TSTP Solution File: SCT179_5 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT179_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:51:10 EDT 2023
% Result : Theorem 15.55s 6.59s
% Output : Refutation 15.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 171
% Syntax : Number of formulae : 299 ( 69 unt; 45 typ; 0 def)
% Number of atoms : 1071 ( 128 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 4603 ( 49 ~; 16 |; 46 &;4306 @)
% ( 22 <=>; 164 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 9 con; 0-6 aty)
% Number of variables : 666 ( 0 ^; 609 !; 10 ?; 666 :)
% ( 47 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(cl_Groups_Ominus_type,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(top_type,type,
top:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(arrow_1985332922le_Lin_type,type,
arrow_1985332922le_Lin: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(order_1409979114der_on_type,type,
order_1409979114der_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(order_915043626der_on_type,type,
order_915043626der_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(order_preorder_on_type,type,
order_preorder_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(order_215145569der_on_type,type,
order_215145569der_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) ) ).
thf(order_well_order_on_type,type,
order_well_order_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(inv_imagep_type,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ bool ) ) > ( fun @ TA @ TB ) > TA > TA > $o ) ).
thf(domain_type,type,
domain:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TA ) @ bool ) > ( fun @ TB @ bool ) ) ).
thf(id_type,type,
id:
!>[TA: $tType] : ( fun @ ( product_prod @ TA @ TA ) @ bool ) ).
thf(id_on_type,type,
id_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).
thf(range_type,type,
range:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TA ) @ bool ) > ( fun @ TA @ bool ) ) ).
thf(antisym_type,type,
antisym:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(irrefl_type,type,
irrefl:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(refl_on_type,type,
refl_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(total_on_type,type,
total_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(trans_type,type,
trans:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(lex_prod_type,type,
lex_prod:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TB ) @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > ( fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool ) ) ).
thf(measure_type,type,
measure:
!>[TA: $tType] : ( ( fun @ TA @ nat ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).
thf(wf_type,type,
wf:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fNot_type,type,
fNot: fun @ bool @ bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(r_type,type,
r: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(324,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(91,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rev__predicate1D) ).
thf(371,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_bot__apply) ).
thf(347,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(76,axiom,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_empty__def) ).
thf(333,plain,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(124,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_equalityD1) ).
thf(468,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(408,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(33,axiom,
cl_Groups_Ominus @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(217,plain,
cl_Groups_Ominus @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(96,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_subset__refl) ).
thf(385,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(125,axiom,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_top__le) ).
thf(472,plain,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(60,axiom,
( arrow_1985332922le_Lin
= ( collect @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( order_215145569der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Lin__def) ).
thf(288,plain,
( arrow_1985332922le_Lin
= ( collect @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( order_215145569der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(64,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_DiffD2) ).
thf(301,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(436,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(98,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_DiffE) ).
thf(389,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(80,axiom,
! [TA: $tType] :
? [A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_UNIV__witness) ).
thf(344,plain,
! [TA: $tType] :
? [A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(120,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_empty__Diff) ).
thf(460,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] : ( ord_less_eq @ ( fun @ TB @ bool ) @ ( minus_minus @ ( fun @ TB @ bool ) @ ( range @ TA @ TB @ B ) @ ( range @ TA @ TB @ A ) ) @ ( range @ TA @ TB @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Range__Diff__subset) ).
thf(189,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] : ( ord_less_eq @ ( fun @ TB @ bool ) @ ( minus_minus @ ( fun @ TB @ bool ) @ ( range @ TA @ TB @ B ) @ ( range @ TA @ TB @ A ) ) @ ( range @ TA @ TB @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(107,axiom,
wf @ arrow_411405190le_alt @ ( minus_minus @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ r @ ( id @ arrow_411405190le_alt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(421,plain,
wf @ arrow_411405190le_alt @ ( minus_minus @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ r @ ( id @ arrow_411405190le_alt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_in__inv__imagep) ).
thf(448,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) )
=> ( inv_imagep @ TB @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(50,axiom,
! [TA: $tType] :
( ( range @ TA @ TA @ ( id @ TA ) )
= ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Range__Id) ).
