%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM176^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:46:18 AM UTC 2026
% Result : Theorem 141.45s 42.15s
% Output : Refutation 132.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 290
% Syntax : Number of formulae : 897 ( 238 unt; 0 typ; 9 def)
% Number of atoms : 3909 ( 797 equ; 6 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 13350 ( 756 ~; 448 |; 100 &;11273 @)
% ( 0 <=>; 773 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 2042 (2042 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 17 con; 0-6 aty)
% Number of variables : 3103 ( 157 ^;2916 !; 21 ?;3103 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(minus_decl,type,
minus:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(uminus_decl,type,
uminus:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_decl,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_bot_decl,type,
order_bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(boolean_algebra_decl,type,
boolean_algebra:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(dense_linorder_decl,type,
dense_linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coinductive_gen_lset_decl,type,
coinductive_gen_lset:
!>[TA: $tType] : ( ( set @ TA ) > ( coinductive_llist @ TA ) > ( set @ TA ) ) ).
thf(coinductive_LCons_decl,type,
coinductive_LCons:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lset_decl,type,
coinductive_lset:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( set @ TA ) ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(koenig916195507_paths_decl,type,
koenig916195507_paths:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(koenig317145564le_via_decl,type,
koenig317145564le_via:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > TA > ( set @ TA ) ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(type2_decl,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_decl,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(is_singleton_decl,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(pairwise_decl,type,
pairwise:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > $o ) ).
thf(remove_decl,type,
remove:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(the_elem_decl,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(graph_decl,type,
graph: a > a > $o ).
thf(n_decl,type,
n: a ).
thf(n2_decl,type,
n2: a ).
thf(ns_decl,type,
ns: set @ a ).
thf(x_decl,type,
x: a ).
thf(xs_decl,type,
xs: coinductive_llist @ a ).
thf(xs2_decl,type,
xs2: coinductive_llist @ a ).
thf(xs3_decl,type,
xs3: coinductive_llist @ a ).
thf(sk1_decl,type,
sk1:
!>[TA: $tType,TB: $tType] : ( TB > TB > ( TB > TA ) > TA > TB ) ).
thf(sk2_decl,type,
sk2:
!>[TA: $tType,TB: $tType] : ( TB > TB > ( TB > TA ) > TA > TB ) ).
thf(sk3_decl,type,
sk3:
!>[TA: $tType,TB: $tType] : ( TB > TB > ( TB > TA ) > TA > TB ) ).
thf(sk4_decl,type,
sk4:
!>[TA: $tType,TB: $tType] : ( TB > TB > ( TB > TA ) > TA > TB ) ).
thf(sk5_decl,type,
sk5:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(sk43_decl,type,
sk43: coinductive_llist @ a ).
thf(sk48_decl,type,
sk48: a ).
thf(sk49_decl,type,
sk49: coinductive_llist @ a ).
thf(sk56_decl,type,
sk56: coinductive_llist @ a ).
thf(sk1_def,definition,
( sk1
= ( ^ [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA,D: TA] :
@+[E: TB] :
~ ! [F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA,D: TA] :
@+[E: TB] :
~ ( ( ord_less_eq @ TB @ ( sk1 @ TB @ TA @ A @ B @ C @ D ) @ E )
=> ( ord_less_eq @ TA @ ( C @ ( sk1 @ TB @ TA @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA,D: TA] :
@+[E: TB] :
~ ! [F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA,D: TA] :
@+[E: TB] :
~ ( ( ord_less @ TB @ ( sk3 @ TB @ TA @ A @ B @ C @ D ) @ E )
=> ( ord_less @ TA @ ( C @ ( sk3 @ TB @ TA @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [TA: $tType,A: TA,B: TA] :
@+[C: TA] :
~ ( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: coinductive_llist @ a] :
~ ( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ( coinductive_lset @ a @ xs2 ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ( member @ a @ n2 @ ( coinductive_lset @ a @ A ) ) ) ) ) ) ) ).
thf(sk48_def,definition,
( sk48
= ( @+[A: a] :
? [B: coinductive_llist @ a] :
( xs3
= ( coinductive_LCons @ a @ A @ B ) ) ) ) ).
thf(sk49_def,definition,
( sk49
= ( @+[A: coinductive_llist @ a] :
( xs3
= ( coinductive_LCons @ a @ sk48 @ A ) ) ) ) ).
thf(sk56_def,definition,
( sk56
= ( @+[A: coinductive_llist @ a] :
~ ( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ns ) ) ) ) ) ).
thf(166,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_insert__Diff__if) ).
thf(760,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(209,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_64_Collect__mono__iff) ).
thf(893,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)],[209]) ).
thf(276,axiom,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_bot_Oextremum__unique) ).
thf(1083,plain,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(96,axiom,
bot @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_14) ).
thf(555,plain,
bot @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(278,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_6) ).
thf(1088,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1089,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[1088]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA @ ( type2 @ TA ) )
=> ( bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(304,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA @ ( type2 @ TA ) )
=> ( bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(305,plain,
! [TA: $tType,TB: $tType] :
( ~ ( bot @ TB @ ( type2 @ TB ) )
| ( bot @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) ) ),
inference(cnf,[status(esa)],[304]) ).
thf(5496,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ~ $true
| ( bot @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
!= ( bot @ TC @ ( type2 @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1089,305]) ).
thf(5497,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( bot @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
!= ( bot @ TC @ ( type2 @ TC ) ) ) ),
inference(simp,[status(thm)],[5496]) ).
thf(5498,plain,
! [TA: $tType,TB: $tType] : ( bot @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[5497:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( set @ TA ))]]) ).
thf(5588,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ~ $true
| ( bot @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
| ( ( bot @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) )
!= ( bot @ TD @ ( type2 @ TD ) ) ) ),
inference(paramod_ordered,[status(thm)],[5498,305]) ).
thf(5589,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( bot @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
| ( ( bot @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) )
!= ( bot @ TD @ ( type2 @ TD ) ) ) ),
inference(simp,[status(thm)],[5588]) ).
thf(5590,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( bot @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[5589:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > ( set @ TA ) ))]]) ).
thf(5656,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ~ $true
| ( bot @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
| ( ( bot @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TE @ ( type2 @ TE ) ) ) ),
inference(paramod_ordered,[status(thm)],[5590,305]) ).
thf(5657,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( bot @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
| ( ( bot @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TE @ ( type2 @ TE ) ) ) ),
inference(simp,[status(thm)],[5656]) ).
thf(5658,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( bot @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[5657:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > ( set @ TA ) ))]]) ).
thf(6210,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ~ $true
| ( bot @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
| ( ( bot @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TF @ ( type2 @ TF ) ) ) ),
inference(paramod_ordered,[status(thm)],[5658,305]) ).
thf(6211,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( bot @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
| ( ( bot @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TF @ ( type2 @ TF ) ) ) ),
inference(simp,[status(thm)],[6210]) ).
thf(6212,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( bot @ ( TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[6211:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > ( set @ TA ) ))]]) ).
thf(6278,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ~ $true
| ( bot @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
| ( ( bot @ ( TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TG @ ( type2 @ TG ) ) ) ),
inference(paramod_ordered,[status(thm)],[6212,305]) ).
thf(6279,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( bot @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
| ( ( bot @ ( TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TG @ ( type2 @ TG ) ) ) ),
inference(simp,[status(thm)],[6278]) ).
thf(6280,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( bot @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[6279:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(6448,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ~ $true
| ( bot @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
| ( ( bot @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TH @ ( type2 @ TH ) ) ) ),
inference(paramod_ordered,[status(thm)],[6280,305]) ).
thf(6449,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( bot @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
| ( ( bot @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TH @ ( type2 @ TH ) ) ) ),
inference(simp,[status(thm)],[6448]) ).
thf(6450,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( bot @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[6449:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(7553,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ~ $true
| ( bot @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
| ( ( bot @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TI @ ( type2 @ TI ) ) ) ),
inference(paramod_ordered,[status(thm)],[6450,305]) ).
thf(7554,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( bot @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
| ( ( bot @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TI @ ( type2 @ TI ) ) ) ),
inference(simp,[status(thm)],[7553]) ).
thf(7555,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( bot @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[7554:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(7633,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ~ $true
| ( bot @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
| ( ( bot @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TJ @ ( type2 @ TJ ) ) ) ),
inference(paramod_ordered,[status(thm)],[7555,305]) ).
thf(7634,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( bot @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
| ( ( bot @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TJ @ ( type2 @ TJ ) ) ) ),
inference(simp,[status(thm)],[7633]) ).
thf(7635,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( bot @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[7634:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(8993,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ~ $true
| ( bot @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
| ( ( bot @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TK @ ( type2 @ TK ) ) ) ),
inference(paramod_ordered,[status(thm)],[7635,305]) ).
thf(8994,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( bot @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
| ( ( bot @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TK @ ( type2 @ TK ) ) ) ),
inference(simp,[status(thm)],[8993]) ).
thf(8995,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( bot @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[8994:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(9091,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ~ $true
| ( bot @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
| ( ( bot @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TL @ ( type2 @ TL ) ) ) ),
inference(paramod_ordered,[status(thm)],[8995,305]) ).
thf(9092,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( bot @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
| ( ( bot @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TL @ ( type2 @ TL ) ) ) ),
inference(simp,[status(thm)],[9091]) ).
thf(9093,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( bot @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[9092:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(9311,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ~ $true
| ( bot @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
| ( ( bot @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TM @ ( type2 @ TM ) ) ) ),
inference(paramod_ordered,[status(thm)],[9093,305]) ).
thf(9312,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( bot @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
| ( ( bot @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TM @ ( type2 @ TM ) ) ) ),
inference(simp,[status(thm)],[9311]) ).
thf(9313,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( bot @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[9312:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(9796,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ~ $true
| ( bot @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
| ( ( bot @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TN @ ( type2 @ TN ) ) ) ),
inference(paramod_ordered,[status(thm)],[9313,305]) ).
thf(9797,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( bot @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
| ( ( bot @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TN @ ( type2 @ TN ) ) ) ),
inference(simp,[status(thm)],[9796]) ).
thf(9798,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( bot @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[9797:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(9894,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ~ $true
| ( bot @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
| ( ( bot @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TO @ ( type2 @ TO ) ) ) ),
inference(paramod_ordered,[status(thm)],[9798,305]) ).
thf(9895,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( bot @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
| ( ( bot @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TO @ ( type2 @ TO ) ) ) ),
inference(simp,[status(thm)],[9894]) ).
thf(9896,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( bot @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[9895:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(10524,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
( ~ $true
| ( bot @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
| ( ( bot @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TP @ ( type2 @ TP ) ) ) ),
inference(paramod_ordered,[status(thm)],[9896,305]) ).
thf(10525,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
( ( bot @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
| ( ( bot @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TP @ ( type2 @ TP ) ) ) ),
inference(simp,[status(thm)],[10524]) ).
thf(10526,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( bot @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[10525:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(10853,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
( ~ $true
| ( bot @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
| ( ( bot @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TQ @ ( type2 @ TQ ) ) ) ),
inference(paramod_ordered,[status(thm)],[10526,305]) ).
thf(10854,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
( ( bot @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
| ( ( bot @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TQ @ ( type2 @ TQ ) ) ) ),
inference(simp,[status(thm)],[10853]) ).
thf(10855,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( bot @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[10854:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(11657,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
( ~ $true
| ( bot @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
| ( ( bot @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TR @ ( type2 @ TR ) ) ) ),
inference(paramod_ordered,[status(thm)],[10855,305]) ).
thf(11658,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
( ( bot @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
| ( ( bot @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) )
!= ( bot @ TR @ ( type2 @ TR ) ) ) ),
inference(simp,[status(thm)],[11657]) ).
thf(11659,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( bot @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[11658:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).
thf(135,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Diff__subset) ).
thf(683,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(155,axiom,
! [TA: $tType,A: set @ TA] :
~ ( ord_less @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_not__psubset__empty) ).
thf(730,plain,
! [TA: $tType,A: set @ TA] :
~ ( ord_less @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(271,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_Diff__insert__absorb) ).
thf(1068,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(187,axiom,
! [TA: $tType] : ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ouminus_7) ).
