum) ).
thf(405,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(207,axiom,
! [A: a,B: a,C: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier )
& ( member @ a @ C @ carrier ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) )
| ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_strict__is__neg__transitive) ).
thf(865,plain,
! [A: a,B: a,C: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier )
& ( member @ a @ C @ carrier ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) )
| ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(163,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_all__not__in__conv) ).
thf(735,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(198,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_subset__iff) ).
thf(833,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(50,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_equalityD1) ).
thf(410,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_prod__eqI) ).
thf(341,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(84,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_the__elem__eq) ).
thf(506,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(141,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_9) ).
thf(664,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_subset__trans) ).
thf(400,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(236,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rational__preference_Ocompl) ).
thf(955,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(226,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_insert__ident) ).
thf(928,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(35,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_5) ).
thf(358,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(188,axiom,
! [A: a,B: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier ) )
=> ( ( ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_strict__not__refl__weak) ).
thf(807,plain,
! [A: a,B: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier ) )
=> ( ( ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(184,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( order_under @ TA @ A @ B ) @ ( order_under @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_under__incr) ).
thf(796,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( order_under @ TA @ A @ B ) @ ( order_under @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( product_snd @ TB @ TA @ ( bot_bot @ ( product_prod @ TB @ TA ) ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_snd__bot) ).
thf(283,plain,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( product_snd @ TB @ TA @ ( bot_bot @ ( product_prod @ TB @ TA ) ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(106,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_is__singletonI) ).
thf(575,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(90,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_insert__commute) ).
thf(528,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(193,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_transD) ).
thf(822,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_fst__eqD) ).
thf(277,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( domain @ TA @ TB @ ( insert @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C ) )
= ( insert @ TA @ A @ ( domain @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_Domain__insert) ).
thf(442,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( domain @ TA @ TB @ ( insert @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C ) )
= ( insert @ TA @ A @ ( domain @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(208,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_at__least__as__goodD) ).
thf(871,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(82,axiom,
! [TA: $tType,A: TA] : ( trans @ TA @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_trans__singleton) ).
thf(501,plain,
! [TA: $tType,A: TA] : ( trans @ TA @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(221,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_singleton__iff) ).
thf(908,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(248,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
= ( ? [C: TA,D: TB] :
( ( A = D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_Range_Osimps) ).
thf(992,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
= ( ? [C: TA,D: TB] :
( ( A = D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(337,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(96,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_subset__singletonD) ).
thf(543,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(177,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(775,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(133,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(639,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(66,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_10) ).
thf(454,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(242,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
=> ~ ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_RangeE) ).
thf(972,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
=> ~ ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1015,plain,
$false,
inference(e,[status(thm)],[629,760,347,846,893,468,941,645,892,481,352,977,1005,741,511,269,597,861,582,762,873,449,533,715,698,538,747,913,829,1001,417,565,436,389,719,934,587,838,802,344,902,559,606,1013,881,325,289,789,591,514,966,905,475,924,602,397,634,877,293,660,428,312,265,849,810,381,798,546,793,957,778,952,302,260,820,424,275,407,693,484,625,879,665,889,493,757,682,710,974,742,650,615,980,356,593,499,989,857,783,420,339,637,471,256,679,970,622,701,738,911,503,647,997,938,360,921,765,718,965,824,573,689,296,562,423,402,772,286,577,281,391,611,713,335,350,540,445,936,831,784,451,599,509,434,631,552,323,726,520,895,943,462,685,695,780,455,608,299,438,431,768,827,394,986,306,722,531,487,749,617,939,458,836,490,675,1003,580,640,707,887,414,263,673,585,840,643,744,703,613,386,1008,571,595,497,859,465,627,931,363,556,588,517,319,304,652,731,995,961,813,946,258,378,478,272,383,899,549,536,800,620,752,447,315,818,405,865,735,833,410,341,506,664,400,955,928,358,807,796,283,575,528,822,277,442,871,501,908,992,337,543,775,639,454,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP153^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.08/0.23 % Computer : n002.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 20:05:07 UTC 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.24 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
% 0.97/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.22/1.20 % [INFO] Parsing done (391ms).
% 2.22/1.21 % [INFO] Running in sequential loop mode.
% 3.09/1.59 % [INFO] eprover registered as external prover.
% 3.09/1.59 % [INFO] Scanning for conjecture ...
% 3.46/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 277 axioms. Running axiom selection ...
% 3.67/1.87 % [INFO] Axiom selection finished. Selected 253 axioms (removed 24 axioms).
% 4.82/2.18 % [INFO] Problem is higher-order (TPTP THF).
% 5.03/2.21 % [INFO] Type checking passed.
% 5.03/2.21 % [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 ...
% 165.54/139.95 % External prover 'e' found a proof!