thf(261,plain,
! [TA: $tType] :
( ( range @ TA @ TA @ ( id @ TA ) )
= ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(126,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( trans @ TA @ A )
=> ( ( antisym @ TA @ A )
=> ( trans @ TA @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_trans__diff__Id) ).
thf(475,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( trans @ TA @ A )
=> ( ( antisym @ TA @ A )
=> ( trans @ TA @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(18,axiom,
! [TA: $tType] : ( antisym @ TA @ ( id @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_antisym__Id) ).
thf(179,plain,
! [TA: $tType] : ( antisym @ TA @ ( id @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(132,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,axiom,
! [TA: $tType] : ( order_1409979114der_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_lnear__order__on__empty) ).
thf(243,plain,
! [TA: $tType] : ( order_1409979114der_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ( domain @ TA @ TB @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ( A
= ( bot_bot @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Domain__empty__iff) ).
thf(312,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ( ( domain @ TA @ TB @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( A
= ( bot_bot @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) )
=> ( ( domain @ TA @ TB @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(307,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(62,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_equalityD2) ).
thf(292,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(39,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( top_top @ ( fun @ TA @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Diff__UNIV) ).
thf(233,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( top_top @ ( fun @ TA @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(45,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Diff__empty) ).
thf(248,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(114,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_subset__empty) ).
thf(439,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(26,axiom,
! [TA: $tType] : ( refl_on @ TA @ ( top_top @ ( fun @ TA @ bool ) ) @ ( id @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_refl__Id) ).
thf(201,plain,
! [TA: $tType] : ( refl_on @ TA @ ( top_top @ ( fun @ TA @ bool ) ) @ ( id @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(35,axiom,
! [TA: $tType] : ( antisym @ TA @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_antisym__empty) ).
thf(220,plain,
! [TA: $tType] : ( antisym @ TA @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(99,axiom,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
<=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_top__unique) ).
thf(392,plain,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) )
& ( ( A
= ( top_top @ TA ) )
=> ( ord_less_eq @ TA @ ( top_top @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(23,axiom,
! [TA: $tType] :
( ( id_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Id__on__empty) ).
thf(192,plain,
! [TA: $tType] :
( ( id_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(110,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_empty__iff) ).
thf(429,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(12,axiom,
! [TA: $tType,A: fun @ TA @ nat] : ( wf @ TA @ ( measure @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_wf__measure) ).
thf(156,plain,
! [TA: $tType,A: fun @ TA @ nat] : ( wf @ TA @ ( measure @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(102,axiom,
! [TA: $tType] : ( order_well_order_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_well__order__on__empty) ).
thf(403,plain,
! [TA: $tType] : ( order_well_order_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(84,axiom,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(356,plain,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(6,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
? [B: fun @ ( product_prod @ TA @ TA ) @ bool] : ( order_well_order_on @ TA @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_well__order__on) ).
thf(141,plain,
! [TA: $tType,A: fun @ TA @ bool] :
? [B: fun @ ( product_prod @ TA @ TA ) @ bool] : ( order_well_order_on @ TA @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(256,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(37,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_empty__Collect__eq) ).
thf(225,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_bot__fun__def) ).
thf(212,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1,conjecture,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( order_215145569der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( order_215145569der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) ) @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( order_215145569der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_set__mp) ).
thf(266,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(86,axiom,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(360,plain,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_subsetD) ).
thf(205,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(69,axiom,
preorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(311,plain,
preorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(100,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(398,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(9,axiom,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_bot__least) ).
thf(148,plain,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Diff__subset) ).
thf(264,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(14,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ D @ C )
= ( minus_minus @ TA @ B @ A ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_diff__eq__diff__eq) ).
thf(161,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ D @ C )
= ( minus_minus @ TA @ B @ A ) )
=> ( ( ( D = C )
=> ( B = A ) )
& ( ( B = A )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ D @ C )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ D @ A ) @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Diff__mono) ).
thf(279,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ D @ C )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ D @ A ) @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(63,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Collect__empty__eq) ).
thf(296,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(93,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(375,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(109,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_ex__in__conv) ).
