TSTP Solution File: DAT206^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT206^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 : Tue May 7 07:39:45 EDT 2024
% Result : Theorem 82.94s 62.74s
% Output : Refutation 83.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 322
% Syntax : Number of formulae : 598 ( 96 unt; 48 typ; 0 def)
% Number of atoms : 2004 ( 406 equ; 4 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 8305 ( 266 ~; 36 |; 128 &;6707 @)
% ( 0 <=>;1168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 403 ( 403 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 50 usr; 12 con; 0-4 aty)
% Number of variables : 2202 ( 76 ^2000 !; 84 ?;2202 :)
% ( 42 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(type_type,type,
type:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(top_type,type,
top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(no_bot_type,type,
no_bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(no_top_type,type,
no_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_top_type,type,
order_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(dense_order_type,type,
dense_order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(dense_linorder_type,type,
dense_linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(condit1656338222tinuum_type,type,
condit1656338222tinuum:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(condit1037483654norder_type,type,
condit1037483654norder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(coset_type,type,
coset:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).
thf(distinct_type,type,
distinct:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(linorder_sorted_type,type,
linorder_sorted:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(set2_type,type,
set2:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).
thf(product_lists_type,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(sublists_type,type,
sublists:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(union_type,type,
union:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(list_c659805718roduct_type,type,
list_c659805718roduct:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(mergesort_remdups_type,type,
mergesort_remdups:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(order_strict_mono_type,type,
order_strict_mono:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(ordering_top_type,type,
ordering_top:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > TA > $o ) > TA > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(remove_type,type,
remove:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(sorted1061247458sorted_type,type,
sorted1061247458sorted:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(l1_type,type,
l1: list @ a ).
thf(l1a_type,type,
l1a: list @ a ).
thf(l2_type,type,
l2: list @ a ).
thf(l2b_type,type,
l2b: list @ a ).
thf(x1_type,type,
x1: a ).
thf(x2_type,type,
x2: a ).
thf(114,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( insert @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_distinct__insert) ).
thf(645,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( insert @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(218,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( top_top @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_top_Oextremum__strict) ).
thf(1036,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( top_top @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(109,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_190_equalityE) ).
thf(629,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)],[109]) ).
thf(154,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_neq__iff) ).
thf(760,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(65,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA] :
( ( linorder_sorted @ TA @ ( cons @ TA @ A @ B ) )
= ( ( linorder_sorted @ TA @ B )
& ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_sorted__Cons) ).
thf(479,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA] :
( ( linorder_sorted @ TA @ ( cons @ TA @ A @ B ) )
= ( ( linorder_sorted @ TA @ B )
& ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(185,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( TA > TB ) > TA > TB > $o] :
( ! [B: TB,C: TA > TB,D: TA > TB,E: TA] :
( ! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( A @ C @ E @ B )
= ( A @ D @ E @ B ) ) )
=> ( ! [B: TA,C: TA > TB] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ B )
=> ( A @ C @ D @ ( C @ D ) ) )
=> ? [D: TB] : ( A @ C @ B @ D ) )
=> ? [B: TA > TB] :
! [C: TA] : ( A @ B @ C @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_dependent__wellorder__choice) ).
thf(846,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( TA > TB ) > TA > TB > $o] :
( ! [B: TB,C: TA > TB,D: TA > TB,E: TA] :
( ! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( A @ C @ E @ B )
= ( A @ D @ E @ B ) ) )
=> ( ! [B: TA,C: TA > TB] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ B )
=> ( A @ C @ D @ ( C @ D ) ) )
=> ? [D: TB] : ( A @ C @ B @ D ) )
=> ? [B: TA > TB] :
! [C: TA] : ( A @ B @ C @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(63,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_list__induct__first2) ).
thf(468,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_list__tail__coinc) ).
thf(352,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(190,axiom,
! [A: a] :
( ( member @ a @ A @ ( set2 @ a @ l2b ) )
=> ( ord_less_eq @ a @ x2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_x2__le) ).
thf(909,plain,
! [A: a] :
( ( member @ a @ A @ ( set2 @ a @ l2b ) )
=> ( ord_less_eq @ a @ x2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(24,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_antisym) ).
thf(333,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(270,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_order_Ostrict__trans1) ).
thf(1200,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(275,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_linordered__field__no__ub) ).
thf(1211,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1,conjecture,
ord_less @ a @ x2 @ x1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less @ a @ x2 @ x1 ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(276,plain,
~ ( ord_less @ a @ x2 @ x1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(231,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_minf_I2_J) ).
thf(1068,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(260,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ 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 @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_order__less__le__subst1) ).
thf(1158,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ 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 @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_list__induct2_H) ).
thf(582,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(272,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_psubset__subset__trans) ).
thf(1205,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(58,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_list_Odistinct_I1_J) ).
thf(449,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(254,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_minf_I6_J) ).
thf(1142,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA > $o ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA > $o] : ( A @ E @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB > TA > $o,F: TB,G: list @ TB,H: TA,I: list @ TA] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
=> ( ! [E: TB > TA > $o,F: TB,G: list @ TB] : ( A @ E @ ( cons @ TB @ F @ G ) @ ( nil @ TA ) )
=> ( ! [E: TB > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TB ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_list__all__zip_Oinduct) ).
thf(379,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA > $o ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA > $o] : ( A @ E @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB > TA > $o,F: TB,G: list @ TB,H: TA,I: list @ TA] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
=> ( ! [E: TB > TA > $o,F: TB,G: list @ TB] : ( A @ E @ ( cons @ TB @ F @ G ) @ ( nil @ TA ) )
=> ( ! [E: TB > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TB ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(41,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_list__nonempty__induct) ).
thf(384,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(252,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_dense__le) ).
thf(1137,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(72,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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_98_le__cases3) ).
thf(500,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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)],[72]) ).
thf(166,axiom,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_psubset__eq) ).
thf(797,plain,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(137,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( set2 @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_the__elem__set) ).
thf(715,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( set2 @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(196,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( top_top @ TA ) )
= ( ord_less @ TA @ A @ ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_top_Onot__eq__extremum) ).
thf(930,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( top_top @ TA ) )
= ( ord_less @ TA @ A @ ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(178,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_neqE) ).
thf(829,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(134,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_top__greatest) ).
thf(709,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(222,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_order_Ostrict__trans2) ).
thf(1046,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(13,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ( A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_ordering__top_Oextremum) ).
thf(301,plain,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ! [B: list @ TA] :
( ( member @ ( list @ TA ) @ B @ ( set2 @ ( list @ TA ) @ A ) )
=> ( distinct @ TA @ B ) )
=> ( distinct @ ( list @ TA ) @ ( product_lists @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_distinct__product__lists) ).
thf(320,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ! [B: list @ TA] :
( ( member @ ( list @ TA ) @ B @ ( set2 @ ( list @ TA ) @ A ) )
=> ( distinct @ TA @ B ) )
=> ( distinct @ ( list @ TA ) @ ( product_lists @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(53,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_insert__Nil) ).
thf(436,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(36,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_dual__order_Otrans) ).
thf(372,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(168,axiom,
! [TA: $tType] :
( ( no_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_gt__ex) ).
