TSTP Solution File: COM181^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COM181^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:30:15 EDT 2024
% Result : Theorem 62.97s 39.07s
% Output : Refutation 63.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 317
% Syntax : Number of formulae : 596 ( 199 unt; 40 typ; 0 def)
% Number of atoms : 2022 ( 430 equ; 6 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 7705 ( 234 ~; 14 |; 124 &;6761 @)
% ( 0 <=>; 572 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 362 ( 362 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 46 usr; 14 con; 0-5 aty)
% Number of variables : 2014 ( 190 ^1736 !; 40 ?;2014 :)
% ( 37 !>; 0 ?*; 0 @-; 11 @+)
% Comments :
%------------------------------------------------------------------------------
thf(node_type,type,
node: $tType ).
thf(uminus_type,type,
uminus:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bot_type,type,
bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(top_type,type,
top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_bot_type,type,
order_bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(boolean_algebra_type,type,
boolean_algebra:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coinductive_lfinite_type,type,
coinductive_lfinite:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lnull_type,type,
coinductive_lnull:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lset_type,type,
coinductive_lset:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( set @ TA ) ) ).
thf(coinductive_ltl_type,type,
coinductive_ltl:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(finite_finite2_type,type,
finite_finite2:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(uminus_uminus_type,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(koenig793108494nected_type,type,
koenig793108494nected:
!>[TA: $tType] : ( ( TA > TA > $o ) > $o ) ).
thf(koenig916195507_paths_type,type,
koenig916195507_paths:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(koenig317145564le_via_type,type,
koenig317145564le_via:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > TA > ( set @ TA ) ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_rec_prod_type,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_case_prod_type,type,
product_case_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(ltl_type,type,
ltl: ( product_prod @ node @ ( set @ node ) ) > ( product_prod @ node @ ( set @ node ) ) ).
thf(f_type,type,
f: ( product_prod @ node @ ( set @ node ) ) > ( coinductive_llist @ node ) ).
thf(graph_type,type,
graph: node > node > $o ).
thf(n_type,type,
n: node ).
thf(na_type,type,
na: node ).
thf(ns_type,type,
ns: set @ node ).
thf(nsa_type,type,
nsa: set @ node ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',fact_222_le__fun__def) ).
thf(325,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)],[18]) ).
thf(277,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_insertI1) ).
thf(1105,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',fact_223_le__funI) ).
thf(347,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)],[26]) ).
thf(177,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_singletonI) ).
thf(846,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(196,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( bot_bot @ TA ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_compl__bot__eq) ).
thf(893,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( bot_bot @ TA ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(269,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Collect__conv__if) ).
thf(1083,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_old_Oprod_Oinject) ).
thf(666,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',fact_217_eq__iff) ).
thf(352,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)],[28]) ).
thf(229,axiom,
! [A: node,B: set @ node] :
( ( coinductive_ltl @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
= ( f
@ ( product_Pair @ node @ ( set @ node )
@ ( '@+' @ node
@ ( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [C: node,D: set @ node,E: node] :
( ( graph @ C @ E )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ C @ ( insert @ node @ E @ D ) ) ) @ E ) )
& ~ ( member @ node @ E @ ( insert @ node @ C @ D ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
@ ( insert @ node @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_f__simps_I3_J) ).
thf(977,plain,
! [A: node,B: set @ node] :
( ( coinductive_ltl @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
= ( f
@ ( product_Pair @ node @ ( set @ node )
@ @+[C: node] :
( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [D: node,E: set @ node,F: node] :
( ( graph @ D @ F )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ D @ ( insert @ node @ F @ E ) ) ) @ F ) )
& ~ ( member @ node @ F @ ( insert @ node @ D @ E ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ A @ B )
@ C )
@ ( insert @ node @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(101,axiom,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( B @ D )
=> ( B @ ( insert @ TA @ C @ D ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_finite__induct) ).
thf(582,plain,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( B @ D )
=> ( B @ ( insert @ TA @ C @ D ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',fact_121_minus__equation__iff) ).
thf(730,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)],[137]) ).
thf(263,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_insert__absorb2) ).
thf(1068,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)],[263]) ).
thf(265,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_pred__equals__eq2) ).
thf(1073,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(190,axiom,
! [TA: $tType,A: $o] :
( ( A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( top_top @ ( set @ TA ) ) ) )
& ( ~ A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Collect__const) ).
thf(873,plain,
! [TA: $tType,A: $o] :
( ( A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( top_top @ ( set @ TA ) ) ) )
& ( ~ A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',fact_208_ord__le__eq__trans) ).
thf(379,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)],[39]) ).
thf(251,axiom,
~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ na @ nsa ) ) @ na ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_Ainsert_An_Ans_J_An_J_092_060close_062) ).
thf(1041,plain,
~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ na @ nsa ) ) @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(191,axiom,
~ ( coinductive_lnull @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ na @ nsa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_ldistinct_I2_J) ).
thf(878,plain,
~ ( coinductive_lnull @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ na @ nsa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(112,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ~ ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_infinite__UNIV__char__0) ).
thf(655,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ~ ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',fact_232_subset__insertI2) ).
thf(511,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)],[79]) ).
thf(267,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_UNIV__witness) ).
thf(1078,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',fact_111_neg__equal__iff__equal) ).
thf(550,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)],[90]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
( ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_case__prodD) ).
thf(472,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
( ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_prod__cases5) ).
thf(670,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(261,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( top_top @ ( TB > TA > $o ) @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_top2I) ).
thf(1063,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( top_top @ ( TB > TA > $o ) @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',fact_221_order__subst1) ).
thf(340,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)],[23]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',fact_76_insert__ident) ).
thf(898,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)],[198]) ).
thf(237,axiom,
! [TA: $tType,TB: $tType] :
( ( bot_bot @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_bot__empty__eq2) ).