thf(423,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(22,axiom,
top @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(191,plain,
top @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(59,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_set__rev__mp) ).
thf(286,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(57,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] : ( total_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_total__on__empty) ).
thf(281,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] : ( total_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(49,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_top1I) ).
thf(259,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(115,axiom,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
!= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_UNIV__not__empty) ).
thf(445,plain,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
!= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(123,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_DiffI) ).
thf(466,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(40,axiom,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_UNIV__def) ).
thf(236,plain,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ D @ C )
= ( minus_minus @ TA @ B @ A ) )
=> ( ( ord_less_eq @ TA @ D @ C )
<=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_diff__eq__diff__less__eq) ).
thf(181,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ D @ C )
= ( minus_minus @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ D @ C )
=> ( ord_less_eq @ TA @ B @ A ) )
& ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(83,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_all__not__in__conv) ).
thf(350,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(16,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(172,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(106,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_emptyE) ).
thf(419,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ( range @ TA @ TB @ A )
= ( bot_bot @ ( fun @ TB @ bool ) ) )
<=> ( A
= ( bot_bot @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Range__empty__iff) ).
thf(377,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ( ( range @ TA @ TB @ A )
= ( bot_bot @ ( fun @ TB @ bool ) ) )
=> ( A
= ( bot_bot @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) )
=> ( ( range @ TA @ TB @ A )
= ( bot_bot @ ( fun @ TB @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( top_top @ ( fun @ TB @ TA ) ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_top__apply) ).
thf(230,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( top_top @ ( fun @ TB @ TA ) ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(44,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Diff__cancel) ).
thf(245,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(71,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
<=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Diff__iff) ).
thf(318,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ ( domain @ TA @ TB @ B ) @ ( domain @ TA @ TB @ A ) ) @ ( domain @ TA @ TB @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Domain__Diff__subset) ).
thf(434,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ ( domain @ TA @ TB @ B ) @ ( domain @ TA @ TB @ A ) ) @ ( domain @ TA @ TB @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( wf @ TB @ B )
=> ( ( wf @ TA @ A )
=> ( wf @ ( product_prod @ TB @ TA ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_wf__lex__prod) ).
thf(303,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( wf @ TB @ B )
=> ( ( wf @ TA @ A )
=> ( wf @ ( product_prod @ TB @ TA ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(87,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_predicate1D) ).
thf(362,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(117,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_equals0D) ).
thf(451,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(127,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( total_on @ TA @ B @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) )
<=> ( total_on @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_total__on__diff__Id) ).
thf(477,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( total_on @ TA @ B @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) )
=> ( total_on @ TA @ B @ A ) )
& ( ( total_on @ TA @ B @ A )
=> ( total_on @ TA @ B @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(97,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_empty__subsetI) ).
thf(387,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(89,axiom,
! [TA: $tType] : ( order_preorder_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_preorder__on__empty) ).
thf(367,plain,
! [TA: $tType] : ( order_preorder_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( minus_minus @ ( fun @ TA @ TB ) @ C @ B ) @ A )
= ( minus_minus @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_minus__apply) ).
thf(251,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( minus_minus @ ( fun @ TA @ TB ) @ C @ B ) @ A )
= ( minus_minus @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( domain @ TA @ TB @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Domain__empty) ).
thf(198,plain,
! [TA: $tType,TB: $tType] :
( ( domain @ TA @ TB @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(75,axiom,
! [TA: $tType] :
( ( domain @ TA @ TA @ ( id @ TA ) )
= ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Domain__Id) ).
thf(330,plain,
! [TA: $tType] :
( ( domain @ TA @ TA @ ( id @ TA ) )
= ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(3,axiom,
! [TA: $tType] : ( trans @ TA @ ( id @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_trans__Id) ).
thf(130,plain,
! [TA: $tType] : ( trans @ TA @ ( id @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
( ( aa @ TA @ TB @ ( minus_minus @ ( fun @ TA @ TB ) @ B @ A ) @ C )
= ( minus_minus @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_fun__diff__def) ).