thf(802,plain,
! [TA: $tType] :
( ( no_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(61,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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_105_linorder__wlog) ).
thf(460,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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)],[61]) ).
thf(225,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_dual__order_Ostrict__trans2) ).
thf(1055,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(140,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_top_Oextremum__unique) ).
thf(724,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(95,axiom,
! [TA: $tType] :
~ ( ord_less_eq @ ( set @ TA ) @ ( coset @ TA @ ( nil @ TA ) ) @ ( set2 @ TA @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_subset__code_I3_J) ).
thf(587,plain,
! [TA: $tType] :
~ ( ord_less_eq @ ( set @ TA ) @ ( coset @ TA @ ( nil @ TA ) ) @ ( set2 @ TA @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(182,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_strict__monoD) ).
thf(838,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct @ TA @ ( cons @ TA @ A @ C ) )
& ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_distinct__length__2__or__more) ).
thf(357,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct @ TA @ ( cons @ TA @ A @ C ) )
& ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(268,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A != B )
=> ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_psubsetI) ).
thf(1191,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A != B )
=> ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
& ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_less__fun__def) ).
thf(817,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
& ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(87,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_list_Oinducts) ).
thf(559,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(111,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_set__rev__mp) ).
thf(638,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(235,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__imp__not__eq) ).
thf(1087,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(48,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_178_Collect__mono__iff) ).
thf(421,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)],[48]) ).
thf(6,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_168_subset__antisym) ).
thf(284,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)],[6]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_subset__refl) ).
thf(416,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8,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(289,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(239,axiom,
( ( distinct @ a @ l1a )
& ( linorder_sorted @ a @ l1a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_l1__props) ).
thf(1100,plain,
( ( distinct @ a @ l1a )
& ( linorder_sorted @ a @ l1a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(245,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_linordered__field__no__lb) ).
thf(1115,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(22,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] :
( ( linorder_sorted @ TA @ A )
=> ( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( ( A
= ( cons @ TA @ C @ B ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ B ) )
=> ( ord_less_eq @ TA @ C @ D ) )
=> ~ ( linorder_sorted @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_sorted_Ocases) ).
thf(325,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] :
( ( linorder_sorted @ TA @ A )
=> ( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( ( A
= ( cons @ TA @ C @ B ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ B ) )
=> ( ord_less_eq @ TA @ C @ D ) )
=> ~ ( linorder_sorted @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(69,axiom,
! [TA: $tType] :
( ( list_c659805718roduct @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_combinatorial__product_Osimps_I1_J) ).
thf(492,plain,
! [TA: $tType] :
( ( list_c659805718roduct @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(163,axiom,
! [TA: $tType] :
( ( ord_less @ ( 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_175_subset__not__subset__eq) ).
thf(789,plain,
! [TA: $tType] :
( ( ord_less @ ( 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)],[163]) ).
thf(97,axiom,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_distinct_Osimps_I1_J) ).
thf(591,plain,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(67,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_quicksort_Ocases) ).
thf(485,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(73,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_180_set__eq__subset) ).
thf(514,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)],[73]) ).
thf(265,axiom,
( ( ( distinct @ a @ l2b )
& ( linorder_sorted @ a @ l2b ) )
=> ( ( sorted1061247458sorted @ a @ ( cons @ a @ x1 @ l1a ) @ l2b )
= ( ord_less_eq @ ( set @ a ) @ ( set2 @ a @ ( cons @ a @ x1 @ l1a ) ) @ ( set2 @ a @ l2b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Cons_Ohyps) ).
thf(1183,plain,
( ( ( distinct @ a @ l2b )
& ( linorder_sorted @ a @ l2b ) )
=> ( ( sorted1061247458sorted @ a @ ( cons @ a @ x1 @ l1a ) @ l2b )
= ( ord_less_eq @ ( set @ a ) @ ( set2 @ a @ ( cons @ a @ x1 @ l1a ) ) @ ( set2 @ a @ l2b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(220,axiom,
! [TA: $tType] :
( ( dense_order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_dense) ).
thf(1040,plain,
! [TA: $tType] :
( ( dense_order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(242,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_dual__order_Ostrict__implies__order) ).
thf(1109,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(27,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_7) ).
thf(348,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(90,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_subset__UNIV) ).
thf(574,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(156,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_minf_I7_J) ).
thf(766,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( remove @ TA @ A @ ( coset @ TA @ B ) )
= ( coset @ TA @ ( insert @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_remove__code_I2_J) ).
thf(280,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( remove @ TA @ A @ ( coset @ TA @ B ) )
= ( coset @ TA @ ( insert @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( 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_89_order__subst2) ).
thf(734,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( 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)],[144]) ).
thf(188,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_minf_I1_J) ).
thf(866,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(210,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_antisym__conv3) ).
thf(988,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ 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_84_le__funD) ).
thf(312,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ 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)],[17]) ).
thf(9,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_order__refl) ).
thf(292,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_list_OdiscI) ).
thf(452,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(661,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(84,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: list @ TA] :
( ( linorder_sorted @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( linorder_sorted @ TA @ ( cons @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_sorted__many__eq) ).
thf(546,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: list @ TA] :
( ( linorder_sorted @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( linorder_sorted @ TA @ ( cons @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(194,axiom,
( ( distinct @ a @ ( cons @ a @ x1 @ l1a ) )
& ( linorder_sorted @ a @ ( cons @ a @ x1 @ l1a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_x1__l1__props) ).
thf(925,plain,
( ( distinct @ a @ ( cons @ a @ x1 @ l1a ) )
& ( linorder_sorted @ a @ ( cons @ a @ x1 @ l1a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(258,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_less__linear) ).
thf(1153,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
=> ( ( A = B )
| ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_set__ConsD) ).
thf(366,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
=> ( ( A = B )
| ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(199,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_pinf_I5_J) ).
thf(942,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(54,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_product__lists_Osimps_I1_J) ).
thf(439,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(226,axiom,
linorder @ a @ ( type2 @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
thf(1057,plain,
linorder @ a @ ( type2 @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(262,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( sorted1061247458sorted @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: list @ TA] : ( B != C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
=> ! [E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ E @ F ) )
=> ~ ( ~ ( ord_less @ TA @ C @ E )
& ( ~ ( ord_less @ TA @ C @ E )
=> ( ( ( C = E )
=> ( sorted1061247458sorted @ TA @ D @ F ) )
& ( ( C != E )
=> ( sorted1061247458sorted @ TA @ ( cons @ TA @ C @ D ) @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_subset__sorted_Oelims_I2_J) ).
thf(1163,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( sorted1061247458sorted @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: list @ TA] : ( B != C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
=> ! [E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ E @ F ) )
=> ~ ( ~ ( ord_less @ TA @ C @ E )
& ( ~ ( ord_less @ TA @ C @ E )
=> ( ( ( C = E )
=> ( sorted1061247458sorted @ TA @ D @ F ) )
& ( ( C != E )
=> ( sorted1061247458sorted @ TA @ ( cons @ TA @ C @ D ) @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(204,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ~ ( sorted1061247458sorted @ TA @ A @ B )
=> ( ( ? [C: TA,D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ( B
!= ( nil @ TA ) ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
=> ! [E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ E @ F ) )
=> ( ~ ( ord_less @ TA @ C @ E )
& ( ~ ( ord_less @ TA @ C @ E )
=> ( ( ( C = E )
=> ( sorted1061247458sorted @ TA @ D @ F ) )
& ( ( C != E )
=> ( sorted1061247458sorted @ TA @ ( cons @ TA @ C @ D ) @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_subset__sorted_Oelims_I3_J) ).