thf(836,plain,
! [TA: $tType] : ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(837,plain,
! [TA: $tType] : ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[836]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(318,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(319,plain,
! [TA: $tType,TB: $tType] :
( ~ ( uminus @ TB @ ( type2 @ TB ) )
| ( uminus @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) ) ),
inference(cnf,[status(esa)],[318]) ).
thf(10448,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ~ $true
| ( uminus @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
!= ( uminus @ TC @ ( type2 @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[837,319]) ).
thf(10449,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( uminus @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
!= ( uminus @ TC @ ( type2 @ TC ) ) ) ),
inference(simp,[status(thm)],[10448]) ).
thf(10450,plain,
! [TA: $tType,TB: $tType] : ( uminus @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[10449:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( set @ TA ))]]) ).
thf(10671,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ~ $true
| ( uminus @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
| ( ( uminus @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) )
!= ( uminus @ TD @ ( type2 @ TD ) ) ) ),
inference(paramod_ordered,[status(thm)],[10450,319]) ).
thf(10672,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( uminus @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
| ( ( uminus @ ( TB > ( set @ TA ) ) @ ( type2 @ ( TB > ( set @ TA ) ) ) )
!= ( uminus @ TD @ ( type2 @ TD ) ) ) ),
inference(simp,[status(thm)],[10671]) ).
thf(10673,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( uminus @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[10672:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > ( set @ TA ) ))]]) ).
thf(244,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_63_contra__subsetD) ).
thf(994,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)],[244]) ).
thf(11,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_add_Oinverse__inverse) ).
thf(306,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(307,plain,
! [TA: $tType,A: TA] :
( ~ ( group_add @ TA @ ( type2 @ TA ) )
| ( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(cnf,[status(esa)],[306]) ).
thf(308,plain,
! [TA: $tType,A: TA] :
( ( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A )
| ~ ( group_add @ TA @ ( type2 @ TA ) ) ),
inference(lifteq,[status(thm)],[307]) ).
thf(273,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_insertE) ).
thf(1073,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(203,axiom,
~ ! [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ns ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062LCons_An_Axs_A_092_060in_062_Apaths_Agraph_059_Ax_A_092_060in_062_Alset_Axs_059_Alset_Axs_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(875,plain,
~ ! [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ns ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(876,plain,
~ ! [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ns ) ) ),
inference(polarity_switch,[status(thm)],[875]) ).
thf(877,plain,
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ sk56 ) @ ( koenig916195507_paths @ a @ graph ) )
& ( member @ a @ x @ ( coinductive_lset @ a @ sk56 ) )
& ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk56 ) @ ns ) ),
inference(cnf,[status(esa)],[876]) ).
thf(880,plain,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk56 ) @ ns,
inference(cnfConj,[status(thm)],[877]) ).
thf(4,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_128_order__class_Oorder_Oantisym) ).
thf(287,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)],[4]) ).
thf(288,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[287]) ).
thf(289,plain,
! [TA: $tType,B: TA,A: TA] :
( ( A = B )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ),
inference(lifteq,[status(thm)],[288]) ).
thf(1,conjecture,
member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(283,plain,
~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1210,plain,
! [B: set @ a,A: set @ a] :
( ~ ( order @ ( set @ a ) @ ( type2 @ ( set @ a ) ) )
| ~ ( ord_less_eq @ ( set @ a ) @ A @ B )
| ~ ( ord_less_eq @ ( set @ a ) @ B @ A )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( B
!= ( bot_bot @ ( set @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[289,283]) ).
thf(1211,plain,
! [A: set @ a] :
( ~ ( order @ ( set @ a ) @ ( type2 @ ( set @ a ) ) )
| ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ ( ord_less_eq @ ( set @ a ) @ ( bot_bot @ ( set @ a ) ) @ A )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) ) ),
inference(pattern_uni,[status(thm)],[1210:[bind(A,$thf( A )),bind(B,$thf( bot_bot @ ( set @ a ) ))]]) ).
thf(156,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_4) ).
thf(732,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(733,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[732]) ).
thf(1413,plain,
! [A: set @ a] :
( ~ $true
| ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ ( ord_less_eq @ ( set @ a ) @ ( bot_bot @ ( set @ a ) ) @ A )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) ) ),
inference(rewrite,[status(thm)],[1211,733]) ).
thf(1414,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ ( ord_less_eq @ ( set @ a ) @ ( bot_bot @ ( set @ a ) ) @ A )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[1413]) ).
thf(3880,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk56 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( bot_bot @ ( set @ a ) ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[880,1414]) ).
thf(3881,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk56 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( bot_bot @ ( set @ a ) ) @ A ) ) ),
inference(simp,[status(thm)],[3880]) ).
thf(3900,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ns != A ) ),
inference(simp,[status(thm)],[3881]) ).
thf(3910,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) ) ),
inference(simp,[status(thm)],[3900]) ).
thf(202,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Diff__single__insert) ).
thf(873,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(128,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_diff__strict__left__mono) ).
thf(655,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(116,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_empty__Diff) ).
thf(614,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(222,axiom,
member @ a @ n2 @ ns,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062n_H_A_092_060in_062_Ans_092_060close_062) ).
thf(933,plain,
member @ a @ n2 @ ns,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(205,axiom,
~ ( member @ a @ n2 @ ( coinductive_lset @ a @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062n_H_A_092_060notin_062_Alset_Axs_H_H_092_060close_062) ).
thf(883,plain,
~ ( member @ a @ n2 @ ( coinductive_lset @ a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(884,plain,
~ ( member @ a @ n2 @ ( coinductive_lset @ a @ xs ) ),
inference(polarity_switch,[status(thm)],[883]) ).
thf(1679,plain,
( ~ $true
| ( ( member @ a @ n2 @ ns )
!= ( member @ a @ n2 @ ( coinductive_lset @ a @ xs ) ) ) ),
inference(paramod_ordered,[status(thm)],[933,884]) ).
thf(1680,plain,
( ( member @ a @ n2 @ ns )
!= ( member @ a @ n2 @ ( coinductive_lset @ a @ xs ) ) ),
inference(simp,[status(thm)],[1679]) ).
thf(1687,plain,
( ( n2 != n2 )
| ( ns
!= ( coinductive_lset @ a @ xs ) ) ),
inference(simp,[status(thm)],[1680]) ).
thf(1692,plain,
( ns
!= ( coinductive_lset @ a @ xs ) ),
inference(simp,[status(thm)],[1687]) ).
thf(260,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_insert__subsetI) ).
thf(1041,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(196,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_is__singleton__the__elem) ).
thf(859,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(860,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(cnf,[status(esa)],[859]) ).
thf(861,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(lifteq,[status(thm)],[860]) ).
thf(38,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_123_dual__order_Oantisym) ).
thf(384,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)],[38]) ).
thf(5481,plain,
! [TA: $tType,TB: $tType] :
( ~ $true
| ( bot @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
| ( ( bot @ $o @ ( type2 @ $o ) )
!= ( bot @ TB @ ( type2 @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[555,305]) ).
thf(5482,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
| ( ( bot @ $o @ ( type2 @ $o ) )
!= ( bot @ TB @ ( type2 @ TB ) ) ) ),
inference(simp,[status(thm)],[5481]) ).
thf(5483,plain,
! [TA: $tType] : ( bot @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[5482:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( $o ))]]) ).
thf(5554,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ~ $true
| ( bot @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( bot @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) )
!= ( bot @ TC @ ( type2 @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[5483,305]) ).
thf(5555,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( bot @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( bot @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) )
!= ( bot @ TC @ ( type2 @ TC ) ) ) ),
inference(simp,[status(thm)],[5554]) ).
thf(5556,plain,
! [TA: $tType,TB: $tType] : ( bot @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[5555:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > $o ))]]) ).
thf(5622,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ~ $true
| ( bot @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
| ( ( bot @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) )
!= ( bot @ TD @ ( type2 @ TD ) ) ) ),
inference(paramod_ordered,[status(thm)],[5556,305]) ).
thf(5623,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( bot @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
| ( ( bot @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) )
!= ( bot @ TD @ ( type2 @ TD ) ) ) ),
inference(simp,[status(thm)],[5622]) ).
thf(5624,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( bot @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[5623:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > $o ))]]) ).
thf(5691,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ~ $true
| ( bot @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
| ( ( bot @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) )
!= ( bot @ TE @ ( type2 @ TE ) ) ) ),
inference(paramod_ordered,[status(thm)],[5624,305]) ).
thf(5692,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( bot @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
| ( ( bot @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) )
!= ( bot @ TE @ ( type2 @ TE ) ) ) ),
inference(simp,[status(thm)],[5691]) ).
thf(5693,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( bot @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[5692:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > $o ))]]) ).
thf(6244,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ~ $true
| ( bot @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
| ( ( bot @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) )
!= ( bot @ TF @ ( type2 @ TF ) ) ) ),
inference(paramod_ordered,[status(thm)],[5693,305]) ).
thf(6245,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( bot @ ( TE > TF ) @ ( type2 @ ( TE > TF ) ) )
| ( ( bot @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) )
!= ( bot @ TF @ ( type2 @ TF ) ) ) ),
inference(simp,[status(thm)],[6244]) ).
thf(6246,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( bot @ ( TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[6245:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > TA > $o ))]]) ).
thf(176,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_Diff__eq__empty__iff) ).
thf(797,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(131,axiom,
~ ! [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ( coinductive_lset @ a @ xs2 ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ( member @ a @ n2 @ ( coinductive_lset @ a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_H_H_O_A_092_060lbrakk_062LCons_An_H_Axs_H_H_A_092_060in_062_Apaths_Agraph_059_Alset_Axs_H_H_A_092_060subseteq_062_Alset_Axs_H_059_Ax_A_092_060in_062_Alset_Axs_H_H_059_An_H_A_092_060notin_062_Alset_Axs_H_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(669,plain,
~ ! [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ( coinductive_lset @ a @ xs2 ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ( member @ a @ n2 @ ( coinductive_lset @ a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(670,plain,
~ ! [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ A ) @ ( koenig916195507_paths @ a @ graph ) )
=> ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ( coinductive_lset @ a @ xs2 ) )
=> ( ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
=> ( member @ a @ n2 @ ( coinductive_lset @ a @ A ) ) ) ) ),
inference(polarity_switch,[status(thm)],[669]) ).
thf(671,plain,
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ sk43 ) @ ( koenig916195507_paths @ a @ graph ) )
& ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
& ( member @ a @ x @ ( coinductive_lset @ a @ sk43 ) )
& ~ ( member @ a @ n2 @ ( coinductive_lset @ a @ sk43 ) ) ),
inference(cnf,[status(esa)],[670]) ).
thf(674,plain,
member @ a @ x @ ( coinductive_lset @ a @ sk43 ),
inference(cnfConj,[status(thm)],[671]) ).
thf(1909,plain,
( ~ $true
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk43 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[674,283]) ).
thf(1910,plain,
( ( member @ a @ x @ ( coinductive_lset @ a @ sk43 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[1909]) ).
thf(1912,plain,
( ( x != x )
| ( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[1910]) ).
thf(1919,plain,
( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ),
inference(simp,[status(thm)],[1912]) ).
thf(24,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_142_order__subst2) ).
thf(340,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)],[24]) ).
thf(89,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_210_order_Ostrict__iff__order) ).
thf(538,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)],[89]) ).
thf(221,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) )
& ( ~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_subset__insert__iff) ).
thf(930,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) )
& ( ~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(46,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 ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_wlog__linorder__le) ).
thf(404,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 ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(247,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_insert__Diff) ).
thf(1001,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(171,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_62_set__eq__subset) ).
thf(782,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)],[171]) ).
thf(146,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_244_subset__psubset__trans) ).
thf(709,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)],[146]) ).
thf(189,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_3) ).
thf(841,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(6312,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ~ $true
| ( bot @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
| ( ( bot @ ( TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TG @ ( type2 @ TG ) ) ) ),
inference(paramod_ordered,[status(thm)],[6246,305]) ).
thf(6313,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( bot @ ( TF > TG ) @ ( type2 @ ( TF > TG ) ) )
| ( ( bot @ ( TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TG @ ( type2 @ TG ) ) ) ),
inference(simp,[status(thm)],[6312]) ).