thf(455,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
( ( aa @ TA @ TB @ ( minus_minus @ ( fun @ TA @ TB ) @ B @ A ) @ C )
= ( minus_minus @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(5,axiom,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
<=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_bot__unique) ).
thf(135,plain,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) )
& ( ( A
= ( bot_bot @ TA ) )
=> ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(111,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combb @ bool @ bool @ TA @ fNot @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_set__diff__eq) ).
thf(431,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combb @ bool @ bool @ TA @ fNot @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(30,axiom,
! [TA: $tType,A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
<=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_bot__empty__eq) ).
thf(209,plain,
! [TA: $tType,A: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(119,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(458,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(10,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( order_915043626der_on @ TA @ B @ A )
<=> ( ( order_preorder_on @ TA @ B @ A )
& ( antisym @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_partial__order__on__def) ).
thf(150,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( order_915043626der_on @ TA @ B @ A )
=> ( ( order_preorder_on @ TA @ B @ A )
& ( antisym @ TA @ A ) ) )
& ( ( ( order_preorder_on @ TA @ B @ A )
& ( antisym @ TA @ A ) )
=> ( order_915043626der_on @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( range @ TB @ TA @ ( bot_bot @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Range__empty) ).
thf(327,plain,
! [TA: $tType,TB: $tType] :
( ( range @ TB @ TA @ ( bot_bot @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(121,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( order_1409979114der_on @ TA @ B @ A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( order_215145569der_on @ TA @ B ) @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_strict__linear__order__on__diff__Id) ).
thf(463,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( order_1409979114der_on @ TA @ B @ A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( order_215145569der_on @ TA @ B ) @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(78,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_double__diff) ).
thf(338,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(77,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_DiffD1) ).
thf(336,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(11,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( trans @ TA @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_trans__Id__on) ).
thf(154,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( trans @ TA @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( order_preorder_on @ TA @ B @ A )
<=> ( ( refl_on @ TA @ B @ A )
& ( trans @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_preorder__on__def) ).
thf(175,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( order_preorder_on @ TA @ B @ A )
=> ( ( refl_on @ TA @ B @ A )
& ( trans @ TA @ A ) ) )
& ( ( ( refl_on @ TA @ B @ A )
& ( trans @ TA @ A ) )
=> ( order_preorder_on @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(143,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(122,axiom,
order_1409979114der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(465,plain,
order_1409979114der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( trans @ TB @ B )
=> ( ( trans @ TA @ A )
=> ( trans @ ( product_prod @ TB @ TA ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_trans__lex__prod) ).
thf(203,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( trans @ TB @ B )
=> ( ( trans @ TA @ A )
=> ( trans @ ( product_prod @ TB @ TA ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(34,axiom,
! [TA: $tType] : ( wf @ TA @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_wf__empty) ).
thf(218,plain,
! [TA: $tType] : ( wf @ TA @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(13,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( domain @ TA @ TA @ ( id_on @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Domain__Id__on) ).
thf(158,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( domain @ TA @ TA @ ( id_on @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_le__bot) ).
thf(186,plain,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(101,axiom,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_top__greatest) ).
thf(401,plain,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_in__mono) ).
thf(290,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(29,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] : ( irrefl @ TA @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_irrefl__diff__Id) ).
thf(207,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] : ( irrefl @ TA @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(54,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( order_215145569der_on @ TA @ B ) @ A ) )
<=> ( ( trans @ TA @ A )
& ( irrefl @ TA @ A )
& ( total_on @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_strict__linear__order__on__def) ).
thf(272,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( order_215145569der_on @ TA @ B ) @ A ) )
=> ( ( trans @ TA @ A )
& ( irrefl @ TA @ A )
& ( total_on @ TA @ B @ A ) ) )
& ( ( ( trans @ TA @ A )
& ( irrefl @ TA @ A )
& ( total_on @ TA @ B @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( order_215145569der_on @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(95,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(383,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(81,axiom,
bot @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(346,plain,
bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(105,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
<=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
& ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_set__eq__subset) ).
thf(410,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( B = A )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
& ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ) )
& ( ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
& ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(15,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( order_1409979114der_on @ TA @ B @ A )
<=> ( ( order_915043626der_on @ TA @ B @ A )
& ( total_on @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_linear__order__on__def) ).