thf(957,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ~ ( sorted1061247458sorted @ TA @ A @ B )
=> ( ( ? [C: TA,D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ( B
!= ( nil @ TA ) ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
=> ! [E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ E @ F ) )
=> ( ~ ( ord_less @ TA @ C @ E )
& ( ~ ( ord_less @ TA @ C @ E )
=> ( ( ( C = E )
=> ( sorted1061247458sorted @ TA @ D @ F ) )
& ( ( C != E )
=> ( sorted1061247458sorted @ TA @ ( cons @ TA @ C @ D ) @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(202,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_le__less__linear) ).
thf(952,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(28,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_list_Oexhaust) ).
thf(349,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(99,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_in__set__insert) ).
thf(598,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_order__less__subst2) ).
thf(820,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(49,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: list @ TA] : ( if @ ( list @ TA ) @ ( member @ TA @ A @ ( set2 @ TA @ B ) ) @ B @ ( cons @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_List_Oinsert__def) ).
thf(424,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: list @ TA] : ( if @ ( list @ TA ) @ ( member @ TA @ A @ ( set2 @ TA @ B ) ) @ B @ ( cons @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(173,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ( ordering_top @ TA @ ( ord_less_eq @ TA ) @ ( ord_less @ TA ) @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_top_Oordering__top__axioms) ).
thf(815,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ( ordering_top @ TA @ ( ord_less_eq @ TA ) @ ( ord_less @ TA ) @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(142,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_not__Cons__self2) ).
thf(729,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(149,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_not__le) ).
thf(746,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(236,axiom,
! [TA: $tType] :
( ( no_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_lt__ex) ).
thf(1091,plain,
! [TA: $tType] :
( ( no_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(32,axiom,
! [TA: $tType,A: set @ TA,B: list @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( coset @ TA @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
=> ~ ( member @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_subset__code_I2_J) ).
thf(361,plain,
! [TA: $tType,A: set @ TA,B: list @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( coset @ TA @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
=> ~ ( member @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(107,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_4) ).
thf(625,plain,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(76,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ( ( D != C )
= ( B @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_ordering__top_Onot__eq__extremum) ).
thf(522,plain,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ( ( D != C )
= ( B @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(248,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order_Ostrict__implies__order) ).
thf(1128,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(60,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_eq__refl) ).
thf(456,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(205,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_dense__le__bounded) ).
thf(974,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(241,axiom,
! [TA: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__induct) ).
thf(1106,plain,
! [TA: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(147,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_dual__order_Oirrefl) ).
thf(742,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(104,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_neq__Nil__conv) ).
thf(615,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(247,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_ord__eq__less__subst) ).
thf(1121,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(229,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_less__not__sym) ).
thf(1064,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(243,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_subset__psubset__trans) ).
thf(1111,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(207,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_le__imp__less__or__eq) ).
thf(980,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(238,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_pinf_I4_J) ).
thf(1096,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(216,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_pinf_I7_J) ).
thf(1006,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(98,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ! [C: list @ TA] :
( B
!= ( cons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_list_Oset__cases) ).
thf(593,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ! [C: list @ TA] :
( B
!= ( cons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(102,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_order__class_Oorder_Oantisym) ).
thf(610,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(187,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_pinf_I2_J) ).
thf(857,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(116,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( ( linorder_sorted @ TA )
= ( ^ [A: list @ TA] :
( ( A
= ( nil @ TA ) )
| ? [B: list @ TA,C: TA] :
( ( A
= ( cons @ TA @ C @ B ) )
& ! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ B ) )
=> ( ord_less_eq @ TA @ C @ D ) )
& ( linorder_sorted @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_sorted_Osimps) ).
thf(650,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( ( linorder_sorted @ TA )
= ( ^ [A: list @ TA] :
( ( A
= ( nil @ TA ) )
| ? [B: list @ TA,C: TA] :
( ( A
= ( cons @ TA @ C @ B ) )
& ! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ B ) )
=> ( ord_less_eq @ TA @ C @ D ) )
& ( linorder_sorted @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(201,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_minf_I4_J) ).
thf(948,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(68,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_187_equalityD2) ).
thf(488,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)],[68]) ).
thf(197,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ( ord_less @ TA @ D @ F )
=> ( A @ E @ ( cons @ TA @ F @ G ) ) )
=> ( ( ~ ( ord_less @ TA @ D @ F )
=> ( ( D = F )
=> ( A @ E @ G ) ) )
=> ( ( ~ ( ord_less @ TA @ D @ F )
=> ( ( D != F )
=> ( A @ ( cons @ TA @ D @ E ) @ G ) ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_inter__sorted_Oinduct) ).
thf(933,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ( ord_less @ TA @ D @ F )
=> ( A @ E @ ( cons @ TA @ F @ G ) ) )
=> ( ( ~ ( ord_less @ TA @ D @ F )
=> ( ( D = F )
=> ( A @ E @ G ) ) )
=> ( ( ~ ( ord_less @ TA @ D @ F )
=> ( ( D != F )
=> ( A @ ( cons @ TA @ D @ E ) @ G ) ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(123,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ E @ ( cons @ TA @ D @ F ) )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_revg_Oinduct) ).
thf(669,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ E @ ( cons @ TA @ D @ F ) )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(273,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_leD) ).
thf(1207,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(133,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct @ TA @ ( union @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_distinct__union) ).
thf(706,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct @ TA @ ( union @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ 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_88_order__subst1) ).
thf(622,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ 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)],[106]) ).
thf(43,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: ( list @ TA ) > $o] :
( ( linorder_sorted @ TA @ A )
=> ( ( B @ ( nil @ TA ) )
=> ( ! [C: list @ TA,D: TA] :
( ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ( ord_less_eq @ TA @ D @ E ) )
=> ( ( linorder_sorted @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( cons @ TA @ D @ C ) ) ) ) )
=> ( B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_sorted_Oinducts) ).
thf(393,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: ( list @ TA ) > $o] :
( ( linorder_sorted @ TA @ A )
=> ( ( B @ ( nil @ TA ) )
=> ( ! [C: list @ TA,D: TA] :
( ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ( ord_less_eq @ TA @ D @ E ) )
=> ( ( linorder_sorted @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( cons @ TA @ D @ C ) ) ) ) )
=> ( B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(213,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_less__imp__triv) ).
thf(997,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ( ( order_strict_mono @ TA @ TB )
= ( ^ [A: TA > TB] :
! [B: TA,C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_strict__mono__def) ).
thf(985,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ( ( order_strict_mono @ TA @ TB )
= ( ^ [A: TA > TB] :
! [B: TA,C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_rev__subsetD) ).
thf(701,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(257,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) )
=> ( order_strict_mono @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_strict__monoI) ).
thf(1150,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) )
=> ( order_strict_mono @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(191,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_ord__eq__less__trans) ).