thf(1001,plain,
! [TA: $tType,TB: $tType] :
( ( bot_bot @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',fact_193_subset__Compl__singleton) ).
thf(709,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)],[129]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > $o] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_pigeonhole__infinite__rel) ).
thf(841,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > $o] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',fact_155_singleton__inject) ).
thf(885,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)],[194]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',fact_199_bot_Oextremum__unique) ).
thf(301,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)],[11]) ).
thf(95,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_7) ).
thf(565,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(273,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_old_Oprod_Orec) ).
thf(1095,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',fact_203_dual__order_Otrans) ).
thf(404,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)],[45]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_prod__induct3) ).
thf(719,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_bot__fun__def) ).
thf(372,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)],[36]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',fact_26_insert__iff) ).
thf(838,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)],[175]) ).
thf(163,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( '@+' @ ( product_prod @ TB @ TA )
@ ( product_case_prod @ TB @ TA @ $o
@ ^ [C: TB,D: TA] :
( ( A = C )
& ( B = D ) ) ) )
= ( product_Pair @ TB @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Eps__case__prod__eq) ).
thf(802,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( @+[C: product_prod @ TB @ TA] :
( product_case_prod @ TB @ TA @ $o
@ ^ [D: TB,E: TA] :
( ( A = D )
& ( B = E ) )
@ C ) )
= ( product_Pair @ TB @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(260,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_equalityD1) ).
thf(1059,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)],[260]) ).
thf(61,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12) ).
thf(460,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(257,axiom,
! [A: node] : ( finite_finite2 @ node @ ( collect @ node @ ( graph @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_finite__branching) ).
thf(1055,plain,
! [A: node] : ( finite_finite2 @ node @ ( collect @ node @ ( graph @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(134,axiom,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Compl__empty__eq) ).
thf(724,plain,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',fact_240_rev__subsetD) ).
thf(917,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)],[205]) ).
thf(127,axiom,
~ ( ( finite_finite2 @ node @ nsa )
=> ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ na @ nsa ) ) @ na ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060lbrakk_062finite_Ans_059_Ainfinite_A_Ireachable__via_Agraph_A_I_N_Ainsert_An_Ans_J_An_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(702,plain,
~ ( ( finite_finite2 @ node @ nsa )
=> ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ na @ nsa ) ) @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(144,axiom,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_finite__UNIV) ).
thf(751,plain,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(212,axiom,
! [TA: $tType,TB: $tType] :
( ( '@+' @ ( product_prod @ TA @ TB ) )
= ( ^ [A: ( product_prod @ TA @ TB ) > $o] :
@+[B: product_prod @ TA @ TB] :
( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
@ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_split__paired__Eps) ).
thf(934,plain,
! [TA: $tType,TB: $tType] :
( ( '@+' @ ( product_prod @ TA @ TB ) )
= ( ^ [A: ( product_prod @ TA @ TB ) > $o] :
@+[B: product_prod @ TA @ TB] :
( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(357,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > $o,B: TC > TA > TB,C: product_prod @ TC @ TA] :
( ( A @ ( product_case_prod @ TC @ TA @ TB @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_case__prodE2) ).
thf(924,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > $o,B: TC > TA > TB,C: product_prod @ TC @ TA] :
( ( A @ ( product_case_prod @ TC @ TA @ TB @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(73,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_iso__tuple__UNIV__I) ).
thf(492,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(146,axiom,
? [A: node] :
( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [B: node,C: set @ node,D: node] :
( ( graph @ B @ D )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ B @ ( insert @ node @ D @ C ) ) ) @ D ) )
& ~ ( member @ node @ D @ ( insert @ node @ B @ C ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ na @ nsa )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062_092_060exists_062n_H_O_A_Icase_A_In_M_Ans_J_Aof_A_In_M_Ans_J_A_092_060Rightarrow_062_A_092_060lambda_062n_H_O_Agraph_An_An_H_A_092_060and_062_Ainfinite_A_Ireachable__via_Agraph_A_I_N_Ainsert_An_A_Iinsert_An_H_Ans_J_J_An_H_J_A_092_060and_062_An_H_A_092_060notin_062_Ainsert_An_Ans_J_An_H_092_060close_062) ).
thf(756,plain,
? [A: node] :
( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [B: node,C: set @ node,D: node] :
( ( graph @ B @ D )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ B @ ( insert @ node @ D @ C ) ) ) @ D ) )
& ~ ( member @ node @ D @ ( insert @ node @ B @ C ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ na @ nsa )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(158,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_14) ).
thf(789,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(213,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_ComplI) ).
thf(937,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)],[213]) ).
thf(224,axiom,
! [TA: $tType,TB: $tType] :
( ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
=> ( finite_finite2 @ ( product_prod @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite__Prod__UNIV) ).
thf(966,plain,
! [TA: $tType,TB: $tType] :
( ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
=> ( finite_finite2 @ ( product_prod @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(255,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/sandbox2/benchmark/theBenchmark.p',fact_109_compl__eq__compl__iff) ).
thf(1051,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)],[255]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',fact_182_neg__le__iff__le) ).
thf(480,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)],[69]) ).
thf(42,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_lnull__imp__lfinite) ).
thf(397,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(280,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',fact_183_compl__le__compl__iff) ).
thf(866,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)],[187]) ).
thf(59,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_equals0D) ).
thf(453,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)],[59]) ).
thf(114,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_singletonD) ).
thf(660,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)],[114]) ).
thf(179,axiom,
ord_less_eq @ ( set @ node ) @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177__092_060open_062_N_A_123n_125_A_092_060subseteq_062_Areachable__via_Agraph_A_I_N_A_123n_125_J_An_092_060close_062) ).
thf(849,plain,
ord_less_eq @ ( set @ node ) @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA @ ( type2 @ TA ) )
=> ( bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(312,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA @ ( type2 @ TA ) )
=> ( bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_255_minus__le__iff) ).