thf(6314,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( bot @ ( TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[6313:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > TA > $o ))]]) ).
thf(7513,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ~ $true
| ( bot @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
| ( ( bot @ ( TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TH @ ( type2 @ TH ) ) ) ),
inference(paramod_ordered,[status(thm)],[6314,305]) ).
thf(7514,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( bot @ ( TG > TH ) @ ( type2 @ ( TG > TH ) ) )
| ( ( bot @ ( TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TH @ ( type2 @ TH ) ) ) ),
inference(simp,[status(thm)],[7513]) ).
thf(7515,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( bot @ ( TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[7514:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(7593,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ~ $true
| ( bot @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
| ( ( bot @ ( TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TI @ ( type2 @ TI ) ) ) ),
inference(paramod_ordered,[status(thm)],[7515,305]) ).
thf(7594,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( bot @ ( TH > TI ) @ ( type2 @ ( TH > TI ) ) )
| ( ( bot @ ( TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TI @ ( type2 @ TI ) ) ) ),
inference(simp,[status(thm)],[7593]) ).
thf(7595,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( bot @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[7594:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(7727,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ~ $true
| ( bot @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
| ( ( bot @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TJ @ ( type2 @ TJ ) ) ) ),
inference(paramod_ordered,[status(thm)],[7595,305]) ).
thf(7728,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( bot @ ( TI > TJ ) @ ( type2 @ ( TI > TJ ) ) )
| ( ( bot @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TJ @ ( type2 @ TJ ) ) ) ),
inference(simp,[status(thm)],[7727]) ).
thf(7729,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( bot @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[7728:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(140,axiom,
member @ a @ x @ ( coinductive_lset @ a @ xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062x_A_092_060in_062_Alset_Axs_H_H_092_060close_062) ).
thf(696,plain,
member @ a @ x @ ( coinductive_lset @ a @ xs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(144,axiom,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062lset_Axs_H_A_092_060subseteq_062_Ans_092_060close_062) ).
thf(705,plain,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(2932,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( bot_bot @ ( set @ a ) ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[705,1414]) ).
thf(2933,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( bot_bot @ ( set @ a ) ) @ A ) ) ),
inference(simp,[status(thm)],[2932]) ).
thf(2952,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ns != A ) ),
inference(simp,[status(thm)],[2933]) ).
thf(2957,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) ) ),
inference(simp,[status(thm)],[2952]) ).
thf(5860,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[696,2957]) ).
thf(5861,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(simp,[status(thm)],[5860]) ).
thf(5864,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( x != x )
| ( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5861]) ).
thf(5903,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5864]) ).
thf(17,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_133_order_Otrans) ).
thf(320,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)],[17]) ).
thf(237,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_bot__set__def) ).
thf(973,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(206,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_gen_lset @ TA @ ( insert @ TA @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_gen__lset__code_I2_J) ).
thf(885,plain,
! [TA: $tType,A: set @ TA,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_gen_lset @ TA @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_gen_lset @ TA @ ( insert @ TA @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(126,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_2) ).
thf(650,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(651,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[650]) ).
thf(265,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ex__in__conv) ).
thf(1055,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1711,plain,
! [B: set @ a,A: set @ a] :
( ~ ( order @ ( set @ a ) @ ( type2 @ ( set @ a ) ) )
| ~ ( ord_less_eq @ ( set @ a ) @ A @ B )
| ~ ( ord_less_eq @ ( set @ a ) @ B @ A )
| ( B != ns )
| ( A
!= ( coinductive_lset @ a @ xs ) ) ),
inference(paramod_ordered,[status(thm)],[289,1692]) ).
thf(1712,plain,
! [A: set @ a] :
( ~ ( order @ ( set @ a ) @ ( type2 @ ( set @ a ) ) )
| ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ A )
| ~ ( ord_less_eq @ ( set @ a ) @ A @ ( coinductive_lset @ a @ xs ) )
| ( A != ns ) ),
inference(pattern_uni,[status(thm)],[1711:[bind(A,$thf( coinductive_lset @ a @ xs )),bind(B,$thf( B ))]]) ).
thf(1721,plain,
( ~ ( order @ ( set @ a ) @ ( type2 @ ( set @ a ) ) )
| ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ ns )
| ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) ) ),
inference(simp,[status(thm)],[1712]) ).
thf(9191,plain,
( ~ $true
| ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ ns )
| ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) ) ),
inference(rewrite,[status(thm)],[1721,733]) ).
thf(9192,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ ns )
| ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) ) ),
inference(simp,[status(thm)],[9191]) ).
thf(9257,plain,
( ~ $true
| ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ ns ) ) ),
inference(paramod_ordered,[status(thm)],[705,9192]) ).
thf(9258,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ ns ) ) ),
inference(simp,[status(thm)],[9257]) ).
thf(9270,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( coinductive_lset @ a @ xs ) )
| ( ns != ns ) ),
inference(simp,[status(thm)],[9258]) ).
thf(9287,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( coinductive_lset @ a @ xs ) ) ),
inference(simp,[status(thm)],[9270]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_llist_Oset__intros_I1_J) ).
thf(719,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(172,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_245_subset__not__subset__eq) ).
thf(785,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)],[172]) ).
thf(25,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_compl__le__swap1) ).
thf(344,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(879,plain,
member @ a @ x @ ( coinductive_lset @ a @ sk56 ),
inference(cnfConj,[status(thm)],[877]) ).
thf(3829,plain,
( ~ $true
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk56 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[879,283]) ).
thf(3830,plain,
( ( member @ a @ x @ ( coinductive_lset @ a @ sk56 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[3829]) ).
thf(3833,plain,
( ( x != x )
| ( ( coinductive_lset @ a @ sk56 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[3830]) ).
thf(3845,plain,
( ( coinductive_lset @ a @ sk56 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ),
inference(simp,[status(thm)],[3833]) ).
thf(223,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_DiffD1) ).
thf(934,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(229,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 )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_double__diff) ).
thf(949,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 )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ( order_bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(372,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ( order_bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(5780,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk56 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[879,2957]) ).
thf(5781,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk56 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(simp,[status(thm)],[5780]) ).
thf(5869,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( x != x )
| ( ( coinductive_lset @ a @ sk56 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5781]) ).
thf(5910,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5869]) ).
thf(107,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( ( ( member @ TA @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) )
& ( ~ ( member @ TA @ B @ C )
=> ( ( ( member @ TA @ B @ A )
=> ( ord_less @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) )
& ( ~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_psubset__insert__iff) ).
thf(587,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( ( ( member @ TA @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) )
& ( ~ ( member @ TA @ B @ C )
=> ( ( ( member @ TA @ B @ A )
=> ( ord_less @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) )
& ( ~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(188,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(838,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(9042,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ~ $true
| ( bot @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
| ( ( bot @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TK @ ( type2 @ TK ) ) ) ),
inference(paramod_ordered,[status(thm)],[7729,305]) ).
thf(9043,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( bot @ ( TJ > TK ) @ ( type2 @ ( TJ > TK ) ) )
| ( ( bot @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TK @ ( type2 @ TK ) ) ) ),
inference(simp,[status(thm)],[9042]) ).
thf(9044,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( bot @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[9043:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(9140,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ~ $true
| ( bot @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
| ( ( bot @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TL @ ( type2 @ TL ) ) ) ),
inference(paramod_ordered,[status(thm)],[9044,305]) ).
thf(9141,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( bot @ ( TK > TL ) @ ( type2 @ ( TK > TL ) ) )
| ( ( bot @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TL @ ( type2 @ TL ) ) ) ),
inference(simp,[status(thm)],[9140]) ).
thf(9142,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( bot @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[9141:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(9747,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ~ $true
| ( bot @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
| ( ( bot @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TM @ ( type2 @ TM ) ) ) ),
inference(paramod_ordered,[status(thm)],[9142,305]) ).
thf(9748,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( bot @ ( TL > TM ) @ ( type2 @ ( TL > TM ) ) )
| ( ( bot @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TM @ ( type2 @ TM ) ) ) ),
inference(simp,[status(thm)],[9747]) ).
thf(9749,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( bot @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[9748:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(9845,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ~ $true
| ( bot @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
| ( ( bot @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TN @ ( type2 @ TN ) ) ) ),
inference(paramod_ordered,[status(thm)],[9749,305]) ).
thf(9846,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( bot @ ( TM > TN ) @ ( type2 @ ( TM > TN ) ) )
| ( ( bot @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TN @ ( type2 @ TN ) ) ) ),
inference(simp,[status(thm)],[9845]) ).
thf(9847,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( bot @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[9846:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(10018,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ~ $true
| ( bot @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
| ( ( bot @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TO @ ( type2 @ TO ) ) ) ),
inference(paramod_ordered,[status(thm)],[9847,305]) ).
thf(10019,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( bot @ ( TN > TO ) @ ( type2 @ ( TN > TO ) ) )
| ( ( bot @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TO @ ( type2 @ TO ) ) ) ),
inference(simp,[status(thm)],[10018]) ).
thf(10020,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( bot @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[10019:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(10573,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
( ~ $true
| ( bot @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
| ( ( bot @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TP @ ( type2 @ TP ) ) ) ),
inference(paramod_ordered,[status(thm)],[10020,305]) ).
thf(10574,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
( ( bot @ ( TO > TP ) @ ( type2 @ ( TO > TP ) ) )
| ( ( bot @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TP @ ( type2 @ TP ) ) ) ),
inference(simp,[status(thm)],[10573]) ).
thf(10575,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( bot @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[10574:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(11510,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
( ~ $true
| ( bot @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
| ( ( bot @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TQ @ ( type2 @ TQ ) ) ) ),
inference(paramod_ordered,[status(thm)],[10575,305]) ).
thf(11511,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
( ( bot @ ( TP > TQ ) @ ( type2 @ ( TP > TQ ) ) )
| ( ( bot @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TQ @ ( type2 @ TQ ) ) ) ),
inference(simp,[status(thm)],[11510]) ).
thf(11512,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( bot @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[11511:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(200,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_diff__left__mono) ).
thf(870,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_insert__not__empty) ).
thf(606,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(204,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_247_psubset__imp__subset) ).
thf(881,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)],[204]) ).
thf(62,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_137_linear) ).
thf(448,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)],[62]) ).
thf(183,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__commute) ).
thf(817,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(212,axiom,
x != n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_False) ).
thf(902,plain,
x != n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(121,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_empty__Collect__eq) ).
thf(638,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(194,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_diff__right__mono) ).
thf(853,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(250,axiom,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_bot_Oextremum) ).
thf(1013,plain,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(3,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_equation__minus__iff) ).
thf(284,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(219,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Diff__insert0) ).
thf(924,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(164,axiom,
! [TA: $tType] : ( minus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ominus_8) ).
thf(755,plain,
! [TA: $tType] : ( minus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(756,plain,
! [TA: $tType] : ( minus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[755]) ).
thf(321,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ C )
| ( ord_less_eq @ TA @ A @ C ) ),
inference(cnf,[status(esa)],[320]) ).
thf(120,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_lset__induct) ).
thf(623,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(124,axiom,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs3 ) @ ns,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062lset_Axs_A_092_060subseteq_062_Ans_092_060close_062) ).
thf(646,plain,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs3 ) @ ns,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1952,plain,
( ~ $true
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[696,283]) ).
thf(1953,plain,
( ( member @ a @ x @ ( coinductive_lset @ a @ xs ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[1952]) ).
thf(1956,plain,
( ( x != x )
| ( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[1953]) ).
thf(1960,plain,
( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ),
inference(simp,[status(thm)],[1956]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_llist_Oinject) ).
thf(353,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(213,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_subset__refl) ).
thf(905,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_singleton__inject) ).
thf(574,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(252,axiom,
! [TA: $tType] :
( ( coinductive_lset @ TA )
= ( coinductive_gen_lset @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_lset__code) ).
thf(1018,plain,
! [TA: $tType] :
( ( coinductive_lset @ TA )
= ( coinductive_gen_lset @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1019,plain,
! [TA: $tType] :
( ( coinductive_lset @ TA )
= ( coinductive_gen_lset @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(cnf,[status(esa)],[1018]) ).