thf(911,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(139,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_splice_Oinduct) ).
thf(721,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(215,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_minf_I3_J) ).
thf(1002,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(31,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_10) ).
thf(360,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(83,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] :
( ( distinct @ TA @ ( mergesort_remdups @ TA @ A ) )
& ( linorder_sorted @ TA @ ( mergesort_remdups @ TA @ A ) )
& ( ( set2 @ TA @ ( mergesort_remdups @ TA @ A ) )
= ( set2 @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_mergesort__remdups__correct) ).
thf(541,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] :
( ( distinct @ TA @ ( mergesort_remdups @ TA @ A ) )
& ( linorder_sorted @ TA @ ( mergesort_remdups @ TA @ A ) )
& ( ( set2 @ TA @ ( mergesort_remdups @ TA @ A ) )
= ( set2 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(125,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_remdups__adj_Oinduct) ).
thf(674,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(79,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_194_set__mp) ).
thf(530,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)],[79]) ).
thf(165,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_less__le) ).
thf(794,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(138,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ( ( A @ C @ D )
=> ( D = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_ordering__top_Oextremum__uniqueI) ).
thf(718,plain,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ( ( A @ C @ D )
=> ( D = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(271,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_order_Onot__eq__order__implies__strict) ).
thf(1202,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(164,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_order_Oasym) ).
thf(792,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(251,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_not__le__imp__less) ).
thf(1135,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(105,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ 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_101_ord__le__eq__trans) ).
thf(618,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ 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)],[105]) ).
thf(240,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_dual__order_Oorder__iff__strict) ).
thf(1103,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( insert @ TA @ A @ B )
= ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_not__in__set__insert) ).
thf(444,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( insert @ TA @ A @ B )
= ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ 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_91_ord__le__eq__subst) ).
thf(601,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ 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)],[100]) ).
thf(256,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_dual__order_Ostrict__implies__not__eq) ).
thf(1146,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_map__tailrec__rev_Oinduct) ).
thf(430,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(126,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: list @ TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( linorder_sorted @ TA @ ( cons @ TA @ B @ C ) )
=> ( linorder_sorted @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_sorted__many) ).
thf(689,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: list @ TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( linorder_sorted @ TA @ ( cons @ TA @ B @ C ) )
=> ( linorder_sorted @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ 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_87_le__fun__def) ).
thf(296,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ 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)],[11]) ).
thf(128,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ~ ( B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_ordering__top_Oextremum__strict) ).
thf(694,plain,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ~ ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(143,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] : ( sorted1061247458sorted @ TA @ ( nil @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_subset__sorted_Osimps_I1_J) ).
thf(732,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] : ( sorted1061247458sorted @ TA @ ( nil @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_order__le__less__subst1) ).
thf(843,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(159,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_pinf_I1_J) ).
thf(772,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_strict__mono__eq) ).
thf(579,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(45,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_transpose_Ocases) ).
thf(413,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(189,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA,C: $o] :
( ( ( sorted1061247458sorted @ TA @ A @ B )
= C )
=> ( ( ( A
= ( nil @ TA ) )
=> ~ C )
=> ( ( ? [D: TA,E: list @ TA] :
( A
= ( cons @ TA @ D @ E ) )
=> ( ( B
= ( nil @ TA ) )
=> C ) )
=> ~ ! [D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ D @ E ) )
=> ! [F: TA,G: list @ TA] :
( ( B
= ( cons @ TA @ F @ G ) )
=> ( C
= ( ~ ( ~ ( ord_less @ TA @ D @ F )
& ( ~ ( ord_less @ TA @ D @ F )
=> ( ( ( D = F )
=> ( sorted1061247458sorted @ TA @ E @ G ) )
& ( ( D != F )
=> ( sorted1061247458sorted @ TA @ ( cons @ TA @ D @ E ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_subset__sorted_Oelims_I1_J) ).
thf(875,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA,C: $o] :
( ( ( sorted1061247458sorted @ TA @ A @ B )
= C )
=> ( ( ( A
= ( nil @ TA ) )
=> ~ C )
=> ( ( ? [D: TA,E: list @ TA] :
( A
= ( cons @ TA @ D @ E ) )
=> ( ( B
= ( nil @ TA ) )
=> C ) )
=> ~ ! [D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ D @ E ) )
=> ! [F: TA,G: list @ TA] :
( ( B
= ( cons @ TA @ F @ G ) )
=> ( C
= ( ~ ( ~ ( ord_less @ TA @ D @ F )
& ( ~ ( ord_less @ TA @ D @ F )
=> ( ( ( D = F )
=> ( sorted1061247458sorted @ TA @ E @ G ) )
& ( ( D != F )
=> ( sorted1061247458sorted @ TA @ ( cons @ TA @ D @ E ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(177,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ A @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_antisym__conv2) ).
thf(826,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ A @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(135,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( linorder_sorted @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_sorted__single) ).
thf(711,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( linorder_sorted @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(113,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_188_equalityD1) ).
thf(641,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)],[113]) ).
thf(42,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ TA @ ( type2 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Opreorder) ).
thf(391,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ TA @ ( type2 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(40,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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_96_le__cases) ).
thf(382,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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)],[40]) ).
thf(162,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_less__imp__le) ).
thf(787,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(227,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_dense__ge) ).
thf(1058,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(169,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_less__imp__not__eq2) ).
thf(804,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(82,axiom,
order_top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_6) ).
thf(540,plain,
order_top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(124,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_193_in__mono) ).
thf(672,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)],[124]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ 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_85_le__funE) ).
thf(713,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ 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)],[136]) ).
thf(71,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( ord @ TA @ ( type2 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oord) ).
thf(498,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( ord @ TA @ ( type2 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(269,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ~ ( ord_less @ TA @ D @ F )
=> ( ( D = F )
=> ( A @ E @ G ) ) )
=> ( ( ~ ( ord_less @ TA @ D @ F )
=> ( ( D != F )
=> ( A @ ( cons @ TA @ D @ E ) @ G ) ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_subset__sorted_Oinduct) ).
thf(1194,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ~ ( ord_less @ TA @ D @ F )
=> ( ( D = F )
=> ( A @ E @ G ) ) )
=> ( ( ~ ( ord_less @ TA @ D @ F )
=> ( ( D != F )
=> ( A @ ( cons @ TA @ D @ E ) @ G ) ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(274,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_pinf_I8_J) ).
thf(1209,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(223,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_pinf_I3_J) ).
thf(1048,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(38,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_3) ).
thf(377,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(255,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_le__less__trans) ).
thf(1144,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(221,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_le__less) ).
thf(1043,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_list_Oinject) ).
thf(303,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(161,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_antisym__conv1) ).
thf(784,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(246,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_ord__less__eq__trans) ).
thf(1117,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(145,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_189_subset__eq) ).
thf(737,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)],[145]) ).
thf(19,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA] :
~ ( sorted1061247458sorted @ TA @ ( cons @ TA @ A @ B ) @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_subset__sorted_Osimps_I2_J) ).
thf(318,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA] :
~ ( sorted1061247458sorted @ TA @ ( cons @ TA @ A @ B ) @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(64,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ 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_97_order_Otrans) ).
thf(477,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ 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)],[64]) ).