thf(602,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)],[103]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',fact_234_Collect__mono__iff) ).
thf(766,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)],[150]) ).
thf(13,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_ltl @ TA @ A ) )
= ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_lfinite__ltl) ).
thf(307,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_ltl @ TA @ A ) )
= ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',fact_213_le__cases) ).
thf(292,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)],[7]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB > TA > ( set @ TC ),C: TB,D: TA] :
( ( member @ TC @ A @ ( B @ C @ D ) )
=> ( member @ TC @ A @ ( product_case_prod @ TB @ TA @ ( set @ TC ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_mem__case__prodI) ).
thf(439,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB > TA > ( set @ TC ),C: TB,D: TA] :
( ( member @ TC @ A @ ( B @ C @ D ) )
=> ( member @ TC @ A @ ( product_case_prod @ TB @ TA @ ( set @ TC ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(160,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_insert__UNIV) ).
thf(793,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_prod__induct5) ).
thf(761,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_209_ord__eq__le__trans) ).
thf(366,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)],[34]) ).
thf(258,axiom,
finite_finite2 @ node @ nsa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062finite_Ans_092_060close_062) ).
thf(1057,plain,
finite_finite2 @ node @ nsa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(21,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_order__refl) ).
thf(334,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(221,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_singleton__conv2) ).
thf(957,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(171,axiom,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Compl__UNIV__eq) ).
thf(825,plain,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(244,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ! [D: TA] :
( ( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ @+[D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_someI2__bex) ).
thf(1021,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ! [D: TA] :
( ( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ @+[D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_202_dual__order_Oantisym) ).
thf(349,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)],[27]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB @ ( type2 @ TB ) )
& ( finite_finite @ TA @ ( type2 @ TA ) ) )
=> ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Finite__Set_Ofinite_19) ).
thf(297,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB @ ( type2 @ TB ) )
& ( finite_finite @ TA @ ( type2 @ TA ) ) )
=> ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(429,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)],[50]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',fact_241_subset__iff) ).
thf(815,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)],[167]) ).
thf(64,axiom,
! [TA: $tType,A: TA > $o] :
( ( collect @ TA
@ ^ [B: TA] :
~ ( A @ B ) )
= ( uminus_uminus @ ( set @ TA ) @ ( collect @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_Collect__neg__eq) ).
thf(467,plain,
! [TA: $tType,A: TA > $o] :
( ( collect @ TA
@ ^ [B: TA] :
~ ( A @ B ) )
= ( uminus_uminus @ ( set @ TA ) @ ( collect @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(248,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/sandbox2/benchmark/theBenchmark.p',fact_242_set__rev__mp) ).
thf(1032,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)],[248]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_old_Oprod_Oinducts) ).
thf(852,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(83,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_UNIV__I) ).
thf(522,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(62,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_UNIV__def) ).
thf(461,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(228,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_prod__cases6) ).
thf(974,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(241,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_6) ).
thf(1012,plain,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(141,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(742,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_prod__cases7) ).
thf(697,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(108,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_8) ).
thf(615,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_finite__set__choice) ).
thf(980,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',fact_230_subset__insert) ).
thf(1006,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)],[239]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( product_case_prod @ TA @ TB @ $o
@ ^ [B: TA,C: TB] : $true
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_prod_Odisc__eq__case) ).
thf(869,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( product_case_prod @ TA @ TB @ $o
@ ^ [B: TA,C: TB] : $true
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(106,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_finite__subset) ).
thf(610,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(110,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_empty__def) ).
thf(650,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(217,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_insert__absorb) ).
thf(948,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)],[217]) ).
thf(156,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_double__compl) ).
thf(783,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)],[156]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',fact_204_linorder__wlog) ).
thf(420,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)],[47]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',fact_220_order__subst2) ).
thf(328,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)],[19]) ).
thf(246,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_infinite__super) ).
thf(1028,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(211,axiom,
koenig793108494nected @ node @ graph,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_connected) ).
thf(933,plain,
koenig793108494nected @ node @ graph,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType] :
( ( top_top @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_top__empty__eq2) ).
thf(753,plain,
! [TA: $tType,TB: $tType] :
( ( top_top @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(117,axiom,
finite_finite @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_13) ).
thf(669,plain,
finite_finite @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TC,C: TA > TB > ( set @ TC )] :
( ! [D: TA,E: TB] :
( ( A
= ( product_Pair @ TA @ TB @ D @ E ) )
=> ( member @ TC @ B @ ( C @ D @ E ) ) )
=> ( member @ TC @ B @ ( product_case_prod @ TA @ TB @ ( set @ TC ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_mem__case__prodI2) ).
thf(526,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TC,C: TA > TB > ( set @ TC )] :
( ! [D: TA,E: TB] :
( ( A
= ( product_Pair @ TA @ TB @ D @ E ) )
=> ( member @ TC @ B @ ( C @ D @ E ) ) )
=> ( member @ TC @ B @ ( product_case_prod @ TA @ TB @ ( set @ TC ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_case__prod__conv) ).
thf(547,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(128,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_all__not__in__conv) ).
thf(706,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)],[128]) ).
thf(199,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_insert__not__empty) ).
thf(901,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TB @ TA] :
( ( product_case_prod @ TB @ TA @ $o @ A @ B )
=> ~ ! [C: TB,D: TA] :
( ( B
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_case__prodE) ).
thf(476,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TB @ TA] :
( ( product_case_prod @ TB @ TA @ $o @ A @ B )
=> ~ ! [C: TB,D: TA] :
( ( B
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(250,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
( ( A @ B @ C )
=> ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_case__prodI) ).
thf(1039,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
( ( A @ B @ C )
=> ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(226,axiom,
top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_15) ).
thf(970,plain,
top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_186_insert__subset) ).
thf(457,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)],[60]) ).
thf(231,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_bot__set__def) ).