thf(1020,plain,
! [TA: $tType] :
( ( coinductive_lset @ TA )
= ( coinductive_gen_lset @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(lifteq,[status(thm)],[1019]) ).
thf(27,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_neg__less__iff__less) ).
thf(348,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(43,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_le__imp__neg__le) ).
thf(397,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(673,plain,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ),
inference(cnfConj,[status(thm)],[671]) ).
thf(5784,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk43 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[674,2957]) ).
thf(5785,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk43 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(simp,[status(thm)],[5784]) ).
thf(5867,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( x != x )
| ( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5785]) ).
thf(5907,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5867]) ).
thf(7894,plain,
( ~ $true
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[673,5907]) ).
thf(7895,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) ) ) ),
inference(simp,[status(thm)],[7894]) ).
thf(7897,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) ) ),
inference(simp,[status(thm)],[7895]) ).
thf(7931,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns ) ),
inference(simp,[status(thm)],[7897]) ).
thf(1214,plain,
! [B: a > a > $o,A: a > a > $o] :
( ~ ( order @ ( a > a > $o ) @ ( type2 @ ( a > a > $o ) ) )
| ~ ( ord_less_eq @ ( a > a > $o ) @ A @ B )
| ~ ( ord_less_eq @ ( a > a > $o ) @ B @ A )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ A @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) )
| ( B != graph ) ),
inference(paramod_ordered,[status(thm)],[289,283]) ).
thf(1215,plain,
! [A: a > a > $o] :
( ~ ( order @ ( a > a > $o ) @ ( type2 @ ( a > a > $o ) ) )
| ~ ( ord_less_eq @ ( a > a > $o ) @ A @ graph )
| ~ ( ord_less_eq @ ( a > a > $o ) @ graph @ A )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ A @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(pattern_uni,[status(thm)],[1214:[bind(A,$thf( A )),bind(B,$thf( graph ))]]) ).
thf(138,axiom,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_bot_Oextremum__strict) ).
thf(691,plain,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(692,plain,
! [TA: $tType,A: TA] :
( ~ ( order_bot @ TA @ ( type2 @ TA ) )
| ~ ( ord_less @ TA @ A @ ( bot_bot @ TA ) ) ),
inference(cnf,[status(esa)],[691]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_bot__apply) ).
thf(734,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(64,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_141_ord__eq__le__subst) ).
thf(453,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)],[64]) ).
thf(168,axiom,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oboolean__algebra_1) ).
thf(774,plain,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
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_127_order__trans) ).
thf(428,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(192,axiom,
member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ xs3 ) @ ( koenig916195507_paths @ a @ graph ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_path) ).
thf(849,plain,
member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ xs3 ) @ ( koenig916195507_paths @ a @ graph ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(240,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_49_in__mono) ).
thf(981,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)],[240]) ).
thf(167,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_is__singletonI_H) ).
thf(766,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(6,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_minus__less__iff) ).
thf(293,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(231,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_emptyE) ).
thf(955,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(956,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[955]) ).
thf(5,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_minus__equation__iff) ).
thf(290,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(291,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( group_add @ TA @ ( type2 @ TA ) )
| ( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(cnf,[status(esa)],[290]) ).
thf(292,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) )
| ~ ( group_add @ TA @ ( type2 @ TA ) ) ),
inference(lifteq,[status(thm)],[291]) ).
thf(217,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o,D: TA,E: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ B ) @ E )
=> ( member @ TA @ D @ ( koenig317145564le_via @ TA @ C @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_reachable__via_Ointros) ).
thf(920,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o,D: TA,E: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ B ) @ E )
=> ( member @ TA @ D @ ( koenig317145564le_via @ TA @ C @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(78,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_11) ).
thf(512,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(133,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Diff__mono) ).
thf(678,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(180,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_subset__empty) ).
thf(810,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(37,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_203_dual__order_Ostrict__iff__order) ).
thf(381,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)],[37]) ).
thf(33,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_125_linorder__wlog) ).
thf(366,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)],[33]) ).
thf(270,axiom,
member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ xs ) @ ( koenig916195507_paths @ a @ graph ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_path_H_H) ).
thf(1067,plain,
member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ xs ) @ ( koenig916195507_paths @ a @ graph ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(92,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_223_antisym__conv1) ).
thf(546,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)],[92]) ).
thf(174,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_58_rev__subsetD) ).
thf(793,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)],[174]) ).
thf(215,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA,E: TA > $o] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
=> ( ! [F: coinductive_llist @ TA,G: TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ F ) @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( member @ TA @ G @ ( coinductive_lset @ TA @ F ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ F ) @ C )
=> ( E @ G ) ) ) )
=> ( E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_reachable__via_Oinducts) ).
thf(910,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA,E: TA > $o] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
=> ( ! [F: coinductive_llist @ TA,G: TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ F ) @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( member @ TA @ G @ ( coinductive_lset @ TA @ F ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ F ) @ C )
=> ( E @ G ) ) ) )
=> ( E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(232,axiom,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_bot_Oextremum__uniqueI) ).
thf(957,plain,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(161,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_doubleton__eq__iff) ).
thf(746,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(253,axiom,
( xs3
= ( coinductive_LCons @ a @ n2 @ xs2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_xs) ).
thf(1021,plain,
( xs3
= ( coinductive_LCons @ a @ n2 @ xs2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(230,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
= ( ( member @ TA @ A @ C )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_member__remove) ).
thf(952,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
= ( ( member @ TA @ A @ C )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(95,axiom,
uminus @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_15) ).
thf(554,plain,
uminus @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(10445,plain,
! [TA: $tType,TB: $tType] :
( ~ $true
| ( uminus @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
| ( ( uminus @ $o @ ( type2 @ $o ) )
!= ( uminus @ TB @ ( type2 @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[554,319]) ).
thf(10446,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) )
| ( ( uminus @ $o @ ( type2 @ $o ) )
!= ( uminus @ TB @ ( type2 @ TB ) ) ) ),
inference(simp,[status(thm)],[10445]) ).
thf(10447,plain,
! [TA: $tType] : ( uminus @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[10446:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( $o ))]]) ).
thf(10622,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ~ $true
| ( uminus @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( uminus @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) )
!= ( uminus @ TC @ ( type2 @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[10447,319]) ).
thf(10623,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( uminus @ ( TB > TC ) @ ( type2 @ ( TB > TC ) ) )
| ( ( uminus @ ( TA > $o ) @ ( type2 @ ( TA > $o ) ) )
!= ( uminus @ TC @ ( type2 @ TC ) ) ) ),
inference(simp,[status(thm)],[10622]) ).
thf(10624,plain,
! [TA: $tType,TB: $tType] : ( uminus @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[10623:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > $o ))]]) ).
thf(11559,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ~ $true
| ( uminus @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
| ( ( uminus @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) )
!= ( uminus @ TD @ ( type2 @ TD ) ) ) ),
inference(paramod_ordered,[status(thm)],[10624,319]) ).
thf(11560,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( uminus @ ( TC > TD ) @ ( type2 @ ( TC > TD ) ) )
| ( ( uminus @ ( TB > TA > $o ) @ ( type2 @ ( TB > TA > $o ) ) )
!= ( uminus @ TD @ ( type2 @ TD ) ) ) ),
inference(simp,[status(thm)],[11559]) ).
thf(11561,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( uminus @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[11560:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > $o ))]]) ).
thf(12508,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ~ $true
| ( uminus @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
| ( ( uminus @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) )
!= ( uminus @ TE @ ( type2 @ TE ) ) ) ),
inference(paramod_ordered,[status(thm)],[11561,319]) ).
thf(12509,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( uminus @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
| ( ( uminus @ ( TC > TB > TA > $o ) @ ( type2 @ ( TC > TB > TA > $o ) ) )
!= ( uminus @ TE @ ( type2 @ TE ) ) ) ),
inference(simp,[status(thm)],[12508]) ).
thf(12510,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( uminus @ ( TD > TC > TB > TA > $o ) @ ( type2 @ ( TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[12509:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > $o ))]]) ).
thf(9,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_229_order__less__le__subst1) ).
thf(300,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)],[9]) ).
thf(301,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB,B: TB > TA,A: TA] :
( ( ~ ( order @ TB @ ( type2 @ TB ) )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less @ TA @ A @ ( B @ C ) )
| ~ ( ord_less_eq @ TB @ C @ D )
| ( ord_less_eq @ TB @ ( sk1 @ TB @ TA @ D @ C @ B @ A ) @ ( sk2 @ TB @ TA @ D @ C @ B @ A ) )
| ( ord_less @ TA @ A @ ( B @ D ) ) )
& ( ~ ( order @ TB @ ( type2 @ TB ) )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less @ TA @ A @ ( B @ C ) )
| ~ ( ord_less_eq @ TB @ C @ D )
| ~ ( ord_less_eq @ TA @ ( B @ ( sk1 @ TB @ TA @ D @ C @ B @ A ) ) @ ( B @ ( sk2 @ TB @ TA @ D @ C @ B @ A ) ) )
| ( ord_less @ TA @ A @ ( B @ D ) ) ) ),
inference(cnf,[status(esa)],[300]) ).
thf(302,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB,B: TB > TA,A: TA] :
( ~ ( order @ TB @ ( type2 @ TB ) )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less @ TA @ A @ ( B @ C ) )
| ~ ( ord_less_eq @ TB @ C @ D )
| ( ord_less_eq @ TB @ ( sk1 @ TB @ TA @ D @ C @ B @ A ) @ ( sk2 @ TB @ TA @ D @ C @ B @ A ) )
| ( ord_less @ TA @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[301]) ).
thf(197,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_is__singletonI) ).
thf(862,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_singleton__iff) ).
thf(598,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(184,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Diff__iff) ).
thf(820,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(41,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_145_le__funI) ).
thf(392,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)],[41]) ).
thf(53,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_13) ).
thf(424,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(139,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_insert__Diff1) ).
thf(693,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(173,axiom,
~ ! [A: a,B: coinductive_llist @ a] :
( xs3
!= ( coinductive_LCons @ a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_Axs_H_O_Axs_A_061_ALCons_An_H_Axs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(788,plain,
~ ! [A: a,B: coinductive_llist @ a] :
( xs3
!= ( coinductive_LCons @ a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(182,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_50_subsetD) ).
thf(815,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)],[182]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( boolean_algebra @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(566,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( boolean_algebra @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(20,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_214_not__le__imp__less) ).
thf(329,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)],[20]) ).
thf(65,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_132_le__cases3) ).
thf(461,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)],[65]) ).
thf(5983,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk56 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[879,3910]) ).
thf(5984,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk56 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(simp,[status(thm)],[5983]) ).
thf(6069,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( x != x )
| ( ( coinductive_lset @ a @ sk56 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5984]) ).
thf(6096,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[6069]) ).
thf(94,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_233_le__less) ).
thf(551,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)],[94]) ).
thf(842,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[841]) ).
thf(18,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_218_dense__le) ).
thf(322,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)],[18]) ).
thf(323,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ~ ( dense_linorder @ TA @ ( type2 @ TA ) )
| ( ord_less @ TA @ ( sk5 @ TA @ B @ A ) @ A )
| ( ord_less_eq @ TA @ A @ B ) )
& ( ~ ( dense_linorder @ TA @ ( type2 @ TA ) )
| ~ ( ord_less_eq @ TA @ ( sk5 @ TA @ B @ A ) @ B )
| ( ord_less_eq @ TA @ A @ B ) ) ),
inference(cnf,[status(esa)],[322]) ).
thf(324,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( dense_linorder @ TA @ ( type2 @ TA ) )
| ( ord_less @ TA @ ( sk5 @ TA @ B @ A ) @ A )
| ( ord_less_eq @ TA @ A @ B ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(31,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_neg__equal__iff__equal) ).
thf(361,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(165,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_singletonD) ).
thf(757,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(81,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_213_order_Ostrict__trans1) ).
thf(519,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)],[81]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB @ ( type2 @ TB ) )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_fun__diff__def) ).
thf(725,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB @ ( type2 @ TB ) )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(30,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_207_dense__ge__bounded) ).
thf(356,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)],[30]) ).
thf(51,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_147_le__funD) ).
thf(420,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)],[51]) ).
thf(73,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_217_le__less__linear) ).