% 165.54/139.95 % [INFO] Killing All external provers ...
% 165.54/139.95 % Time passed: 139571ms (effective reasoning time: 138728ms)
% 165.54/139.95 % 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)>
% 165.54/139.95 % Axioms used in derivation (253): fact_210_total__on__singleton, fact_226_lnear__order__on__empty, tcon_fun___Orderings_Obot, fact_110_bot__apply, fact_2_preference__axioms, fact_59_prod__cases, fact_197_insertI2, fact_244_Range__empty__iff, fact_121_le__fun__def, fact_206_fst__eqD, fact_44_prod__induct7, fact_21_preference_Oindiff__trans, fact_65_no__better__thansubset__rel, fact_35_total__on__def, tcon_HOL_Obool___Orderings_Opreorder_7, fact_218_the__elem__eq, fact_1_rational__preference__axioms, fact_29_worse__in__no__better, fact_53_prod__cases7, fact_152_transI, fact_149_internal__case__prod__conv, fact_182_singleton__inject, fact_222_is__singletonE, fact_37_refl__onD1, fact_104_subset__eq, fact_87_empty__iff, fact_113_bot_Oextremum__uniqueI, fact_234_Range__Id__on, fact_14_pref__in__at__least__as, tcon_HOL_Obool___Orderings_Oord_9, tcon_Set_Oset___Orderings_Oorder__bot_1, fact_64_no__better__subset__pref, fact_27_rational__preference_Ostrict__not__refl__weak, fact_229_eq__fst__iff, fact_74_rational__preference_Onbt__nest, fact_36_refl__onD, fact_250_ComplI, fact_187_subset__insertI2, fact_34_total__onI, fact_227_fstI, fact_84_Pair__le, fact_50_prod__induct5, fact_71_refl__on__empty, tcon_fun___Orderings_Oord, fact_97_set__eq__subset, fact_238_RangeE, fact_83_empty__subsetI, fact_161_Id__on__iff, fact_5_reflexivity, fact_100_subset__refl, fact_200_prod__eq__iff, tcon_HOL_Obool___Orderings_Olinorder, tcon_Product__Type_Oprod___Orderings_Oorder__bot_11, fact_224_linear__order__on__singleton, fact_13_strict__trans, fact_148_Set_Ois__empty__def, fact_94_equals0D, fact_135_ord__eq__le__trans, fact_185_singleton__iff, fact_235_Range__empty, fact_162_Id__on__eqI, tcon_HOL_Obool___Orderings_Oorder__bot_6, fact_128_linear, fact_228_eq__snd__iff, fact_252_Compl__subset__Compl__iff, fact_106_subsetD, fact_107_in__mono, fact_79_rational__preference_Ono__better__subset__pref, fact_240_Range_Ocases, fact_231_Range__insert, fact_201_prod_Oexpand, fact_221_is__singletonI_H, fact_173_insert__iff, fact_46_Collect__mem__eq, fact_57_prod__cases3, fact_204_prod_Oexhaust__sel, fact_255_subset__Compl__self__eq, fact_32_old_Oprod_Oinject, fact_220_is__singleton__the__elem, fact_144_bot__fun__def, fact_191_mk__disjoint__insert, fact_98_subset__trans, fact_88_all__not__in__conv, fact_80_rational__preference_Ono__better__thansubset__rel, fact_69_rational__preference_Ointro, fact_73_total__on__empty, fact_155_preference_Otransitivity, fact_190_insert__mono, fact_195_insert__ident, fact_146_less__by__empty, fact_202_prod__eqI, fact_41_at__lst__asgd__ge, fact_223_is__singleton__def, fact_251_Compl__anti__mono, fact_249_Compl__iff, fact_115_bot_Oextremum, fact_26_rational__preference_Oweak__is__transitive, fact_246_Domain__insert, fact_33_rational__preference_Oas__good__as__sameIff, fact_96_Collect__mono__iff, fact_208_snd__eqD, tcon_Product__Type_Oprod___Orderings_Oord_14, fact_63_at__lst__asgd__not__ge, fact_68_old_Oprod_Orec, fact_7_completeD, fact_18_preference_Otrans__refl, fact_196_Set_Oset__insert, fact_170_snd__bot, fact_76_rational__preference__axioms__def, fact_213_snd__mono, fact_217_exI__realizer, fact_179_prod_Ocollapse, fact_119_le__funE, fact_90_Collect__empty__eq, fact_243_Range_Oinducts, fact_85_subsetI, fact_11_strict__not__refl__weak, fact_254_Domain__empty, fact_164_trans__Id__on, fact_156_preorder__on__def, fact_55_prod__cases5, fact_177_singleton__insert__inj__eq, fact_61_rational__preference_Oworse__in__no__better, fact_58_Pair__inject, fact_45_mem__Collect__eq, fact_95_emptyE, fact_67_nbt__nest, fact_105_equalityE, fact_4_total, fact_86_subset__antisym, fact_101_subset__iff, fact_207_snd__conv, fact_3_trans__refl, fact_160_Id__onI, fact_103_equalityD1, fact_245_Range__mono, fact_151_transE, tcon_Product__Type_Oprod___Orderings_Obot_15, fact_75_rational__preference_Ono__better__than__nonepty, fact_180_insert__subsetI, fact_117_bot__empty__eq, fact_214_fst__mono, fact_6_compl, fact_150_transD, fact_109_bot__prod__def, fact_93_equals0I, fact_178_singleton__insert__inj__eq_H, fact_129_eq__refl, fact_203_surjective__pairing, fact_125_ord__le__eq__subst, fact_241_Range_Osimps, fact_111_order__refl, fact_8_not__outside, fact_199_insertE, fact_183_insert__not__empty, fact_102_equalityD2, fact_39_refl__on__domain, fact_49_prod__induct6, fact_20_preference_Oreflexivity, fact_108_Pair__mono, fact_157_Collect__empty__eq__bot, fact_81_rational__preference_Oat__lst__asgd__not__ge, fact_17_preference_Ointro, fact_47_Collect__cong, fact_82_subset__empty, fact_91_subrelI, fact_112_subset__emptyI, fact_19_preference_Onot__outside, fact_165_refl__on__Id__on, fact_163_Id__onE, fact_158_relChain__def, fact_136_ord__le__eq__trans, fact_216_conjI__realizer, tcon_fun___Orderings_Oorder__bot, fact_132_le__cases3, fact_194_insert__absorb, fact_54_prod__cases6, fact_51_prod__induct4, fact_31_prod_Oinject, fact_166_under__incr, fact_212_subset__singleton__iff, fact_154_trans__empty, fact_15_rational__preference_Oaxioms_I1_J, fact_198_insertI1, fact_205_fst__conv, fact_248_Compl__eq__Compl__iff, fact_169_fst__bot, fact_16_preference__def, fact_23_rational__preference_Ototal, fact_114_bot_Oextremum__unique, fact_184_doubleton__eq__iff, fact_188_subset__insertI, fact_24_rational__preference_OcompleteD, fact_25_rational__preference_Ostrict__trans, tcon_fun___Orderings_Opreorder, fact_239_Range__iff, fact_242_Range_Ointros, fact_70_rational__preference__def, fact_40_at__least__as__goodD, fact_118_le__funD, fact_171_trans__singleton, fact_120_le__funI, fact_247_subset__Compl__singleton, fact_193_insert__eq__iff, fact_189_subset__insert, tcon_Set_Oset___Orderings_Obot_5, fact_116_bot__set__def, fact_176_insert__subset, fact_175_singletonI, fact_10_weak__is__transitive, fact_43_old_Oprod_Oexhaust, fact_77_rational__preference__axioms_Ointro, fact_140_linorder__wlog, fact_138_order__trans, fact_60_surj__pair, fact_172_insert__absorb2, fact_78_rational__preference_Oaxioms_I2_J, fact_66_no__better__than__nonepty, tcon_HOL_Obool___Orderings_Obot_10, fact_153_trans__def, fact_145_ssubst__Pair__rhs, fact_225_sndI, tcon_Set_Oset___Orderings_Opreorder_2, fact_174_insertCI, fact_28_rational__preference_Ostrict__is__neg__transitive, fact_253_Domain__Id__on, fact_209_refl__on__singleton, fact_89_empty__Collect__eq, fact_124_ord__eq__le__subst, fact_159_Id__on__empty, fact_30_as__good__as__sameIff, fact_72_preorder__on__empty, fact_0_assms, fact_52_prod__induct3, fact_186_singletonD, fact_99_Collect__mono, fact_42_old_Oprod_Oinducts, fact_22_rational__preference_Ocompl, fact_38_refl__onD2, fact_9_strict__is__neg__transitive, tcon_Set_Oset___Orderings_Oord_4, tcon_Product__Type_Oprod___Orderings_Opreorder_12, fact_62_rational__preference_Opref__in__at__least__as, fact_92_ex__in__conv, fact_219_is__singletonI, fact_192_insert__commute, fact_215_BNF__Greatest__Fixpoint_Osubst__Pair, fact_147_transitivity, fact_130_le__cases, fact_181_less__eq__prod__def, fact_12_indiff__trans, fact_211_subset__singletonD, fact_56_prod__cases4
% 165.54/139.95 % No. of inferences in proof: 510
% 165.54/139.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 139571 ms resp. 138728 ms w/o parsing
% 166.22/140.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 166.22/140.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------