thf(984,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',fact_191_singleton__insert__inj__eq) ).
thf(721,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)],[133]) ).
thf(97,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_insert__compr) ).
thf(569,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(154,axiom,
boolean_algebra @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_10) ).
thf(779,plain,
boolean_algebra @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',fact_113_uminus__apply) ).
thf(503,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)],[76]) ).
thf(104,axiom,
( ltl
= ( product_case_prod @ node @ ( set @ node ) @ ( product_prod @ node @ ( set @ node ) )
@ ^ [A: node,B: set @ node] :
( product_Pair @ node @ ( set @ node )
@ @+[C: node] :
( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [D: node,E: set @ node,F: node] :
( ( graph @ D @ F )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ D @ ( insert @ node @ F @ E ) ) ) @ F ) )
& ~ ( member @ node @ F @ ( insert @ node @ D @ E ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ A @ B )
@ C )
@ ( insert @ node @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_LTL__def) ).
thf(605,plain,
( ltl
= ( product_case_prod @ node @ ( set @ node ) @ ( product_prod @ node @ ( set @ node ) )
@ ^ [A: node,B: set @ node] :
( product_Pair @ node @ ( set @ node )
@ @+[C: node] :
( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [D: node,E: set @ node,F: node] :
( ( graph @ D @ F )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ D @ ( insert @ node @ F @ E ) ) ) @ F ) )
& ~ ( member @ node @ F @ ( insert @ node @ D @ E ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ A @ B )
@ C )
@ ( insert @ node @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ( order_bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(343,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)],[24]) ).
thf(164,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
& ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__Collect__disjI) ).
thf(805,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
& ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(207,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_equals0I) ).
thf(921,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)],[207]) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',fact_74_insert__eq__iff) ).
thf(541,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)],[87]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( finite_finite2 @ TA @ ( insert @ TA @ A @ B ) )
= ( finite_finite2 @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__insert) ).
thf(657,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( finite_finite2 @ TA @ ( insert @ TA @ A @ B ) )
= ( finite_finite2 @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(256,axiom,
uminus @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_18) ).
thf(1054,plain,
uminus @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(264,axiom,
! [A: node,B: node,C: set @ node] :
( ( member @ node @ A @ ( coinductive_lset @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ B @ C ) ) ) )
=> ( ~ ( member @ node @ B @ C )
=> ( ( finite_finite2 @ node @ C )
=> ( ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ B @ C ) ) @ B ) )
=> ~ ( member @ node @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_lset) ).
thf(1071,plain,
! [A: node,B: node,C: set @ node] :
( ( member @ node @ A @ ( coinductive_lset @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ B @ C ) ) ) )
=> ( ~ ( member @ node @ B @ C )
=> ( ( finite_finite2 @ node @ C )
=> ( ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ B @ C ) ) @ B ) )
=> ~ ( member @ node @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(86,axiom,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] : ( B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ( D
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( B @ D )
=> ( B @ ( insert @ TA @ C @ D ) ) ) ) ) )
=> ( B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_finite__ne__induct) ).
thf(530,plain,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] : ( B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ( D
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( B @ D )
=> ( B @ ( insert @ TA @ C @ D ) ) ) ) ) )
=> ( B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(219,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_3) ).
thf(953,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(195,axiom,
? [A: node,B: set @ node] :
( ( ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ( bot_bot @ ( set @ node ) ) ) )
= ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
& ( finite_finite2 @ node @ B )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_X) ).
thf(888,plain,
? [A: node,B: set @ node] :
( ( ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ( bot_bot @ ( set @ node ) ) ) )
= ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) )
& ( finite_finite2 @ node @ B )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',fact_235_contra__subsetD) ).
thf(906,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)],[201]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',fact_215_linear) ).
thf(425,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)],[48]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_73_insert__commute) ).
thf(513,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)],[80]) ).
thf(276,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/sandbox2/benchmark/theBenchmark.p',fact_237_subset__trans) ).
thf(1103,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)],[276]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_prod__cases) ).
thf(856,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(142,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB > TD,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TD @ B @ C ) )
= ( product_case_prod @ TA @ TB @ TC
@ ^ [D: TA,E: TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_prod_Ocase__distrib) ).
thf(745,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB > TD,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TD @ B @ C ) )
= ( product_case_prod @ TA @ TB @ TC
@ ^ [D: TA,E: TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1,conjecture,
( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [A: node,B: set @ node,C: node] :
( ( graph @ A @ C )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ ( insert @ node @ C @ B ) ) ) @ C ) )
& ~ ( member @ node @ C @ ( insert @ node @ A @ B ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ na @ nsa )
@ ( '@+' @ node
@ ( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [A: node,B: set @ node,C: node] :
( ( graph @ A @ C )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ ( insert @ node @ C @ B ) ) ) @ C ) )
& ~ ( member @ node @ C @ ( insert @ node @ A @ B ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ na @ nsa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [A: node,B: set @ node,C: node] :
( ( graph @ A @ C )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ ( insert @ node @ C @ B ) ) ) @ C ) )
& ~ ( member @ node @ C @ ( insert @ node @ A @ B ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ na @ nsa )
@ ( '@+' @ node
@ ( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [A: node,B: set @ node,C: node] :
( ( graph @ A @ C )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ ( insert @ node @ C @ B ) ) ) @ C ) )
& ~ ( member @ node @ C @ ( insert @ node @ A @ B ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ na @ nsa ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(279,plain,
~ ( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [A: node,B: set @ node,C: node] :
( ( graph @ A @ C )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ ( insert @ node @ C @ B ) ) ) @ C ) )
& ~ ( member @ node @ C @ ( insert @ node @ A @ B ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ na @ nsa )
@ @+[A: node] :
( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [B: node,C: set @ node,D: node] :
( ( graph @ B @ D )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ B @ ( insert @ node @ D @ C ) ) ) @ D ) )
& ~ ( member @ node @ D @ ( insert @ node @ B @ C ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ na @ nsa )
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,axiom,
( ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ns ) ) @ n ) )
& ( finite_finite2 @ node @ ns ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_Ainsert_An_Ans_____J_An_J_A_092_060and_062_Afinite_Ans_____092_060close_062) ).