thf(499,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)],[73]) ).
thf(141,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_28_subsetI) ).
thf(697,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)],[141]) ).
thf(10806,plain,
( ~ $true
| ( ( coinductive_lset @ a @ xs2 )
!= ( coinductive_lset @ a @ xs ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) ) ) ),
inference(paramod_ordered,[status(thm)],[673,9287]) ).
thf(10807,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( coinductive_lset @ a @ xs ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) ) ) ),
inference(simp,[status(thm)],[10806]) ).
thf(10809,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( coinductive_lset @ a @ xs ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns )
| ( ( coinductive_lset @ a @ xs2 )
!= ( coinductive_lset @ a @ xs ) ) ),
inference(simp,[status(thm)],[10807]) ).
thf(10830,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( coinductive_lset @ a @ xs ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns ) ),
inference(simp,[status(thm)],[10809]) ).
thf(66,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_134_le__cases) ).
thf(476,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)],[66]) ).
thf(70,axiom,
minus @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ominus_16) ).
thf(489,plain,
minus @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(108,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_52_equalityE) ).
thf(590,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)],[108]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_bot__fun__def) ).
thf(970,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(145,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_Compl__subset__Compl__iff) ).
thf(706,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(256,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_ComplD) ).
thf(1028,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(275,axiom,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_remove__def) ).
thf(1080,plain,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1081,plain,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(cnf,[status(esa)],[1080]) ).
thf(1082,plain,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(lifteq,[status(thm)],[1081]) ).
thf(84,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_dual__order_Orefl) ).
thf(526,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(114,axiom,
member @ a @ x @ ( coinductive_lset @ a @ xs2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__092_060open_062x_A_092_060in_062_Alset_Axs_H_092_060close_062) ).
thf(611,plain,
member @ a @ x @ ( coinductive_lset @ a @ xs2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(5854,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs2 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[611,2957]) ).
thf(5855,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs2 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(simp,[status(thm)],[5854]) ).
thf(5865,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( x != x )
| ( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5855]) ).
thf(5905,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5865]) ).
thf(148,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_bot__empty__eq) ).
thf(713,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(714,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(cnf,[status(esa)],[713]) ).
thf(715,plain,
! [TA: $tType] :
( ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= ( bot_bot @ ( TA > $o ) ) ),
inference(lifteq,[status(thm)],[714]) ).
thf(1643,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : $false ) ),
inference(rewrite,[status(thm)],[715,956]) ).
thf(1644,plain,
! [TA: $tType,A: TA] :
~ ( bot_bot @ ( TA > $o ) @ A ),
inference(func_ext,[status(esa)],[1643]) ).
thf(125,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_Set_Ois__empty__def) ).
thf(647,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(142,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ D ) @ ( koenig916195507_paths @ TA @ A ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) @ ( koenig916195507_paths @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_paths_OLCons) ).
thf(701,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ D ) @ ( koenig916195507_paths @ TA @ A ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) @ ( koenig916195507_paths @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(151,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_subset__insertI) ).
thf(721,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(11608,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ~ $true
| ( uminus @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
| ( ( uminus @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) )
!= ( uminus @ TE @ ( type2 @ TE ) ) ) ),
inference(paramod_ordered,[status(thm)],[10673,319]) ).
thf(11609,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( uminus @ ( TD > TE ) @ ( type2 @ ( TD > TE ) ) )
| ( ( uminus @ ( TC > TB > ( set @ TA ) ) @ ( type2 @ ( TC > TB > ( set @ TA ) ) ) )
!= ( uminus @ TE @ ( type2 @ TE ) ) ) ),
inference(simp,[status(thm)],[11608]) ).
thf(11610,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( uminus @ ( TD > TC > TB > ( set @ TA ) ) @ ( type2 @ ( TD > TC > TB > ( set @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[11609:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > ( set @ TA ) ))]]) ).
thf(170,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_243_subset__iff__psubset__eq) ).
thf(779,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)],[170]) ).
thf(75,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_compl__le__compl__iff) ).
thf(503,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(119,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_53_subset__eq) ).
thf(620,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)],[119]) ).
thf(621,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(cnf,[status(esa)],[620]) ).
thf(622,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(lifteq,[status(thm)],[621]) ).
thf(267,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Set_Oinsert__mono) ).
thf(1060,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(263,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_all__not__in__conv) ).
thf(1050,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(277,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_lset__intros_I2_J) ).
thf(1086,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(14,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_231_order__le__less__subst1) ).
thf(311,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)],[14]) ).
thf(90,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_212_order_Ostrict__trans2) ).
thf(541,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)],[90]) ).
thf(129,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_psubsetD) ).
thf(657,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(258,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Collect__empty__eq) ).
thf(1035,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(86,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_order__refl) ).
thf(530,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(98,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_219_dense__ge) ).
thf(558,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)],[98]) ).
thf(272,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_subset__insertI2) ).
thf(1071,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(149,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_248_psubset__eq) ).
thf(716,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)],[149]) ).
thf(717,plain,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( A != B ) ) ) ),
inference(cnf,[status(esa)],[716]) ).
thf(718,plain,
! [TA: $tType] :
( ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( A != B ) ) )
= ( ord_less @ ( set @ TA ) ) ),
inference(lifteq,[status(thm)],[717]) ).
thf(207,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_diff__eq__diff__less__eq) ).
thf(888,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(7,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_201_order_Onot__eq__order__implies__strict) ).
thf(296,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)],[7]) ).
thf(297,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( order @ TA @ ( type2 @ TA ) )
| ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ A @ B ) ),
inference(cnf,[status(esa)],[296]) ).
thf(298,plain,
! [TA: $tType,B: TA,A: TA] :
( ( A = B )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(54,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_neg__le__iff__le) ).
thf(425,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(61,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_143_order__subst1) ).
thf(444,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)],[61]) ).
thf(110,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_is__singletonE) ).
thf(601,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(118,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_DiffI) ).
thf(618,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(79,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_130_ord__eq__le__trans) ).
thf(513,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)],[79]) ).
thf(56,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_221_le__less__trans) ).
thf(430,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)],[56]) ).
thf(190,axiom,
member @ a @ x @ ( coinductive_lset @ a @ xs3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062x_A_092_060in_062_Alset_Axs_092_060close_062) ).
thf(843,plain,
member @ a @ x @ ( coinductive_lset @ a @ xs3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(285,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( group_add @ TA @ ( type2 @ TA ) )
| ( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(cnf,[status(esa)],[284]) ).
thf(286,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) )
| ~ ( group_add @ TA @ ( type2 @ TA ) ) ),
inference(lifteq,[status(thm)],[285]) ).
thf(160,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_diff__right__commute) ).
thf(743,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(104,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_is__singleton__def) ).
thf(577,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(578,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(cnf,[status(esa)],[577]) ).
thf(579,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(lifteq,[status(thm)],[578]) ).
thf(48,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_209_dual__order_Ostrict__trans1) ).
thf(413,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)],[48]) ).
thf(99,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_228_order__less__le__subst2) ).
thf(562,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)],[99]) ).
thf(903,plain,
x != n2,
inference(polarity_switch,[status(thm)],[902]) ).
thf(904,plain,
x != n2,
inference(lifteq,[status(thm)],[903]) ).
thf(147,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_lset__intros_I1_J) ).
thf(711,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(122,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_insert__absorb2) ).
thf(641,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(6611,plain,
( ~ $true
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[673,5903]) ).
thf(6612,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) ) ) ),
inference(simp,[status(thm)],[6611]) ).
thf(6615,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) ) ),
inference(simp,[status(thm)],[6612]) ).
thf(6649,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns ) ),
inference(simp,[status(thm)],[6615]) ).
thf(22,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_224_less__imp__le) ).
thf(335,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)],[22]) ).
thf(279,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_insert__eq__iff) ).
thf(1090,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(179,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_llist_Oset__cases) ).
thf(804,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(9253,plain,
( ~ $true
| ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk56 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ ns ) ) ),
inference(paramod_ordered,[status(thm)],[880,9192]) ).
thf(9254,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk56 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ ns ) ) ),
inference(simp,[status(thm)],[9253]) ).
thf(9268,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( coinductive_lset @ a @ xs ) )
| ( ns != ns ) ),
inference(simp,[status(thm)],[9254]) ).
thf(9285,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( coinductive_lset @ a @ xs ) ) ),
inference(simp,[status(thm)],[9268]) ).
thf(224,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_subset__singleton__iff) ).
thf(936,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(974,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(cnf,[status(esa)],[973]) ).
thf(975,plain,
! [TA: $tType] :
( ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(lifteq,[status(thm)],[974]) ).
thf(1702,plain,
! [TB: $tType] :
( ( ( collect @ TB
@ ^ [A: TB] : $false )
= ( bot_bot @ ( set @ TB ) ) )
| ( ( bot_bot @ ( TB > $o ) )
!= ( bot_bot @ ( TB > $o ) ) ) ),
inference(paramod_ordered,[status(thm)],[1643,975]) ).
thf(1703,plain,
! [TB: $tType] :
( ( collect @ TB
@ ^ [A: TB] : $false )
= ( bot_bot @ ( set @ TB ) ) ),
inference(pattern_uni,[status(thm)],[1702:[]]) ).
thf(1707,plain,
! [TA: $tType] :
( ( collect @ TA
@ ^ [A: TA] : $false )
= ( bot_bot @ ( set @ TA ) ) ),
inference(simp,[status(thm)],[1703]) ).
thf(312,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB,B: TB > TA,A: TA] :
( ( ~ ( order @ TB @ ( type2 @ TB ) )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less_eq @ TA @ A @ ( B @ C ) )
| ~ ( ord_less @ TB @ C @ D )
| ( ord_less @ TB @ ( sk3 @ TB @ TA @ D @ C @ B @ A ) @ ( sk4 @ TB @ TA @ D @ C @ B @ A ) )
| ( ord_less @ TA @ A @ ( B @ D ) ) )
& ( ~ ( order @ TB @ ( type2 @ TB ) )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less_eq @ TA @ A @ ( B @ C ) )
| ~ ( ord_less @ TB @ C @ D )
| ~ ( ord_less @ TA @ ( B @ ( sk3 @ TB @ TA @ D @ C @ B @ A ) ) @ ( B @ ( sk4 @ TB @ TA @ D @ C @ B @ A ) ) )
| ( ord_less @ TA @ A @ ( B @ D ) ) ) ),
inference(cnf,[status(esa)],[311]) ).
thf(313,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB,B: TB > TA,A: TA] :
( ~ ( order @ TB @ ( type2 @ TB ) )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less_eq @ TA @ A @ ( B @ C ) )
| ~ ( ord_less @ TB @ C @ D )
| ( ord_less @ TB @ ( sk3 @ TB @ TA @ D @ C @ B @ A ) @ ( sk4 @ TB @ TA @ D @ C @ B @ A ) )
| ( ord_less @ TA @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[312]) ).
thf(5776,plain,
( ~ $true
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[673,2957]) ).
thf(5777,plain,
( ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) ) ) ),
inference(simp,[status(thm)],[5776]) ).
thf(5868,plain,
( ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) ) ),
inference(simp,[status(thm)],[5777]) ).
thf(5908,plain,
( ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns ) ),
inference(simp,[status(thm)],[5868]) ).
thf(786,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(cnf,[status(esa)],[785]) ).
thf(787,plain,
! [TA: $tType] :
( ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) )
= ( ord_less @ ( set @ TA ) ) ),
inference(lifteq,[status(thm)],[786]) ).
thf(6063,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[696,3910]) ).
thf(6064,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(simp,[status(thm)],[6063]) ).
thf(6065,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( x != x )
| ( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[6064]) ).
thf(6091,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[6065]) ).
thf(266,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_empty__iff) ).
thf(1058,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(783,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(cnf,[status(esa)],[782]) ).
thf(784,plain,
! [TA: $tType] :
( ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) )
= ( (=) @ ( set @ TA ) ) ),
inference(lifteq,[status(thm)],[783]) ).
thf(262,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_5) ).