thf(171,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_less__le__trans) ).
thf(811,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(153,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_less__asym_H) ).
thf(758,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ 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_90_ord__eq__le__subst) ).
thf(552,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ 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)],[86]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: list @ TA] :
( ( A @ E @ F )
=> ( A @ ( cons @ TB @ D @ E ) @ F ) )
=> ( ! [D: TA,E: list @ TB,F: list @ TA] :
( ( A @ E @ F )
=> ( A @ E @ ( cons @ TA @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_list__2pre__induct) ).
thf(535,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: list @ TA] :
( ( A @ E @ F )
=> ( A @ ( cons @ TB @ D @ E ) @ F ) )
=> ( ! [D: TA,E: list @ TB,F: list @ TA] :
( ( A @ E @ F )
=> ( A @ E @ ( cons @ TA @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(21,axiom,
! [TA: $tType] : ( order_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_1) ).
thf(323,plain,
! [TA: $tType] : ( order_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(520,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(192,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_linorder__cases) ).
thf(915,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(263,axiom,
( ( distinct @ a @ l2 )
& ( linorder_sorted @ a @ l2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_l2__OK) ).
thf(1177,plain,
( ( distinct @ a @ l2 )
& ( linorder_sorted @ a @ l2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(228,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_not__less__iff__gr__or__eq) ).
thf(1061,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(208,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_less__irrefl) ).
thf(983,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(157,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( sorted1061247458sorted @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( ~ ( ord_less @ TA @ A @ C )
& ( ~ ( ord_less @ TA @ A @ C )
=> ( ( ( A = C )
=> ( sorted1061247458sorted @ TA @ B @ D ) )
& ( ( A != C )
=> ( sorted1061247458sorted @ TA @ ( cons @ TA @ A @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_subset__sorted_Osimps_I3_J) ).
thf(768,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( sorted1061247458sorted @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( ~ ( ord_less @ TA @ A @ C )
& ( ~ ( ord_less @ TA @ A @ C )
=> ( ( ( A = C )
=> ( sorted1061247458sorted @ TA @ B @ D ) )
& ( ( A != C )
=> ( sorted1061247458sorted @ TA @ ( cons @ TA @ A @ B ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(110,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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_94_linear) ).
thf(636,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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)],[110]) ).
thf(230,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_dual__order_Ostrict__trans1) ).
thf(1066,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(101,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( linorder_sorted @ TA @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_sorted_ONil) ).
thf(608,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( linorder_sorted @ TA @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(15,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ( C = D )
=> ( ord_less_eq @ TA @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_ord__eq__le__eq__trans) ).
thf(306,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ( C = D )
=> ( ord_less_eq @ TA @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(244,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_dual__order_Oasym) ).
thf(1113,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(12,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( type @ TA @ ( type2 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___HOL_Otype) ).
thf(299,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( type @ TA @ ( type2 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(117,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_182_Collect__mono) ).
thf(653,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)],[117]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ 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_86_le__funI) ).
thf(589,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ 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)],[96]) ).
thf(200,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_order_Ostrict__implies__not__eq) ).
thf(944,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(121,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ 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_100_ord__eq__le__trans) ).
thf(663,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ 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)],[121]) ).
thf(37,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ 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_92_eq__iff) ).
thf(374,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ 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)],[37]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_contra__subsetD) ).
thf(648,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(176,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_order_Ostrict__iff__order) ).
thf(823,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(233,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_order_Oorder__iff__strict) ).
thf(1081,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(150,axiom,
! [A: list @ a] :
( ( ( distinct @ a @ A )
& ( linorder_sorted @ a @ A ) )
=> ( ( sorted1061247458sorted @ a @ l1a @ A )
= ( ord_less_eq @ ( set @ a ) @ ( set2 @ a @ l1a ) @ ( set2 @ a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ind__hyp__l1) ).
thf(749,plain,
! [A: list @ a] :
( ( ( distinct @ a @ A )
& ( linorder_sorted @ a @ A ) )
=> ( ( sorted1061247458sorted @ a @ l1a @ A )
= ( ord_less_eq @ ( set @ a ) @ ( set2 @ a @ l1a ) @ ( set2 @ a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(77,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_167_subsetI) ).
thf(525,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)],[77]) ).
thf(186,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_order_Ostrict__trans) ).
thf(855,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(112,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_8) ).
thf(640,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(259,axiom,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_ex__gt__or__lt) ).
thf(1156,plain,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_order__less__le__subst2) ).
thf(954,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(16,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_192_subsetD) ).
thf(310,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)],[16]) ).
thf(183,axiom,
( ( distinct @ a @ ( cons @ a @ x2 @ l2b ) )
& ( linorder_sorted @ a @ ( cons @ a @ x2 @ l2b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_x2__l2__props) ).
thf(840,plain,
( ( distinct @ a @ ( cons @ a @ x2 @ l2b ) )
& ( linorder_sorted @ a @ ( cons @ a @ x2 @ l2b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
( ! [E: list @ TB] : ( A @ E @ ( nil @ TA ) )
=> ( ! [E: list @ TA] : ( A @ ( nil @ TB ) @ E )
=> ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
( ( B @ E @ G )
=> ( ( A @ F @ ( cons @ TA @ G @ H ) )
=> ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
=> ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
( ~ ( B @ E @ G )
=> ( ( A @ ( cons @ TB @ E @ F ) @ H )
=> ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
=> ( A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_mergesort__by__rel__merge__induct) ).
thf(338,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
( ! [E: list @ TB] : ( A @ E @ ( nil @ TA ) )
=> ( ! [E: list @ TA] : ( A @ ( nil @ TB ) @ E )
=> ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
( ( B @ E @ G )
=> ( ( A @ F @ ( cons @ TA @ G @ H ) )
=> ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
=> ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
( ~ ( B @ E @ G )
=> ( ( A @ ( cons @ TB @ E @ F ) @ H )
=> ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
=> ( A @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(91,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_antisym__conv) ).
thf(576,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(170,axiom,
( ( distinct @ a @ l1 )
& ( linorder_sorted @ a @ l1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_l1__OK) ).
thf(808,plain,
( ( distinct @ a @ l1 )
& ( linorder_sorted @ a @ l1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(249,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_order__le__less__subst2) ).
thf(1130,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(267,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_order__less__subst1) ).
thf(1188,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(266,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_minf_I5_J) ).
thf(1186,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(219,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_pinf_I6_J) ).
thf(1038,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(94,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_181_subset__trans) ).
thf(585,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)],[94]) ).
thf(148,axiom,
! [A: a] :
( ( member @ a @ A @ ( set2 @ a @ l1a ) )
=> ( ord_less_eq @ a @ x1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_x1__le) ).
thf(744,plain,
! [A: a] :
( ( member @ a @ A @ ( set2 @ a @ l1a ) )
=> ( ord_less_eq @ a @ x1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(25,axiom,
! [TA: $tType,A: list @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ ( cons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_set__subset__Cons) ).
thf(336,plain,
! [TA: $tType,A: list @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ ( cons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(132,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_subset__Collect__conv) ).
thf(703,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(118,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: TA] :
( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( linorder_sorted @ TA @ A )
=> ( linorder_sorted @ TA @ ( cons @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_sorted_OCons) ).