thf(444,plain,
( ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ns ) ) @ n ) )
& ( finite_finite2 @ node @ ns ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',fact_212_order_Otrans) ).
thf(375,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)],[37]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_old_Oprod_Ocase) ).
thf(733,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(169,axiom,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite__code) ).
thf(819,plain,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(123,axiom,
member @ node @ n @ ( coinductive_lset @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ns ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138__092_060open_062n_A_092_060in_062_Alset_A_If_A_In_M_Ans_____J_J_092_060close_062) ).
thf(694,plain,
member @ node @ n @ ( coinductive_lset @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ns ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TB,B: TC > TB > TA > $o,C: TA] :
( ! [D: TC,E: TB] :
( ( ( product_Pair @ TC @ TB @ D @ E )
= A )
=> ( B @ D @ E @ C ) )
=> ( product_case_prod @ TC @ TB @ ( TA > $o ) @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_case__prodI2_H) ).
thf(772,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TB,B: TC > TB > TA > $o,C: TA] :
( ! [D: TC,E: TB] :
( ( ( product_Pair @ TC @ TB @ D @ E )
= A )
=> ( B @ D @ E @ C ) )
=> ( product_case_prod @ TC @ TB @ ( TA > $o ) @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_old_Oprod_Oexhaust) ).
thf(579,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(94,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/sandbox2/benchmark/theBenchmark.p',fact_80_insertE) ).
thf(562,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)],[94]) ).
thf(200,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ TA @ ( insert @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_finite_OinsertI) ).
thf(904,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ TA @ ( insert @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A
= ( product_Pair @ TA @ TB @ C @ D ) )
=> ( B @ C @ D ) )
=> ( product_case_prod @ TA @ TB @ $o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_case__prodI2) ).
thf(572,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A
= ( product_Pair @ TA @ TB @ C @ D ) )
=> ( B @ C @ D ) )
=> ( product_case_prod @ TA @ TB @ $o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(271,axiom,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( ^ [A: set @ TA] :
( collect @ TA
@ ( uminus_uminus @ ( TA > $o )
@ ^ [B: TA] : ( member @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_uminus__set__def) ).
thf(1090,plain,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( ^ [A: set @ TA] :
( collect @ TA
@ ( uminus_uminus @ ( TA > $o )
@ ^ [B: TA] : ( member @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(206,axiom,
! [TA: $tType,TB: $tType] :
( ( finite_finite2 @ ( TB > TA ) @ ( top_top @ ( set @ ( TB > TA ) ) ) )
=> ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_finite__fun__UNIVD2) ).
thf(919,plain,
! [TA: $tType,TB: $tType] :
( ( finite_finite2 @ ( TB > TA ) @ ( top_top @ ( set @ ( TB > TA ) ) ) )
=> ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(259,axiom,
order_bot @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_11) ).
thf(1058,plain,
order_bot @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(278,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ ( coinductive_ltl @ TA @ A ) ) @ ( coinductive_lset @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_lset__ltl) ).
thf(1107,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coinductive_lset @ TA @ ( coinductive_ltl @ TA @ A ) ) @ ( coinductive_lset @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',fact_211_le__cases3) ).
thf(406,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)],[46]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',fact_120_equation__minus__iff) ).
thf(599,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)],[102]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_prod__cases3) ).
thf(863,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(254,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_case_prod @ TA @ TB @ ( TC > TD ) )
= ( ^ [A: TA > TB > TC > TD,B: product_prod @ TA @ TB,C: TC] :
( product_case_prod @ TA @ TB @ TD
@ ^ [D: TA,E: TB] : ( A @ D @ E @ C )
@ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_case__prod__app) ).
thf(1048,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_case_prod @ TA @ TB @ ( TC > TD ) )
= ( ^ [A: TA > TB > TC > TD,B: product_prod @ TA @ TB,C: TC] :
( product_case_prod @ TA @ TB @ TD
@ ^ [D: TA,E: TB] : ( A @ D @ E @ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(139,axiom,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( ^ [A: set @ TA] :
( collect @ TA
@ ^ [B: TA] :
~ ( member @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Compl__eq) ).
thf(736,plain,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( ^ [A: set @ TA] :
( collect @ TA
@ ^ [B: TA] :
~ ( member @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(377,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(233,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Compl__eq__Compl__iff) ).
thf(990,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)],[233]) ).
thf(235,axiom,
! [TA: $tType] :
( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ? [B: set @ TA,C: TA] :
( ( A
= ( insert @ TA @ C @ B ) )
& ( finite_finite2 @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_finite_Osimps) ).
thf(996,plain,
! [TA: $tType] :
( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ? [B: set @ TA,C: TA] :
( ( A
= ( insert @ TA @ C @ B ) )
& ( finite_finite2 @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(362,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',fact_229_Set_Oinsert__mono) ).
thf(567,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)],[96]) ).
thf(78,axiom,
! [A: node,B: set @ node] :
( ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ B ) ) @ A ) )
=> ? [C: node] :
( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [D: node,E: set @ node,F: node] :
( ( graph @ D @ F )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ D @ ( insert @ node @ F @ E ) ) ) @ F ) )
& ~ ( member @ node @ F @ ( insert @ node @ D @ E ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ A @ B )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ex__P__I) ).