thf(1048,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(303,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB,B: TB > TA,A: TA] :
( ~ ( order @ TB @ ( type2 @ TB ) )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less @ TA @ A @ ( B @ C ) )
| ~ ( ord_less_eq @ TB @ C @ D )
| ~ ( ord_less_eq @ TA @ ( B @ ( sk1 @ TB @ TA @ D @ C @ B @ A ) ) @ ( B @ ( sk2 @ TB @ TA @ D @ C @ B @ A ) ) )
| ( ord_less @ TA @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[301]) ).
thf(239,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( pairwise @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_pairwise__singleton) ).
thf(979,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( pairwise @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(111,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_ComplI) ).
thf(604,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(36,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_136_eq__refl) ).
thf(377,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)],[36]) ).
thf(243,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_55_equalityD2) ).
thf(990,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)],[243]) ).
thf(245,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_insert__absorb) ).
thf(996,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(158,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( minus_minus @ TA @ A @ B ) )
= ( minus_minus @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_minus__diff__eq) ).
thf(737,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( minus_minus @ TA @ A @ B ) )
= ( minus_minus @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_uminus__apply) ).
thf(509,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(648,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(cnf,[status(esa)],[647]) ).
thf(649,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(lifteq,[status(thm)],[648]) ).
thf(261,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Set_Oset__insert) ).
thf(1043,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(58,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_204_dual__order_Oorder__iff__strict) ).
thf(434,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)],[58]) ).
thf(88,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(535,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)],[88]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_DiffD2) ).
thf(609,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(68,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_216_le__imp__less__or__eq) ).
thf(483,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)],[68]) ).
thf(10755,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( xs2 != xs ) ),
inference(simp,[status(thm)],[9287]) ).
thf(39,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_226_not__less) ).
thf(387,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)],[39]) ).
thf(227,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_57_subset__iff) ).
thf(943,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)],[227]) ).
thf(1022,plain,
( xs3
= ( coinductive_LCons @ a @ n2 @ xs2 ) ),
inference(lifteq,[status(thm)],[1021]) ).
thf(241,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_60_Collect__mono) ).
thf(983,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)],[241]) ).
thf(44,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_208_dual__order_Ostrict__trans2) ).
thf(399,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)],[44]) ).
thf(251,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Diff__insert) ).
thf(1015,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(8,axiom,
boolean_algebra @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_9) ).
thf(299,plain,
boolean_algebra @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9921,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( coinductive_lset @ a @ xs ) )
| ( sk56 != xs ) ),
inference(simp,[status(thm)],[9285]) ).
thf(136,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_equals0I) ).
thf(685,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(82,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_compl__eq__compl__iff) ).
thf(521,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(42,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_225_le__neq__trans) ).
thf(394,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)],[42]) ).
thf(218,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_diff__strict__right__mono) ).
thf(922,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(274,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_54_equalityD1) ).
thf(1076,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)],[274]) ).
thf(162,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_subset__insert) ).
thf(749,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(117,axiom,
member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ xs2 ) @ ( koenig916195507_paths @ a @ graph ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_path_H) ).
thf(617,plain,
member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ xs2 ) @ ( koenig916195507_paths @ a @ graph ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(225,axiom,
member @ a @ x @ ( koenig317145564le_via @ a @ graph @ ns @ n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__092_060open_062x_A_092_060in_062_Areachable__via_Agraph_Ans_An_092_060close_062) ).
thf(939,plain,
member @ a @ x @ ( koenig317145564le_via @ a @ graph @ ns @ n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(185,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o,D: TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( A != D )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ E ) @ ( koenig916195507_paths @ TA @ C ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ ( coinductive_lset @ TA @ B ) )
& ( member @ TA @ D @ ( coinductive_lset @ TA @ E ) )
& ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_path__avoid__node) ).
thf(823,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o,D: TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( ( member @ TA @ D @ ( coinductive_lset @ TA @ B ) )
=> ( ( A != D )
=> ? [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ E ) @ ( koenig916195507_paths @ TA @ C ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ ( coinductive_lset @ TA @ B ) )
& ( member @ TA @ D @ ( coinductive_lset @ TA @ E ) )
& ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1049,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[1048]) ).
thf(71,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_12) ).
thf(490,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(675,plain,
~ ( member @ a @ n2 @ ( coinductive_lset @ a @ sk43 ) ),
inference(cnfConj,[status(thm)],[671]) ).
thf(175,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_44_set__mp) ).
thf(795,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)],[175]) ).
thf(134,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_subset__singletonD) ).
thf(680,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(220,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Diff__cancel) ).
thf(927,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(35,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_144_le__fun__def) ).
thf(374,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)],[35]) ).
thf(169,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_diff__eq__diff__less) ).
thf(776,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(201,axiom,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ ( coinductive_lset @ a @ xs2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__092_060open_062lset_Axs_H_H_A_092_060subseteq_062_Alset_Axs_H_092_060close_062) ).
thf(872,plain,
ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs ) @ ( coinductive_lset @ a @ xs2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(789,plain,
~ ! [A: a,B: coinductive_llist @ a] :
( xs3
!= ( coinductive_LCons @ a @ A @ B ) ),
inference(polarity_switch,[status(thm)],[788]) ).
thf(790,plain,
~ ~ ? [A: a,B: coinductive_llist @ a] :
( xs3
= ( coinductive_LCons @ a @ A @ B ) ),
inference(miniscope,[status(thm)],[789]) ).
thf(791,plain,
( xs3
= ( coinductive_LCons @ a @ sk48 @ sk49 ) ),
inference(cnf,[status(esa)],[790]) ).
thf(792,plain,
( xs3
= ( coinductive_LCons @ a @ sk48 @ sk49 ) ),
inference(lifteq,[status(thm)],[791]) ).
thf(3071,plain,
( ~ $true
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs3 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[843,283]) ).
thf(3072,plain,
( ( member @ a @ x @ ( coinductive_lset @ a @ xs3 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[3071]) ).
thf(3074,plain,
( ( x != x )
| ( ( coinductive_lset @ a @ xs3 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[3072]) ).
thf(3078,plain,
( ( coinductive_lset @ a @ xs3 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ),
inference(simp,[status(thm)],[3074]) ).
thf(3259,plain,
( ( ( coinductive_lset @ a @ ( coinductive_LCons @ a @ sk48 @ sk49 ) )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) )
| ( xs3 != xs3 ) ),
inference(paramod_ordered,[status(thm)],[792,3078]) ).
thf(3260,plain,
( ( coinductive_lset @ a @ ( coinductive_LCons @ a @ sk48 @ sk49 ) )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[3259:[]]) ).
thf(13,axiom,
order_bot @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_10) ).
thf(310,plain,
order_bot @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(105,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] : ( C @ D @ ( coinductive_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coinductive_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_llist_Oset__induct) ).
thf(580,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] : ( C @ D @ ( coinductive_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coinductive_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(195,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_249_psubsetE) ).
thf(855,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)],[195]) ).
thf(255,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Diff__empty) ).
thf(1025,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(294,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
| ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[293]) ).
thf(295,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) )
| ~ ( ordered_ab_group_add @ TA @ ( type2 @ TA ) ) ),
inference(lifteq,[status(thm)],[294]) ).
thf(264,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_diff__strict__mono) ).
thf(1053,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(7691,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ~ ( ord_less @ TA @ A @ ( bot_bot @ TA ) )
| ( ( order_bot @ $o @ ( type2 @ $o ) )
!= ( order_bot @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[310,692]) ).
thf(7692,plain,
! [TA: $tType,A: TA] :
( ~ ( ord_less @ TA @ A @ ( bot_bot @ TA ) )
| ( ( order_bot @ $o @ ( type2 @ $o ) )
!= ( order_bot @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[7691]) ).
thf(7693,plain,
! [A: $o] :
~ ( ord_less @ $o @ A @ ( bot_bot @ $o ) ),
inference(pattern_uni,[status(thm)],[7692:[bind_type(TA,$thf( $o ))]]) ).
thf(21,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_129_ord__le__eq__trans) ).
thf(331,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)],[21]) ).
thf(60,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_double__compl) ).
thf(441,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(6057,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs2 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[611,3910]) ).
thf(6058,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs2 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(simp,[status(thm)],[6057]) ).
thf(6066,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( x != x )
| ( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[6058]) ).
thf(6093,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[6066]) ).
thf(214,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_diff__eq__diff__eq) ).
thf(907,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(259,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_singleton__insert__inj__eq_H) ).
thf(1038,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(106,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_llist_Oset__intros_I2_J) ).
thf(585,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(143,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_51_subsetCE) ).
thf(703,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)],[143]) ).
thf(254,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insertI2) ).
thf(1023,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1259,plain,
! [B: a,A: a] :
( ~ ( order @ a @ ( type2 @ a ) )
| ~ ( ord_less_eq @ a @ A @ B )
| ~ ( ord_less_eq @ a @ B @ A )
| ( B != n2 )
| ( A != x ) ),
inference(paramod_ordered,[status(thm)],[289,904]) ).
thf(1260,plain,
! [A: a] :
( ~ ( order @ a @ ( type2 @ a ) )
| ~ ( ord_less_eq @ a @ x @ A )
| ~ ( ord_less_eq @ a @ A @ x )
| ( A != n2 ) ),
inference(pattern_uni,[status(thm)],[1259:[bind(A,$thf( x ))]]) ).
thf(1353,plain,
( ~ ( order @ a @ ( type2 @ a ) )
| ~ ( ord_less_eq @ a @ x @ n2 )
| ~ ( ord_less_eq @ a @ n2 @ x ) ),
inference(simp,[status(thm)],[1260]) ).
thf(198,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_29_subset__antisym) ).
thf(864,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)],[198]) ).
thf(314,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB,B: TB > TA,A: TA] :
( ~ ( order @ TB @ ( type2 @ TB ) )
| ~ ( order @ TA @ ( type2 @ TA ) )
| ~ ( ord_less_eq @ TA @ A @ ( B @ C ) )
| ~ ( ord_less @ TB @ C @ D )
| ~ ( ord_less @ TA @ ( B @ ( sk3 @ TB @ TA @ D @ C @ B @ A ) ) @ ( B @ ( sk4 @ TB @ TA @ D @ C @ B @ A ) ) )
| ( ord_less @ TA @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[312]) ).
thf(102,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(571,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(3914,plain,
( ( coinductive_lset @ a @ ( coinductive_LCons @ a @ n2 @ xs2 ) )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ),
inference(rewrite,[status(thm)],[3078,1022]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Compl__anti__mono) ).
thf(612,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(63,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_131_antisym__conv) ).
thf(450,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)],[63]) ).
thf(97,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_146_le__funE) ).
thf(556,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)],[97]) ).
thf(83,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(524,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(208,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_246_psubset__subset__trans) ).
thf(891,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)],[208]) ).
thf(249,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ C @ D ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ D ) )
& ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_subset__Diff__insert) ).
thf(1010,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ C @ D ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ D ) )
& ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(191,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_mk__disjoint__insert) ).
thf(844,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(282,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insertCI) ).
thf(1108,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(238,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_insert__ident) ).
thf(976,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1837,plain,
( ~ $true
| ( ( member @ a @ x @ ( coinductive_lset @ a @ xs2 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[611,283]) ).
thf(1838,plain,
( ( member @ a @ x @ ( coinductive_lset @ a @ xs2 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[1837]) ).
thf(1840,plain,
( ( x != x )
| ( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[1838]) ).
thf(1844,plain,
( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ( bot_bot @ ( set @ a ) ) ) ) @ n2 ) ) ),
inference(simp,[status(thm)],[1840]) ).
thf(137,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Diff__insert2) ).
thf(688,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1876,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs3 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( bot_bot @ ( set @ a ) ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[646,1414]) ).
thf(1877,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs3 ) @ ns )
!= ( ord_less_eq @ ( set @ a ) @ ( bot_bot @ ( set @ a ) ) @ A ) ) ),
inference(simp,[status(thm)],[1876]) ).
thf(1879,plain,
! [A: set @ a] :
( ~ ( ord_less_eq @ ( set @ a ) @ A @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ A ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ xs3 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ns != A ) ),
inference(simp,[status(thm)],[1877]) ).
thf(1884,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ xs3 )
!= ( bot_bot @ ( set @ a ) ) ) ),
inference(simp,[status(thm)],[1879]) ).