thf(168,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( order_1409979114der_on @ TA @ B @ A )
=> ( ( order_915043626der_on @ TA @ B @ A )
& ( total_on @ TA @ B @ A ) ) )
& ( ( ( order_915043626der_on @ TA @ B @ A )
& ( total_on @ TA @ B @ A ) )
=> ( order_1409979114der_on @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_order__refl) ).
thf(146,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(405,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(108,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(422,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(92,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_subset__UNIV) ).
thf(373,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(305,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(79,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_equals0I) ).
thf(341,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(53,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( order_well_order_on @ TA @ B @ A )
<=> ( ( order_1409979114der_on @ TA @ B @ A )
& ( wf @ TA @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_well__order__on__def) ).
thf(268,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( order_well_order_on @ TA @ B @ A )
=> ( ( order_1409979114der_on @ TA @ B @ A )
& ( wf @ TA @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ) ) )
& ( ( ( order_1409979114der_on @ TA @ B @ A )
& ( wf @ TA @ ( minus_minus @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ A @ ( id @ TA ) ) ) )
=> ( order_well_order_on @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ord_less_eq @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( domain @ TA @ TB @ B ) @ ( domain @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Domain__mono) ).
thf(358,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ord_less_eq @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( domain @ TA @ TB @ B ) @ ( domain @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(24,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(195,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(283,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(41,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) @ A )
= ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Diff__idemp) ).
thf(239,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) @ A )
= ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(42,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(242,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(55,axiom,
! [TA: $tType] : ( order_915043626der_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_partial__order__on__empty) ).
thf(277,plain,
! [TA: $tType] : ( order_915043626der_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(90,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_iso__tuple__UNIV__I) ).
thf(369,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(47,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(254,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(72,axiom,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_refl__on__empty) ).
thf(322,plain,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(309,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(32,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_UNIV__I) ).
thf(215,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(36,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( top_top @ ( fun @ TA @ bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_UNIV__eq__I) ).
thf(222,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( top_top @ ( fun @ TA @ bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(88,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_equalityI) ).
thf(364,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(480,plain,
$false,
inference(e,[status(thm)],[324,371,347,333,468,408,217,385,472,288,301,436,389,344,460,189,421,448,261,475,179,132,243,312,307,292,233,248,439,201,220,392,192,429,156,403,356,141,256,225,212,128,266,360,205,311,398,148,264,161,279,296,375,423,191,286,281,259,445,466,236,181,350,172,419,377,230,245,318,434,303,362,451,477,387,367,251,198,330,130,455,135,431,209,458,150,327,463,338,336,154,175,143,465,203,218,158,186,401,290,207,272,383,346,410,168,146,405,422,373,305,341,268,358,195,283,239,242,277,369,254,322,309,215,222,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SCT179_5 : TPTP v8.1.2. Released v6.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 15:41:44 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.88/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/1.05 % [INFO] Parsing done (194ms).
% 1.54/1.06 % [INFO] Running in sequential loop mode.
% 2.15/1.25 % [INFO] eprover registered as external prover.
% 2.15/1.25 % [INFO] cvc4 registered as external prover.
% 2.15/1.26 % [INFO] Scanning for conjecture ...
% 2.41/1.36 % [INFO] Found a conjecture and 125 axioms. Running axiom selection ...
% 2.60/1.43 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 3.13/1.54 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.13/1.56 % [INFO] Type checking passed.
% 3.13/1.56 % [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 ...
% 3.57/1.72 % [INFO] [Domain constraints] Detected constraint on bool
% 3.57/1.72 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 3.57/1.77 % [INFO] [Domain constraints] Detected constraint on bool
% 3.57/1.77 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 15.55/6.58 % External prover 'e' found a proof!
% 15.55/6.58 % [INFO] Killing All external provers ...