thf(509,plain,
! [A: node,B: set @ node] :
( ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ A @ B ) ) @ A ) )
=> ? [C: node] :
( product_case_prod @ node @ ( set @ node ) @ ( node > $o )
@ ^ [D: node,E: set @ node,F: node] :
( ( graph @ D @ F )
& ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ D @ ( insert @ node @ F @ E ) ) ) @ F ) )
& ~ ( member @ node @ F @ ( insert @ node @ D @ E ) ) )
@ ( product_Pair @ node @ ( set @ node ) @ A @ B )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(192,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_empty__not__UNIV) ).
thf(880,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(252,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_empty__iff) ).
thf(1043,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(52,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_add_Oinverse__inverse) ).
thf(434,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)],[52]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',fact_72_mk__disjoint__insert) ).
thf(811,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)],[166]) ).
thf(147,axiom,
! [TA: $tType] :
( ( finite_finite2 @ ( set @ TA ) @ ( top_top @ ( set @ ( set @ TA ) ) ) )
= ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Finite__Set_Ofinite__set) ).
thf(758,plain,
! [TA: $tType] :
( ( finite_finite2 @ ( set @ TA ) @ ( top_top @ ( set @ ( set @ TA ) ) ) )
= ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB @ ( type2 @ TB ) )
& ( finite_finite @ TA @ ( type2 @ TA ) ) )
=> ( finite_finite @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(323,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB @ ( type2 @ TB ) )
& ( finite_finite @ TA @ ( type2 @ TA ) ) )
=> ( finite_finite @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(162,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_top__conj_I1_J) ).
thf(799,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(70,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_singleton__conv) ).
thf(483,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(204,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_rev__finite__subset) ).
thf(915,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(151,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_bot__empty__eq) ).
thf(769,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_246_equalityE) ).
thf(494,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)],[74]) ).
thf(268,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Compl__iff) ).
thf(1080,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)],[268]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( boolean_algebra @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(345,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)],[25]) ).
thf(184,axiom,
~ ( coinductive_lfinite @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ns ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178__092_060open_062_092_060not_062_Alfinite_A_If_A_In_M_Ans_____J_J_092_060close_062) ).
thf(858,plain,
~ ( coinductive_lfinite @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ns ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(178,axiom,
bot @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_17) ).
thf(848,plain,
bot @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(126,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_subset__UNIV) ).
thf(700,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(82,axiom,
( ns
= ( bot_bot @ ( set @ node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_ns__def) ).
thf(520,plain,
( ns
= ( bot_bot @ ( set @ node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(203,axiom,
! [TA: $tType] :
( ( finite_finite2 @ ( option @ TA ) @ ( top_top @ ( set @ ( option @ TA ) ) ) )
= ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_finite__option__UNIV) ).
thf(912,plain,
! [TA: $tType] :
( ( finite_finite2 @ ( option @ TA ) @ ( top_top @ ( set @ ( option @ TA ) ) ) )
= ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(43,axiom,
! [TA: $tType] :
( ( order_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_bot_Oextremum) ).
thf(399,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)],[43]) ).
thf(124,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_empty__subsetI) ).
thf(695,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',fact_190_singleton__insert__inj__eq_H) ).
thf(780,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)],[155]) ).
thf(193,axiom,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_finite_OemptyI) ).
thf(883,plain,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(299,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(111,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_5) ).
thf(653,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(266,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/sandbox2/benchmark/theBenchmark.p',fact_188_Compl__anti__mono) ).
thf(1076,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)],[266]) ).
thf(249,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/sandbox2/benchmark/theBenchmark.p',fact_27_insertCI) ).
thf(1034,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)],[249]) ).
thf(120,axiom,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: set @ TA,D: TA] :
( ( finite_finite2 @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( insert @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_finite_Oinducts) ).
thf(675,plain,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: set @ TA,D: TA] :
( ( finite_finite2 @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( insert @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(215,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: TB,C: TC,D: TA] :
( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ ( product_Pair @ TB @ TC @ B @ C ) @ D )
=> ( A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_case__prodD_H) ).
thf(944,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: TB,C: TC,D: TA] :
( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ ( product_Pair @ TB @ TC @ B @ C ) @ D )
=> ( A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_prod__cases4) ).
thf(663,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(72,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ~ ! [B: set @ TA] :
( ? [C: TA] :
( A
= ( insert @ TA @ C @ B ) )
=> ~ ( finite_finite2 @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_finite_Ocases) ).
thf(487,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ~ ! [B: set @ TA] :
( ? [C: TA] :
( A
= ( insert @ TA @ C @ B ) )
=> ~ ( finite_finite2 @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(214,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Collect__conv__if2) ).
thf(939,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(29,axiom,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( finite_finite @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Option_Ooption___Finite__Set_Ofinite_20) ).
thf(355,plain,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( finite_finite @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',fact_77_Set_Oset__insert) ).
thf(553,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)],[91]) ).
thf(225,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_2) ).
thf(968,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(109,axiom,
! [TA: $tType,A: ( set @ TA ) > $o,B: set @ TA] :
( ! [C: set @ TA] :
( ~ ( finite_finite2 @ TA @ C )
=> ( A @ C ) )
=> ( ( A @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert @ TA @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_infinite__finite__induct) ).
thf(617,plain,
! [TA: $tType,A: ( set @ TA ) > $o,B: set @ TA] :
( ! [C: set @ TA] :
( ~ ( finite_finite2 @ TA @ C )
=> ( A @ C ) )
=> ( ( A @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA,D: set @ TA] :
( ( finite_finite2 @ TA @ D )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert @ TA @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(81,axiom,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_infinite__imp__nonempty) ).
thf(516,plain,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(153,axiom,
! [TA: $tType,A: TA > $o] :
( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [B: TA] :
~ ( A @ B ) ) )
= ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_finite__Collect__not) ).
thf(776,plain,
! [TA: $tType,A: TA > $o] :
( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [B: TA] :
~ ( A @ B ) ) )
= ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(245,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TA @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_finite__compl) ).
thf(1025,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TA @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',fact_233_wlog__linorder__le) ).