thf(5258,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ ( coinductive_LCons @ a @ n2 @ xs2 ) )
!= ( bot_bot @ ( set @ a ) ) ) ),
inference(rewrite,[status(thm)],[1884,1022]) ).
thf(181,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_subset__emptyI) ).
thf(813,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(210,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Collect__empty__eq__bot) ).
thf(896,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(268,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
= ( ? [E: coinductive_llist @ TA,F: TA] :
( ( A = F )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) )
& ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_reachable__via_Osimps) ).
thf(1062,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
= ( ? [E: coinductive_llist @ TA,F: TA] :
( ( A = F )
& ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) )
& ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
& ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(228,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_insert__Diff__single) ).
thf(946,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(40,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(390,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(45,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_minus__le__iff) ).
thf(401,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(780,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
| ( A = B ) ) ) ),
inference(cnf,[status(esa)],[779]) ).
thf(781,plain,
! [TA: $tType] :
( ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
| ( A = B ) ) )
= ( ord_less_eq @ ( set @ TA ) ) ),
inference(lifteq,[status(thm)],[780]) ).
thf(234,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_equals0D) ).
thf(963,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(80,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_compl__mono) ).
thf(517,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(11745,plain,
( ( xs2 != xs )
| ( ( coinductive_lset @ a @ sk43 )
!= ns ) ),
inference(simp,[status(thm)],[10830]) ).
thf(127,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_the__elem__eq) ).
thf(652,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(28,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_220_less__le__trans) ).
thf(351,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)],[28]) ).
thf(731,plain,
! [TA: $tType,A: set @ TA] :
~ ( ord_less @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[730]) ).
thf(50,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_235_leD) ).
thf(418,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)],[50]) ).
thf(257,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
=> ~ ! [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ~ ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_reachable__via_Ocases) ).
thf(1030,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( koenig317145564le_via @ TA @ B @ C @ D ) )
=> ~ ! [E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ D @ E ) @ ( koenig916195507_paths @ TA @ B ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ~ ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_singleton__insert__inj__eq) ).
thf(568,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(67,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_206_dense__le__bounded) ).
thf(478,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)],[67]) ).
thf(211,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_insert__subset) ).
thf(899,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(26,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(346,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(93,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_202_dual__order_Ostrict__implies__order) ).
thf(549,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)],[93]) ).
thf(177,axiom,
graph @ n @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__092_060open_062graph_An_An_H_092_060close_062) ).
thf(800,plain,
graph @ n @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(163,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Diff__idemp) ).
thf(752,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(15,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_138_antisym) ).
thf(315,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)],[15]) ).
thf(281,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_lset__induct_H) ).
thf(1097,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TA @ ( type2 @ TA ) )
=> ( minus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ominus) ).
thf(422,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TA @ ( type2 @ TA ) )
=> ( minus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(199,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_Compl__iff) ).
thf(867,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(246,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_insertI1) ).
thf(999,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(57,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_124_dual__order_Otrans) ).
thf(432,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)],[57]) ).
thf(6805,plain,
( ~ $true
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[673,5905]) ).
thf(6806,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ sk43 ) @ ( coinductive_lset @ a @ xs2 ) )
!= ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) ) ) ),
inference(simp,[status(thm)],[6805]) ).
thf(6809,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns )
| ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) ) ),
inference(simp,[status(thm)],[6806]) ).
thf(6822,plain,
( ( ( coinductive_lset @ a @ xs2 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ xs2 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ns ) ),
inference(simp,[status(thm)],[6809]) ).
thf(186,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ~ ( member @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_subset__Compl__singleton) ).
thf(833,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ~ ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(47,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_211_order_Oorder__iff__strict) ).
thf(410,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)],[47]) ).
thf(235,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( insert @ TA @ A @ ( coinductive_lset @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_lset__LCons) ).
thf(967,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( insert @ TA @ A @ ( coinductive_lset @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_le__minus__iff) ).
thf(326,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(76,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_232_less__le) ).
thf(506,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)],[76]) ).
thf(233,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_insert__iff) ).
thf(960,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(49,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_222_antisym__conv2) ).
thf(415,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)],[49]) ).
thf(216,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_56_set__rev__mp) ).
thf(918,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)],[216]) ).
thf(178,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB @ ( type2 @ TB ) )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_minus__apply) ).
thf(801,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB @ ( type2 @ TB ) )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(59,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_230_order__le__less__subst2) ).
thf(437,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)],[59]) ).
thf(1683,plain,
( ~ $true
| ( ( member @ a @ n2 @ ns )
!= ( member @ a @ n2 @ ( coinductive_lset @ a @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[933,675]) ).
thf(1684,plain,
( ( member @ a @ n2 @ ns )
!= ( member @ a @ n2 @ ( coinductive_lset @ a @ sk43 ) ) ),
inference(simp,[status(thm)],[1683]) ).
thf(1688,plain,
( ( n2 != n2 )
| ( ns
!= ( coinductive_lset @ a @ sk43 ) ) ),
inference(simp,[status(thm)],[1684]) ).
thf(1693,plain,
( ns
!= ( coinductive_lset @ a @ sk43 ) ),
inference(simp,[status(thm)],[1688]) ).
thf(87,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_139_eq__iff) ).
thf(532,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)],[87]) ).
thf(269,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_singletonI) ).
thf(1065,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(280,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_DiffE) ).
thf(1093,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(242,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( insert @ TA @ A @ ( coinductive_lset @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_llist_Osimps_I19_J) ).
thf(987,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( insert @ TA @ A @ ( coinductive_lset @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(11824,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
( ~ $true
| ( bot @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
| ( ( bot @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TR @ ( type2 @ TR ) ) ) ),
inference(paramod_ordered,[status(thm)],[11512,305]) ).
thf(11825,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
( ( bot @ ( TQ > TR ) @ ( type2 @ ( TQ > TR ) ) )
| ( ( bot @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) )
!= ( bot @ TR @ ( type2 @ TR ) ) ) ),
inference(simp,[status(thm)],[11824]) ).
thf(11826,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( bot @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) @ ( type2 @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ) ),
inference(pattern_uni,[status(thm)],[11825:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).
thf(85,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_compl__le__swap2) ).
thf(528,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(123,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_empty__subsetI) ).
thf(644,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(152,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_paths__LConsD) ).
thf(723,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( koenig916195507_paths @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( koenig916195507_paths @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(193,axiom,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( bot_bot @ TA ) )
= ( ord_less @ TA @ ( bot_bot @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_bot_Onot__eq__extremum) ).
thf(850,plain,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( bot_bot @ TA ) )
= ( ord_less @ TA @ ( bot_bot @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(248,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_lset__cases) ).
thf(1004,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(74,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_234_leI) ).
thf(501,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)],[74]) ).
thf(154,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_diff__mono) ).
thf(728,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(159,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_192_psubsetI) ).
thf(740,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)],[159]) ).
thf(69,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_less__minus__iff) ).
thf(486,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(23,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_227_not__le) ).
thf(337,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)],[23]) ).
thf(226,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_Compl__eq__Compl__iff) ).
thf(940,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(91,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_215_less__le__not__le) ).
thf(543,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)],[91]) ).
thf(775,plain,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[774]) ).
thf(32,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_205_order_Ostrict__implies__order) ).
thf(364,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)],[32]) ).
thf(5987,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ~ $true
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk43 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[674,3910]) ).
thf(5988,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( member @ a @ x @ ( coinductive_lset @ a @ sk43 ) )
!= ( member @ a @ x @ ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ) ),
inference(simp,[status(thm)],[5987]) ).
thf(6067,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( x != x )
| ( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[5988]) ).
thf(6094,plain,
( ~ ( ord_less_eq @ ( set @ a ) @ ns @ ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk56 )
!= ( bot_bot @ ( set @ a ) ) )
| ( ( coinductive_lset @ a @ sk43 )
!= ( insert @ a @ n2 @ ( koenig317145564le_via @ a @ graph @ ( minus_minus @ ( set @ a ) @ ns @ ( insert @ a @ n2 @ ns ) ) @ n2 ) ) ) ),
inference(simp,[status(thm)],[6067]) ).
thf(12,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(309,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(130,axiom,
( ( n2 != x )
=> ? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ A ) @ ( koenig916195507_paths @ a @ graph ) )
& ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ( coinductive_lset @ a @ xs2 ) )
& ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
& ~ ( member @ a @ n2 @ ( coinductive_lset @ a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__092_060open_062n_H_A_092_060noteq_062_Ax_A_092_060Longrightarrow_062_A_092_060exists_062xs_Ha_O_ALCons_An_H_Axs_Ha_A_092_060in_062_Apaths_Agraph_A_092_060and_062_Alset_Axs_Ha_A_092_060subseteq_062_Alset_Axs_H_A_092_060and_062_Ax_A_092_060in_062_Alset_Axs_Ha_A_092_060and_062_An_H_A_092_060notin_062_Alset_Axs_Ha_092_060close_062) ).
thf(659,plain,
( ( n2 != x )
=> ? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n2 @ A ) @ ( koenig916195507_paths @ a @ graph ) )
& ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ A ) @ ( coinductive_lset @ a @ xs2 ) )
& ( member @ a @ x @ ( coinductive_lset @ a @ A ) )
& ~ ( member @ a @ n2 @ ( coinductive_lset @ a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(132,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_61_subset__trans) ).
thf(676,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)],[132]) ).
thf(72,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_140_ord__le__eq__subst) ).
thf(491,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)],[72]) ).
thf(15940,plain,
$false,
inference(e,[status(thm)],[760,893,1083,555,11659,683,730,1068,10673,994,308,1073,3910,873,655,614,1692,1041,861,384,6246,797,1919,340,538,930,404,1001,782,709,841,7729,5903,320,973,885,651,2957,1055,9287,719,785,344,3845,934,949,372,5910,587,838,11512,870,606,881,289,448,817,902,638,853,1013,284,924,756,321,623,646,1960,353,905,574,1020,348,397,9749,7931,1215,692,734,453,774,428,849,9896,981,766,293,956,292,920,512,678,810,381,366,1067,10855,546,793,910,957,746,1021,952,12510,302,862,598,820,392,424,693,788,815,566,879,329,461,6096,551,842,324,361,7555,757,5658,519,650,725,356,420,499,697,1089,884,10830,933,554,669,476,489,590,970,706,1028,1082,1414,526,5905,1644,647,701,5498,721,6450,8995,11610,779,503,622,837,10575,1060,1050,1086,311,9044,541,657,1035,674,530,10624,558,1071,718,888,298,6314,425,296,444,11561,733,601,618,5483,513,430,9798,732,9142,843,286,743,579,413,562,904,875,577,711,641,713,6649,335,1090,804,5556,9285,936,1707,313,611,5908,787,6091,1058,784,1048,303,979,604,377,990,996,737,318,509,880,649,1043,434,1080,535,609,483,10755,10450,387,943,1022,983,399,10020,883,1015,299,9921,5693,685,521,394,306,6212,922,1076,749,617,939,1018,823,836,1049,490,675,795,680,927,374,776,5624,7635,872,705,3260,310,580,855,9847,1025,295,1053,6280,673,7693,331,441,6093,9313,9093,907,1038,585,703,1023,7515,1353,864,314,859,7595,571,3914,612,450,9192,556,10526,524,891,5907,1010,844,1108,976,1844,688,5258,813,319,896,304,1062,946,390,10447,401,781,963,517,11745,652,351,731,418,1030,568,290,478,899,5590,346,549,716,800,287,300,752,315,1097,422,867,999,620,432,6822,833,410,967,305,326,506,960,696,955,283,415,918,801,437,1693,532,1065,1093,987,11826,528,644,723,850,1004,691,501,728,740,322,486,337,940,543,775,364,6094,309,659,755,676,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM176^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:50:56 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.08/1.17 % [INFO] Parsing done (393ms).
% 2.08/1.19 % [INFO] Running in sequential loop mode.
% 3.73/1.62 % [INFO] eprover registered as external prover.
% 3.73/1.63 % [INFO] Scanning for conjecture ...
% 3.93/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 281 axioms. Running axiom selection ...
% 4.48/1.93 % [INFO] Axiom selection finished. Selected 280 axioms (removed 1 axioms).