thf(656,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: TA] :
( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( linorder_sorted @ TA @ A )
=> ( linorder_sorted @ TA @ ( cons @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(103,axiom,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_distinct__singleton) ).
thf(613,plain,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(224,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_le__neq__trans) ).
thf(1052,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ( order_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top) ).
thf(727,plain,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ( order_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(217,axiom,
! [TA: $tType] :
( ( condit1037483654norder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_complete__interval) ).
thf(1008,plain,
! [TA: $tType] :
( ( condit1037483654norder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(18,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA,D: list @ TA] :
( ! [E: TA > TA > $o,F: TA,G: list @ TA,H: TA,I: list @ TA] :
( ( ( E @ F @ H )
=> ( A @ E @ G @ ( cons @ TA @ H @ I ) ) )
=> ( ( ~ ( E @ F @ H )
=> ( A @ E @ ( cons @ TA @ F @ G ) @ I ) )
=> ( A @ E @ ( cons @ TA @ F @ G ) @ ( cons @ TA @ H @ I ) ) ) )
=> ( ! [E: TA > TA > $o,F: list @ TA] : ( A @ E @ F @ ( nil @ TA ) )
=> ( ! [E: TA > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TA ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_mergesort__by__rel__merge_Oinduct) ).
thf(314,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA,D: list @ TA] :
( ! [E: TA > TA > $o,F: TA,G: list @ TA,H: TA,I: list @ TA] :
( ( ( E @ F @ H )
=> ( A @ E @ G @ ( cons @ TA @ H @ I ) ) )
=> ( ( ~ ( E @ F @ H )
=> ( A @ E @ ( cons @ TA @ F @ G ) @ I ) )
=> ( A @ E @ ( cons @ TA @ F @ G ) @ ( cons @ TA @ H @ I ) ) ) )
=> ( ! [E: TA > TA > $o,F: list @ TA] : ( A @ E @ F @ ( nil @ TA ) )
=> ( ! [E: TA > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TA ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(89,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(571,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(211,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_less__imp__neq) ).
thf(991,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(206,axiom,
~ ( member @ a @ x1 @ ( set2 @ a @ l1a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_x1__nin__l1) ).
thf(978,plain,
~ ( member @ a @ x1 @ ( set2 @ a @ l1a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(253,axiom,
( ( sorted1061247458sorted @ a @ ( cons @ a @ x1 @ l1a ) @ l2b )
= ( ord_less_eq @ ( set @ a ) @ ( set2 @ a @ ( cons @ a @ x1 @ l1a ) ) @ ( set2 @ a @ l2b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_ind__hyp__l2) ).
thf(1140,plain,
( ( sorted1061247458sorted @ a @ ( cons @ a @ x1 @ l1a ) @ l2b )
= ( ord_less_eq @ ( set @ a ) @ ( set2 @ a @ ( cons @ a @ x1 @ l1a ) ) @ ( set2 @ a @ l2b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(62,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( linorder_sorted @ TA @ A )
=> ( ( distinct @ TA @ A )
=> ( ( linorder_sorted @ TA @ B )
=> ( ( distinct @ TA @ B )
=> ( ( ( set2 @ TA @ A )
= ( set2 @ TA @ B ) )
=> ( A = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_sorted__distinct__set__unique) ).
thf(465,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( linorder_sorted @ TA @ A )
=> ( ( distinct @ TA @ A )
=> ( ( linorder_sorted @ TA @ B )
=> ( ( distinct @ TA @ B )
=> ( ( ( set2 @ TA @ A )
= ( set2 @ TA @ B ) )
=> ( A = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(627,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(234,axiom,
x1 != x2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_x1__neq__x2) ).
thf(1084,plain,
x1 != x2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_linorder__neqE__linordered__idom) ).
thf(1180,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(66,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: TA] :
( ( linorder_sorted @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( linorder_sorted @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_sorted__append__bigger) ).
thf(482,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: TA] :
( ( linorder_sorted @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( linorder_sorted @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(70,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( coset @ TA @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_UNIV__coset) ).
thf(495,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( coset @ TA @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ C @ B )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_minf_I11_J) ).
thf(771,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(130,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_dual__order_Orefl) ).
thf(699,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(172,axiom,
~ ( member @ a @ x2 @ ( set2 @ a @ l2b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_x2__nin__l2) ).
thf(813,plain,
~ ( member @ a @ x2 @ ( set2 @ a @ l2b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(74,axiom,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_top_Oextremum__uniqueI) ).
thf(517,plain,
! [TA: $tType] :
( ( order_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_distinct_Osimps_I2_J) ).
thf(418,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(160,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_dual__order_Ostrict__iff__order) ).
thf(781,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(212,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_psubset__imp__subset) ).
thf(995,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_strict__mono__less__eq) ).
thf(568,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(52,axiom,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_sublists_Osimps_I1_J) ).
thf(433,plain,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(122,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_5) ).
thf(667,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(232,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_dense__ge__bounded) ).
thf(1077,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_strict__mono__less) ).
thf(763,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ B @ C )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pinf_I11_J) ).
thf(832,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( TC > TA > TB ) > ( list @ TC ) > ( list @ TA ) > $o,B: TC > TA > TB,C: list @ TC,D: list @ TA] :
( ! [E: TC > TA > TB] : ( A @ E @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TC > TA > TB,F: TC,G: list @ TC,H: TA,I: list @ TA] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons @ TC @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
=> ( ! [E: TC > TA > TB,F: TC,G: list @ TC] : ( A @ E @ ( cons @ TC @ F @ G ) @ ( nil @ TA ) )
=> ( ! [E: TC > TA > TB,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TC ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_zipf_Oinduct) ).
thf(549,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( TC > TA > TB ) > ( list @ TC ) > ( list @ TA ) > $o,B: TC > TA > TB,C: list @ TC,D: list @ TA] :
( ! [E: TC > TA > TB] : ( A @ E @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TC > TA > TB,F: TC,G: list @ TC,H: TA,I: list @ TA] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons @ TC @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
=> ( ! [E: TC > TA > TB,F: TC,G: list @ TC] : ( A @ E @ ( cons @ TC @ F @ G ) @ ( nil @ TA ) )
=> ( ! [E: TC > TA > TB,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TC ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(261,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_leI) ).
thf(1161,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(167,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_less__imp__not__less) ).
thf(800,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_list_Oset__intros_I2_J) ).
thf(287,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(250,axiom,
~ ( ord_less @ a @ x1 @ x2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_x2__le__x1) ).
thf(1133,plain,
~ ( ord_less @ a @ x1 @ x2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(214,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_not__less) ).
thf(999,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(151,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( 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_171_psubsetE) ).
thf(752,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( 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)],[151]) ).
thf(57,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_2) ).
thf(447,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(181,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_subset__iff__psubset__eq) ).
thf(835,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(180,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_dual__order_Ostrict__trans) ).
thf(833,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(44,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_remdups__adj_Ocases) ).
thf(410,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(80,axiom,
! [TA: $tType,A: list @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_subset__code_I1_J) ).
thf(532,plain,
! [TA: $tType,A: list @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(129,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ( ( A @ C @ D )
= ( D = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_ordering__top_Oextremum__unique) ).