thf(282,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)],[4]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_case_prod @ TA @ TB @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_case__prod__Pair__iden) ).
thf(971,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_case_prod @ TA @ TB @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(140,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_subset__empty) ).
thf(739,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)],[140]) ).
thf(234,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( top_top @ TA ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_compl__top__eq) ).
thf(993,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( top_top @ TA ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC > TA > ( set @ TB ),C: product_prod @ TC @ TA] :
( ( member @ TB @ A @ ( product_case_prod @ TC @ TA @ ( set @ TB ) @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( member @ TB @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__case__prodE) ).
thf(712,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC > TA > ( set @ TB ),C: product_prod @ TC @ TA] :
( ( member @ TB @ A @ ( product_case_prod @ TC @ TA @ ( set @ TB ) @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( member @ TB @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(92,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_insert__Collect) ).
thf(557,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',fact_181_subsetI) ).
thf(1098,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)],[274]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',fact_225_le__funD) ).
thf(310,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)],[14]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',fact_254_le__imp__neg__le) ).
thf(673,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)],[119]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',fact_207_order__class_Oorder_Oantisym) ).
thf(331,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)],[20]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',fact_187_Compl__subset__Compl__iff) ).
thf(441,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)],[55]) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',fact_206_order__trans) ).
thf(370,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)],[35]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_bot__apply) ).
thf(359,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)],[31]) ).
thf(88,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_empty__Collect__eq) ).
thf(544,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)],[88]) ).
thf(65,axiom,
~ ( finite_finite2 @ node @ ( top_top @ ( set @ node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_infinite) ).
thf(470,plain,
~ ( finite_finite2 @ node @ ( top_top @ ( set @ node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',fact_245_subset__eq) ).
thf(576,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)],[99]) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',fact_249_in__mono) ).
thf(951,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)],[218]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType] :
( ( finite_finite2 @ ( sum_sum @ TB @ TA ) @ ( top_top @ ( set @ ( sum_sum @ TB @ TA ) ) ) )
= ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
& ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_finite__Plus__UNIV__iff) ).
thf(808,plain,
! [TA: $tType,TB: $tType] :
( ( finite_finite2 @ ( sum_sum @ TB @ TA ) @ ( top_top @ ( set @ ( sum_sum @ TB @ TA ) ) ) )
= ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
& ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(22,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_eq__refl) ).
thf(336,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)],[22]) ).
thf(135,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_16) ).
thf(727,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(16,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ! [C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ C )
=> ( B @ C ) )
=> ( ! [C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ C )
=> ( ~ ( coinductive_lnull @ TA @ C )
=> ( ( B @ ( coinductive_ltl @ TA @ C ) )
=> ( B @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_lfinite__induct) ).
thf(314,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: ( coinductive_llist @ TA ) > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ! [C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ C )
=> ( B @ C ) )
=> ( ! [C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ C )
=> ( ~ ( coinductive_lnull @ TA @ C )
=> ( ( B @ ( coinductive_ltl @ TA @ C ) )
=> ( B @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(107,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ( coinductive_lset @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_lset__eq__empty) ).
thf(612,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ( coinductive_lset @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',fact_238_Collect__mono) ).
thf(450,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)],[58]) ).
thf(210,axiom,
! [TA: $tType] : ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ouminus_9) ).
thf(931,plain,
! [TA: $tType] : ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',fact_236_set__eq__subset) ).
thf(688,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)],[121]) ).
thf(84,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_top1I) ).
thf(524,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',fact_119_fun__Compl__def) ).
thf(963,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)],[223]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',fact_200_bot_Oextremum__uniqueI) ).
thf(304,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)],[12]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',fact_219_ord__eq__le__subst) ).
thf(390,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)],[41]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',fact_210_antisym__conv) ).
thf(401,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)],[44]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_prod_Oinject) ).
thf(786,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(197,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_prod__induct7) ).
thf(896,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(143,axiom,
! [A: node,B: set @ node] :
~ ( coinductive_lnull @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_f__simps_I1_J) ).
thf(748,plain,
! [A: node,B: set @ node] :
~ ( coinductive_lnull @ node @ ( f @ ( product_Pair @ node @ ( set @ node ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(216,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_subset__refl) ).
thf(946,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(275,axiom,
~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_A_123n_125_J_An_J_092_060close_062) ).
thf(1101,plain,
~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(247,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_emptyE) ).
thf(1030,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',fact_224_le__funE) ).
thf(290,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)],[6]) ).
thf(149,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Collect__empty__eq) ).
thf(763,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)],[149]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',fact_218_ord__le__eq__subst) ).
thf(383,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)],[40]) ).
thf(173,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_top__set__def) ).
thf(832,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(253,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ TB ) > TC] :
( ( product_case_prod @ TA @ TB @ TC
@ ^ [B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_case__prod__eta) ).
thf(1045,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ TB ) > TC] :
( ( product_case_prod @ TA @ TB @ TC
@ ^ [B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',fact_157_doubleton__eq__iff) ).
thf(716,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)],[131]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',fact_216_antisym) ).