% 5.32/2.18 % [INFO] Problem is higher-order (TPTP THF).
% 5.59/2.20 % [INFO] Type checking passed.
% 5.59/2.21 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 141.45/42.14 % External prover 'e' found a proof!
% 141.45/42.14 % [INFO] Killing All external provers ...
% 141.45/42.14 % Time passed: 41808ms (effective reasoning time: 40939ms)
% 141.45/42.14 % 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)>
% 141.45/42.15 % Axioms used in derivation (280): fact_61_subset__trans, tcon_fun___Orderings_Obot, fact_237_diff__eq__diff__less, fact_64_Collect__mono__iff, fact_220_less__le__trans, fact_65_path__avoid__node, fact_42__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_H_H_O_A_092_060lbrakk_062LCons_An_H_Axs_H_H_A_092_060in_062_Apaths_Agraph_059_Alset_Axs_H_H_A_092_060subseteq_062_Alset_Axs_H_059_Ax_A_092_060in_062_Alset_Axs_H_H_059_An_H_A_092_060notin_062_Alset_Axs_H_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, tcon_fun___Groups_Ominus, fact_73_reachable__via_Ointros, fact_35_DiffI, fact_203_dual__order_Ostrict__iff__order, fact_112_llist_Oinject, fact_142_order__subst2, fact_121_is__singleton__the__elem, fact_18_Diff__empty, fact_223_antisym__conv1, fact_41_Diff__eq__empty__iff, fact_221_le__less__trans, fact_98_Diff__single__insert, fact_148_fun__diff__def, fact_145_le__funI, fact_131_antisym__conv, fact_10__092_060open_062x_A_092_060in_062_Areachable__via_Agraph_Ans_An_092_060close_062, fact_78_Diff__mono, fact_248_psubset__eq, fact_173_member__remove, fact_124_dual__order_Otrans, fact_108_insert__Diff, fact_168_diff__eq__diff__less__eq, fact_116_order__refl, fact_101_insert__not__empty, fact_3_xs, fact_249_psubsetE, fact_5_False, fact_218_dense__le, fact_254_ComplD, fact_165_diff__left__mono, fact_31_insert__iff, fact_90_insertI1, fact_149_bot__fun__def, fact_226_not__less, fact_43__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062LCons_An_Axs_A_092_060in_062_Apaths_Agraph_059_Ax_A_092_060in_062_Alset_Axs_059_Alset_Axs_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_113_the__elem__eq, tcon_HOL_Obool___Orderings_Oorder__bot_10, fact_252_less__minus__iff, fact_22__092_060open_062n_H_A_092_060noteq_062_Ax_A_092_060Longrightarrow_062_A_092_060exists_062xs_Ha_O_ALCons_An_H_Axs_Ha_A_092_060in_062_Apaths_Agraph_A_092_060and_062_Alset_Axs_Ha_A_092_060subseteq_062_Alset_Axs_H_A_092_060and_062_Ax_A_092_060in_062_Alset_Axs_Ha_A_092_060and_062_An_H_A_092_060notin_062_Alset_Axs_Ha_092_060close_062, fact_171_Collect__empty__eq__bot, fact_156_llist_Oset__cases, fact_225_le__neq__trans, fact_154_bot_Oextremum__uniqueI, fact_11__092_060open_062graph_An_An_H_092_060close_062, fact_196_minus__le__iff, fact_175_gen__lset__code_I2_J, fact_27_empty__iff, tcon_HOL_Obool___Groups_Ominus_16, fact_160_llist_Oset__intros_I1_J, fact_12_path_H, fact_55_equalityD2, fact_87_insert__ident, fact_134_le__cases, fact_244_subset__psubset__trans, fact_195_le__imp__neg__le, fact_200_compl__mono, fact_229_order__less__le__subst1, fact_79_ex__in__conv, tcon_fun___Orderings_Oord, fact_17_insert__Diff1, fact_191_minus__diff__eq, fact_205_order_Ostrict__implies__order, fact_186_Compl__iff, fact_85_insert__eq__iff, fact_91_insertE, fact_147_le__funD, tcon_HOL_Obool___Orderings_Olinorder, fact_197_le__minus__iff, fact_97_subset__Diff__insert, tcon_Set_Oset___Orderings_Oord_5, fact_162_insert__subsetI, fact_152_bot_Oextremum, fact_232_less__le, fact_150_is__singletonE, tcon_Set_Oset___Orderings_Oorder__bot_2, fact_96_subset__singletonD, fact_170_bot__empty__eq, fact_184_compl__eq__compl__iff, tcon_HOL_Obool___Orderings_Opreorder_11, fact_102_doubleton__eq__iff, fact_216_le__imp__less__or__eq, fact_29_subset__antisym, fact_243_subset__iff__psubset__eq, fact_60_Collect__mono, fact_52_equalityE, fact_206_dense__le__bounded, tcon_HOL_Obool___Lattices_Oboolean__algebra_9, fact_50_subsetD, fact_2__092_060open_062x_A_092_060in_062_Alset_Axs_H_H_092_060close_062, fact_111_llist_Osimps_I19_J, fact_193_Compl__anti__mono, fact_136_eq__refl, fact_130_ord__eq__le__trans, fact_86_insert__absorb, fact_19_empty__Diff, fact_46_Collect__mem__eq, fact_204_dual__order_Oorder__iff__strict, fact_67_paths_OLCons, fact_14_path, fact_227_not__le, fact_192_psubsetI, fact_161_llist_Oset__intros_I2_J, fact_247_psubset__imp__subset, fact_122_is__singletonI_H, fact_133_order_Otrans, fact_72_reachable__via_Oinducts, fact_26_all__not__in__conv, fact_141_ord__eq__le__subst, fact_127_order__trans, fact_92_DiffD2, fact_21_singletonI, fact_9__092_060open_062x_A_092_060in_062_Alset_Axs_H_092_060close_062, fact_16_Diff__insert0, fact_255_psubsetD, fact_213_order_Ostrict__trans1, fact_40_singleton__insert__inj__eq, fact_140_ord__le__eq__subst, fact_181_neg__equal__iff__equal, fact_119_lset__intros_I1_J, fact_62_set__eq__subset, fact_128_order__class_Oorder_Oantisym, fact_59_subset__refl, fact_110_lset__LCons, fact_187_Compl__eq__Compl__iff, fact_39_singleton__insert__inj__eq_H, tcon_HOL_Obool___Orderings_Oorder_12, fact_49_in__mono, fact_207_dense__ge__bounded, fact_176_Set_Ois__empty__def, fact_76_double__diff, fact_217_le__less__linear, fact_71_Set_Oinsert__mono, fact_188_neg__le__iff__le, fact_45_mem__Collect__eq, fact_139_eq__iff, fact_58_rev__subsetD, fact_77_Diff__subset, fact_236_diff__strict__mono, fact_84_insert__commute, fact_89_insertI2, fact_70_subset__insert, fact_242_not__psubset__empty, tcon_Set_Oset___Orderings_Obot_6, fact_235_leD, fact_157_lset__induct_H, tcon_Set_Oset___Orderings_Opreorder_3, fact_245_subset__not__subset__eq, fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_Axs_H_O_Axs_A_061_ALCons_An_H_Axs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_163_subset__emptyI, fact_224_less__imp__le, fact_228_order__less__le__subst2, fact_33_Diff__idemp, fact_57_subset__iff, fact_214_not__le__imp__less, fact_24_empty__Collect__eq, fact_8__092_060open_062n_H_A_092_060in_062_Ans_092_060close_062, fact_68_subset__insertI2, fact_25_Collect__empty__eq, fact_185_ComplI, fact_6__092_060open_062x_A_092_060in_062_Alset_Axs_092_060close_062, fact_190_neg__less__iff__less, fact_30_insert__absorb2, fact_104_singletonD, fact_240_bot_Oextremum__strict, fact_212_order_Ostrict__trans2, tcon_Set_Oset___Groups_Ouminus_7, fact_129_ord__le__eq__trans, fact_146_le__funE, fact_117_is__singletonI, fact_103_singleton__iff, fact_47_Collect__cong, fact_81_equals0D, fact_209_dual__order_Ostrict__trans1, fact_241_bot_Onot__eq__extremum, fact_95_subset__singleton__iff, fact_239_diff__strict__right__mono, fact_238_diff__strict__left__mono, fact_182_uminus__apply, tcon_fun___Lattices_Oboolean__algebra, fact_167_diff__eq__diff__eq, fact_75_reachable__via_Ocases, fact_15_insert__Diff__single, fact_100_singleton__inject, fact_82_emptyE, fact_151_is__singleton__def, fact_198_compl__le__swap2, tcon_fun___Orderings_Oorder__bot, fact_132_le__cases3, fact_174_lset__code, fact_234_leI, tcon_HOL_Obool___Orderings_Obot_14, fact_222_antisym__conv2, fact_69_subset__insertI, fact_109_Diff__insert, fact_38_insert__subset, fact_106_Diff__insert__absorb, fact_199_compl__le__swap1, fact_180_add_Oinverse__inverse, fact_80_equals0I, tcon_Set_Oset___Lattices_Oboolean__algebra_1, tcon_HOL_Obool___Orderings_Oord_13, fact_155_llist_Oset__induct, fact_138_antisym, tcon_fun___Orderings_Opreorder, fact_20_Diff__cancel, tcon_HOL_Obool___Groups_Ouminus_15, fact_54_equalityD1, fact_183_double__compl, fact_123_dual__order_Oantisym, fact_179_subset__Compl__singleton, fact_194_Compl__subset__Compl__iff, fact_178_pairwise__singleton, fact_105_insert__Diff__if, fact_158_lset__induct, fact_189_compl__le__compl__iff, fact_63_contra__subsetD, fact_201_order_Onot__eq__order__implies__strict, fact_126_dual__order_Orefl, fact_153_bot_Oextremum__unique, fact_34_Diff__iff, fact_210_order_Ostrict__iff__order, fact_51_subsetCE, fact_159_lset__cases, fact_208_dual__order_Ostrict__trans2, fact_172_remove__def, fact_164_diff__mono, fact_37_subset__empty, tcon_fun___Orderings_Oorder, fact_144_le__fun__def, fact_83_mk__disjoint__insert, fact_7_path_H_H, fact_4__092_060open_062lset_Axs_A_092_060subseteq_062_Ans_092_060close_062, fact_88_Set_Oset__insert, fact_115_minus__apply, fact_32_insertCI, fact_107_Diff__insert2, fact_13__092_060open_062lset_Axs_H_A_092_060subseteq_062_Ans_092_060close_062, tcon_fun___Groups_Ouminus, fact_233_le__less, fact_74_reachable__via_Osimps, fact_166_diff__right__commute, fact_94_DiffE, fact_135_wlog__linorder__le, fact_0__092_060open_062n_H_A_092_060notin_062_Alset_Axs_H_H_092_060close_062, fact_66_paths__LConsD, fact_230_order__le__less__subst2, fact_177_psubset__insert__iff, fact_118_lset__intros_I2_J, fact_143_order__subst1, fact_211_order_Oorder__iff__strict, fact_53_subset__eq, fact_231_order__le__less__subst1, fact_36_empty__subsetI, fact_246_psubset__subset__trans, fact_137_linear, fact_23__092_060open_062lset_Axs_H_H_A_092_060subseteq_062_Alset_Axs_H_092_060close_062, fact_253_minus__less__iff, fact_251_minus__equation__iff, fact_169_diff__right__mono, fact_44_set__mp, fact_93_DiffD1, fact_125_linorder__wlog, fact_99_subset__insert__iff, fact_114_bot__apply, tcon_Set_Oset___Groups_Ominus_8, fact_219_dense__ge, fact_28_subsetI, fact_56_set__rev__mp, fact_250_equation__minus__iff, fact_202_dual__order_Ostrict__implies__order, fact_120_bot__set__def, fact_215_less__le__not__le, tcon_Set_Oset___Orderings_Oorder_4
% 141.45/42.15 % No. of inferences in proof: 888
% 141.45/42.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 41808 ms resp. 40939 ms w/o parsing
% 132.68/42.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 132.68/42.48 % [INFO] Killing All external provers ...
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