thf(696,plain,
! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
( ( ordering_top @ TA @ A @ B @ C )
=> ( ( A @ C @ D )
= ( D = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(5,axiom,
top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_9) ).
thf(283,plain,
top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(195,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_less__trans) ).
thf(928,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_list_Oset__intros_I1_J) ).
thf(294,plain,
! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(193,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_ord__less__eq__subst) ).
thf(918,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(237,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ 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_less__le__not__le) ).
thf(1093,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ 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)],[237]) ).
thf(146,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_minf_I8_J) ).
thf(740,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(23,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(332,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_top__apply) ).
thf(427,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(78,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_191_subsetCE) ).
thf(528,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)],[78]) ).
thf(55,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ 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_103_order__trans) ).
thf(442,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ 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)],[55]) ).
thf(35,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_dual__order_Oantisym) ).
thf(369,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,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(277,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)],[3]) ).
thf(127,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_185_subset__iff) ).
thf(691,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)],[127]) ).
thf(198,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__asym) ).
thf(940,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(119,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( order @ TA @ ( type2 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oorder) ).
thf(659,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( order @ TA @ ( type2 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(152,axiom,
( ( distinct @ a @ l2b )
& ( linorder_sorted @ a @ l2b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_l2__props) ).
thf(755,plain,
( ( distinct @ a @ l2b )
& ( linorder_sorted @ a @ l2b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(364,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1213,plain,
$false,
inference(cvc4,[status(thm)],[645,1036,629,760,479,846,468,352,909,333,1200,1211,276,1068,1158,582,1205,449,1142,379,384,1137,500,797,715,930,829,709,1046,301,320,436,372,802,460,1055,724,587,838,357,1191,817,559,638,1087,421,284,416,289,1100,1115,325,492,789,591,485,514,1183,1040,1109,348,574,766,280,734,866,988,312,292,452,661,546,925,1153,366,942,439,1057,1163,957,952,349,598,820,424,815,729,746,1091,361,625,522,1128,456,974,1106,742,615,1121,1064,1111,980,1096,1006,593,610,857,650,948,488,933,669,1207,706,622,393,997,985,701,1150,911,721,1002,360,541,674,530,794,718,1202,792,1135,618,1103,444,601,1146,430,689,296,694,732,843,772,579,413,875,826,711,641,391,382,787,1058,804,540,672,713,498,1194,1209,1048,377,1144,1043,303,784,1117,737,318,477,811,758,552,535,323,520,915,1177,1061,983,768,636,1066,608,306,1113,299,653,589,944,663,374,648,823,1081,749,525,855,640,1156,954,310,840,338,576,808,1130,1188,1186,1038,585,744,336,703,656,613,1052,727,1008,314,571,991,978,1140,465,627,1084,1180,482,495,771,699,813,517,418,781,995,568,433,667,1077,763,832,549,1161,800,287,1133,999,752,447,835,833,410,532,696,283,928,294,918,1093,740,332,427,528,442,369,277,691,940,659,755,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : DAT206^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.17 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n004.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 11:29:09 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.86/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.09 % [INFO] Parsing done (310ms).
% 1.82/1.10 % [INFO] Running in sequential loop mode.
% 2.51/1.33 % [INFO] eprover registered as external prover.
% 2.51/1.33 % [INFO] cvc4 registered as external prover.
% 2.51/1.34 % [INFO] Scanning for conjecture ...
% 2.89/1.44 % [INFO] Found a conjecture and 279 axioms. Running axiom selection ...
% 3.18/1.54 % [INFO] Axiom selection finished. Selected 273 axioms (removed 6 axioms).
% 3.89/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 4.18/1.77 % [INFO] Type checking passed.
% 4.18/1.78 % [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 ...
% 82.94/62.74 % External prover 'cvc4' found a proof!
% 82.94/62.74 % [INFO] Killing All external provers ...
% 82.94/62.74 % Time passed: 62269ms (effective reasoning time: 61638ms)
% 82.94/62.74 % 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)>
% 82.94/62.74 % Axioms used in derivation (273): fact_233_the__elem__set, fact_232_sorted_Ocases, fact_17_linorder__neqE__linordered__idom, fact_56_linorder__cases, fact_37_less__imp__neq, fact_27_ord__eq__less__subst, fact_164_subset__code_I1_J, fact_142_order_Onot__eq__order__implies__strict, fact_238_list__tail__coinc, fact_173_psubset__imp__subset, fact_219_splice_Oinduct, fact_179_contra__subsetD, fact_159_not__Cons__self2, fact_20_linordered__field__no__lb, fact_53_antisym__conv3, fact_91_ord__le__eq__subst, tcon_HOL_Obool___Orderings_Opreorder_7, fact_196_top_Oordering__top__axioms, fact_6_minf_I3_J, tfree_0, fact_106_dual__order_Otrans, fact_249_subset__code_I3_J, fact_39_less__asym_H, fact_16_ex__gt__or__lt, fact_96_le__cases, fact_157_list_Oinject, fact_251_UNIV__coset, fact_4_minf_I5_J, fact_167_subsetI, fact_186_set__rev__mp, fact_111_less__le, fact_36_dense, fact_97_order_Otrans, fact_199_distinct__insert, fact_66_top_Oextremum__strict, fact_83_subset__sorted_Osimps_I3_J, fact_195_distinct__union, fact_137_dense__le__bounded, fact_239_subset__Collect__conv, fact_250_combinatorial__product_Osimps_I1_J, fact_140_dual__order_Ostrict__iff__order, fact_171_psubsetE, fact_92_eq__iff, fact_108_leD, fact_169_psubsetI, fact_150_top_Oextremum__uniqueI, fact_101_ord__le__