% 15.55/6.58 % Time passed: 6049ms (effective reasoning time: 5519ms)
% 15.55/6.58 % 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)>
% 15.55/6.59 % Axioms used in derivation (125): arity_HOL_Obool___Groups_Ominus, fact_9_well__order__on__def, fact_92_set__eq__subset, fact_21_diff__eq__diff__eq, fact_99_set__mp, fact_23_well__order__on, fact_70_subsetD, fact_60_trans__diff__Id, fact_1_Lin__def, fact_10_fun__diff__def, fact_18_UNIV__witness, fact_78_trans__Id__on, fact_52_Domain__empty__iff, fact_56_partial__order__on__empty, help_COMBS_1_1_U, fact_61_antisym__empty, arity_HOL_Obool___Orderings_Opreorder, arity_fun___Orderings_Obot, fact_42_Diff__empty, help_fconj_3_1_U, fact_38_total__on__empty, fact_3_Diff__idemp, fact_41_UNIV__not__empty, fact_27_empty__iff, fact_32_bot__empty__eq, help_fTrue_1_1_T, fact_91_subset__refl, fact_94_equalityD1, fact_51_Range__empty, fact_8_iso__tuple__UNIV__I, fact_25_all__not__in__conv, fact_65_preorder__on__empty, fact_44_linear__order__on__def, fact_2_Diff__iff, fact_74_Domain__Id__on, help_fNot_2_1_U, help_fTrue_1_1_U, fact_30_empty__Diff, fact_47_Range__Id, fact_54_refl__on__empty, help_fNot_1_1_U, fact_7_UNIV__I, fact_37_bot__fun__def, fact_97_predicate1D, help_fFalse_1_1_T, fact_87_subset__UNIV, fact_73_empty__subsetI, fact_33_empty__def, fact_4_DiffI, fact_64_preorder__on__def, fact_40_well__order__on__empty, fact_85_top__unique, fact_88_double__diff, fact_95_equalityD2, help_COMBB_1_1_U, fact_45_strict__linear__order__on__def, fact_93_rev__predicate1D, fact_5_DiffE, fact_96_in__mono, fact_46_equals0I, arity_fun___Orderings_Opreorder, fact_17_UNIV__eq__I, help_fconj_2_1_U, fact_80_bot__least, fact_62_antisym__Id, fact_86_top__greatest, fact_39_lnear__order__on__empty, fact_58_wf__lex__prod, fact_84_top__le, fact_13_DiffD2, fact_79_Domain__mono, fact_63_partial__order__on__def, fact_24_Diff__UNIV, fact_72_subset__empty, fact_67_Range__Diff__subset, fact_35_equals0D, fact_20_total__on__diff__Id, fact_81_bot__unique, arity_HOL_Obool___Orderings_Otop, fact_50_Domain__empty, fact_71_equalityI, fact_55_trans__Id, fact_59_wf__measure, fact_22_in__inv__imagep, fact_28_Collect__empty__eq, fact_90_Diff__subset, fact_82_le__bot, fact_76_mem__def, fact_6_top1I, fact_36_bot__apply, help_COMBK_1_1_U, fact_83_diff__eq__diff__less__eq, fact_89_Diff__mono, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, conj_1, fact_98_set__rev__mp, fact_31_Diff__cancel, fact_29_emptyE, help_fconj_1_1_U, fact_15_set__diff__eq, fact_0_strict__linear__order__on__diff__Id, fact_16_top__apply, fact_66_Id__on__empty, fact_14_DiffD1, help_fFalse_1_1_U, fact_43_wf__empty, fact_77_Collect__def, fact_12_UNIV__def, fact_19_irrefl__diff__Id, help_pp_1_1_U, fact_11_minus__apply, fact_34_ex__in__conv, fact_48_Domain__Id, fact_57_trans__lex__prod, fact_75_ext, fact_53_Range__empty__iff, arity_fun___Orderings_Otop, fact_49_refl__Id, conj_0, fact_26_empty__Collect__eq, help_pp_2_1_U, arity_fun___Groups_Ominus, fact_68_Domain__Diff__subset, fact_69_order__refl
% 15.55/6.59 % No. of inferences in proof: 254
% 15.55/6.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6049 ms resp. 5519 ms w/o parsing
% 15.92/6.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.92/6.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------