eq__trans, fact_24_dual__order_Ostrict__trans, fact_119_less__imp__le, fact_49_dual__order_Oasym, fact_135_dual__order_Ostrict__trans2, fact_231_subset__sorted_Oelims_I1_J, fact_147_pinf_I6_J, fact_13_pinf_I3_J, fact_3_minf_I7_J, tcon_fun___Orderings_Oord, fact_241_mergesort__by__rel__merge_Oinduct, tcon_Set_Oset___Orderings_Oorder_3, fact_9_pinf_I11_J, fact_12_pinf_I4_J, fact_176_subset__psubset__trans, fact_122_le__less__trans, fact_88_order__subst1, fact_74_x1__l1__props, fact_69_top_Onot__eq__extremum, tcon_HOL_Obool___Orderings_Olinorder, fact_1_x2__le__x1, tcon_Set_Oset___Orderings_Oord_5, fact_126_le__less__linear, fact_215_list__nonempty__induct, fact_100_ord__eq__le__trans, fact_155_distinct_Osimps_I2_J, fact_212_distinct__singleton, fact_15_pinf_I2_J, fact_10_pinf_I7_J, fact_5_minf_I4_J, fact_129_not__le__imp__less, fact_213_sorted_ONil, fact_133_order_Ostrict__iff__order, fact_235_sublists_Osimps_I1_J, fact_229_subset__sorted_Oelims_I3_J, fact_14_pinf_I1_J, fact_191_subsetCE, fact_40_less__trans, fact_151_sorted__many__eq, fact_63_x1__nin__l1, fact_41_less__linear, fact_218_transpose_Ocases, fact_52_less__induct, fact_141_dual__order_Ostrict__implies__order, fact_228_subset__sorted_Osimps_I2_J, fact_73_x2__l2__props, fact_182_Collect__mono, fact_62_x2__nin__l2, fact_244_list__2pre__induct, fact_8_minf_I1_J, fact_202_ordering__top_Oextremum__unique, fact_43_ord__eq__less__trans, fact_208_sorted__single, fact_162_list_Oset__intros_I1_J, fact_79_order__refl, fact_46_Collect__mem__eq, fact_183_subset__refl, fact_33_neqE, fact_156_sorted__many, fact_145_minf_I6_J, fact_224_list_OdiscI, fact_154_sorted__distinct__set__unique, fact_78_l1__OK, fact_204_ordering__top_Oextremum, fact_55_less__imp__triv, fact_90_ord__eq__le__subst, fact_134_dual__order_Ostrict__trans1, fact_54_less__imp__not__eq2, fact_75_Cons_Ohyps, fact_149_top_Oextremum__unique, fact_22_dependent__wellorder__choice, fact_206_sorted_Oinducts, fact_187_equalityD2, fact_110_le__less, fact_31_lt__ex, fact_205_List_Oinsert__def, fact_89_order__subst2, fact_180_set__eq__subset, fact_32_gt__ex, fact_130_order_Ostrict__trans1, fact_201_ordering__top_Onot__eq__extremum, fact_132_order_Oorder__iff__strict, fact_0_x1__neq__x2, fact_184_rev__subsetD, fact_222_list_Oinducts, fact_28_ord__less__eq__subst, tcon_Set_Oset___Orderings_Oorder__top_1, fact_35_order_Oasym, fact_112_order__le__less__subst1, fact_68_strict__mono__eq, fact_161_set__ConsD, fact_123_less__le__trans, tcon_HOL_Obool___Orderings_Otop_9, fact_23_not__less__iff__gr__or__eq, fact_121_antisym__conv2, tcon_HOL_Obool___Orderings_Oord_10, fact_45_mem__Collect__eq, fact_61_strict__mono__less, fact_246_mergesort__remdups__correct, fact_194_set__mp, fact_138_order_Ostrict__implies__order, fact_50_less__imp__not__eq, fact_34_neq__iff, fact_253_remove__code_I2_J, fact_7_minf_I2_J, fact_158_less__fun__def, fact_198_in__set__insert, fact_128_less__le__not__le, fact_102_order__class_Oorder_Oantisym, fact_19_linordered__field__no__ub, fact_245_zipf_Oinduct, fact_185_subset__iff, fact_26_order_Ostrict__trans, fact_172_psubset__eq, fact_174_psubset__subset__trans, tcon_HOL_Obool___Orderings_Oorder_8, fact_114_order__less__le__subst1, fact_189_subset__eq, fact_226_list_Odistinct_I1_J, fact_76_strict__mono__less__eq, fact_25_less__imp__not__less, fact_77_l2__OK, fact_210_inter__sorted_Oinduct, fact_2_minf_I11_J, fact_214_map__tailrec__rev_Oinduct, fact_220_list__induct2_H, fact_47_Collect__cong, subcl_Orderings_Olinorder___Orderings_Oorder, fact_207_sorted_Osimps, fact_105_linorder__wlog, fact_113_order__le__less__subst2, fact_188_equalityD1, fact_243_list__induct__first2, fact_225_distinct_Osimps_I1_J, fact_152_sorted_OCons, fact_200_ordering__top_Oextremum__uniqueI, tcon_fun___Orderings_Otop, fact_236_revg_Oinduct, subcl_Orderings_Olinorder___Orderings_Oord, fact_190_equalityE, fact_237_ord__eq__le__eq__trans, fact_248_distinct__product__lists, fact_252_subset__code_I2_J, fact_29_order__less__subst1, fact_177_subset__iff__psubset__eq, fact_60_strict__mono__def, tcon_Set_Oset___Orderings_Otop_4, fact_175_subset__not__subset__eq, fact_124_dense__ge, fact_193_in__mono, fact_51_less__not__sym, fact_70_x2__le, fact_71_x1__le, fact_216_remdups__adj_Oinduct, fact_118_le__neq__trans, fact_87_le__fun__def, tcon_fun___Orderings_Oorder__top, fact_98_le__cases3, fact_86_le__funI, tcon_fun___Orderings_Opreorder, fact_163_list_Oset__intros_I2_J, fact_115_order__less__le__subst2, fact_82_ind__hyp__l1, fact_80_l2__props, fact_67_top__apply, fact_211_subset__sorted_Oinduct, fact_234_quicksort_Ocases, fact_81_l1__props, fact_107_dual__order_Oantisym, fact_217_remdups__adj_Ocases, fact_116_not__le, fact_181_subset__trans, fact_58_strict__monoD, fact_72_ind__hyp__l2, fact_30_order__less__subst2, tcon_HOL_Obool___Orderings_Oorder__top_6, fact_197_not__in__set__insert, fact_230_subset__sorted_Oelims_I2_J, fact_84_le__funD, fact_254_sorted__append__bigger, fact_203_ordering__top_Oextremum__strict, tcon_fun___Orderings_Oorder, fact_104_dual__order_Orefl, fact_178_Collect__mono__iff, fact_165_distinct__length__2__or__more, fact_44_ord__less__eq__trans, fact_136_dense__ge__bounded, tcon_Set_Oset___Orderings_Opreorder_2, fact_221_neq__Nil__conv, fact_99_antisym__conv, fact_153_sorted__Cons, fact_11_pinf_I5_J, fact_227_subset__sorted_Osimps_I1_J, fact_120_antisym__conv1, fact_18_dual__order_Ostrict__implies__not__eq, fact_117_not__less, fact_166_set__subset__Cons, fact_93_antisym, fact_139_dual__order_Oorder__iff__strict, subcl_Orderings_Olinorder___Orderings_Opreorder, fact_57_dual__order_Oirrefl, fact_146_pinf_I8_J, subcl_Orderings_Olinorder___HOL_Otype, fact_242_list__all__zip_Oinduct, fact_103_order__trans, fact_59_strict__monoI, fact_247_product__lists_Osimps_I1_J, fact_94_linear, fact_160_list_Oset__cases, fact_170_subset__UNIV, fact_192_subsetD, fact_143_complete__interval, fact_209_insert__Nil, fact_144_minf_I8_J, fact_42_less__irrefl, fact_148_top__greatest, fact_85_le__funE, fact_240_mergesort__by__rel__merge__induct, fact_95_eq__refl, fact_125_dense__le, fact_131_order_Ostrict__trans2, fact_127_le__imp__less__or__eq, fact_21_order_Ostrict__implies__not__eq, fact_38_less__asym, fact_109_leI, fact_223_list_Oexhaust, fact_168_subset__antisym
% 82.94/62.74 % No. of inferences in proof: 550
% 82.94/62.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 62269 ms resp. 61638 ms w/o parsing
% 83.47/62.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 83.47/62.91 % [INFO] Killing All external provers ...
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