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)],[5]) ).
thf(236,axiom,
! [TA: $tType,A: TA > $o] :
( ~ ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ? [B: TA] : ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_not__finite__existsD) ).
thf(999,plain,
! [TA: $tType,A: TA > $o] :
( ~ ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ? [B: TA] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(57,axiom,
! [TA: $tType,A: set @ TA] :
( ( member @ TA
@ @+[B: TA] : ( member @ TA @ B @ A )
@ A )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_some__in__eq) ).
thf(447,plain,
! [TA: $tType,A: set @ TA] :
( ( member @ TA
@ @+[B: TA] : ( member @ TA @ B @ A )
@ A )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(51,axiom,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ A )
=> ? [B: TA] :
~ ( member @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_ex__new__if__finite) ).
thf(432,plain,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ A )
=> ? [B: TA] :
~ ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType] :
( ( finite_finite2 @ ( product_prod @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
& ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_finite__prod) ).
thf(835,plain,
! [TA: $tType,TB: $tType] :
( ( finite_finite2 @ ( product_prod @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
& ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(168,axiom,
member @ ( coinductive_llist @ node ) @ ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ ( koenig916195507_paths @ node @ graph ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175__092_060open_062f_A_In_M_A_123_125_J_A_092_060in_062_Apaths_Agraph_092_060close_062) ).
thf(818,plain,
member @ ( coinductive_llist @ node ) @ ( f @ ( product_Pair @ node @ ( set @ node ) @ n @ ( bot_bot @ ( set @ node ) ) ) ) @ ( koenig916195507_paths @ node @ graph ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(182,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_insertI2) ).
thf(854,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)],[182]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_ex__in__conv) ).
thf(790,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)],[159]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_top__apply) ).
thf(294,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(77,axiom,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_double__complement) ).
thf(506,plain,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',fact_247_subsetCE) ).
thf(437,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)],[53]) ).
thf(67,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ComplD) ).
thf(474,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)],[67]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: product_prod @ TB @ TC,C: TA] :
( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ B @ C )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( product_Pair @ TB @ TC @ D @ E ) )
=> ~ ( A @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_case__prodE_H) ).
thf(828,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: product_prod @ TB @ TC,C: TA] :
( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ B @ C )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( product_Pair @ TB @ TC @ D @ E ) )
=> ~ ( A @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(222,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
| ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__Collect__conjI) ).
thf(960,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
| ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(262,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: ( product_prod @ TA @ TB ) > TC] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
= ( B @ ( product_Pair @ TA @ TB @ C @ D ) ) )
=> ( ( product_case_prod @ TA @ TB @ TC @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_cond__case__prod__eta) ).
thf(1065,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: ( product_prod @ TA @ TB ) > TC] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
= ( B @ ( product_Pair @ TA @ TB @ C @ D ) ) )
=> ( ( product_case_prod @ TA @ TB @ TC @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(220,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_prod__induct6) ).
thf(955,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(161,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_singleton__iff) ).
thf(796,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)],[161]) ).
thf(209,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_top__conj_I2_J) ).
thf(928,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',fact_250_set__mp) ).
thf(1093,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)],[272]) ).
thf(136,axiom,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( finite_finite @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_4) ).
thf(728,plain,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ( finite_finite @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(232,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(987,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(63,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_top__empty__eq) ).
thf(464,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB @ ( type2 @ TB ) )
& ( finite_finite @ TA @ ( type2 @ TA ) ) )
=> ( finite_finite @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Finite__Set_Ofinite_21) ).
thf(427,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB @ ( type2 @ TB ) )
& ( finite_finite @ TA @ ( type2 @ TA ) ) )
=> ( finite_finite @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(185,axiom,
! [TA: $tType,TB: $tType,A: $o,B: TA > TB > $o] :
( ( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] :
( A
& ( B @ C @ D ) ) )
= ( ^ [C: product_prod @ TA @ TB] :
( A
& ( product_case_prod @ TA @ TB @ $o @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_split__part) ).
thf(860,plain,
! [TA: $tType,TB: $tType,A: $o,B: TA > TB > $o] :
( ( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] :
( A
& ( B @ C @ D ) ) )
= ( ^ [C: product_prod @ TA @ TB] :
( A
& ( product_case_prod @ TA @ TB @ $o @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(243,axiom,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_finite) ).
thf(1019,plain,
! [TA: $tType] :
( ( finite_finite @ TA @ ( type2 @ TA ) )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(202,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_equalityD2) ).
thf(908,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)],[202]) ).
thf(170,axiom,
( ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ na @ nsa ) ) @ na ) )
& ( finite_finite2 @ node @ nsa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ldistinct_I1_J) ).
thf(822,plain,
( ~ ( finite_finite2 @ node @ ( koenig317145564le_via @ node @ graph @ ( uminus_uminus @ ( set @ node ) @ ( insert @ node @ na @ nsa ) ) @ na ) )
& ( finite_finite2 @ node @ nsa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(180,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_subset__insertI) ).
thf(850,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)],[180]) ).
thf(238,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_prod__induct4) ).
thf(1004,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(122,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_UNIV__eq__I) ).
thf(691,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(189,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ ( set @ TA )
@ ( collect @ ( set @ TA )
@ ^ [B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_finite__Collect__subsets) ).
thf(871,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ ( set @ TA )
@ ( collect @ ( set @ TA )
@ ^ [B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(75,axiom,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oboolean__algebra_1) ).
thf(501,plain,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_surj__pair) ).
thf(607,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(71,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(486,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',fact_180_subset__antisym) ).
thf(1009,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)],[240]) ).
thf(93,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( finite_finite2 @ TA @ ( coinductive_lset @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_lfinite__imp__finite__lset) ).
thf(560,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( finite_finite2 @ TA @ ( coinductive_lset @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(270,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/sandbox2/benchmark/theBenchmark.p',fact_248_subsetD) ).
thf(1088,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)],[270]) ).
thf(33,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_dual__order_Orefl) ).
thf(364,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(242,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Pair__inject) ).
thf(1014,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1109,plain,
$false,
inference(e,[status(thm)],[325,1105,347,846,893,1083,666,352,977,582,730,1068,1073,873,379,1041,878,655,511,1078,550,472,670,1063,340,898,1001,709,841,885,301,565,1095,404,719,372,838,802,1059,460,1055,724,917,702,751,934,357,924,492,756,789,937,966,1051,480,397,280,866,453,660,849,312,602,766,307,292,439,793,761,366,1057,334,957,825,1021,349,297,429,815,467,1032,852,522,461,974,1012,742,697,615,980,1006,869,610,650,948,783,420,328,1028,933,753,669,526,547,706,901,476,1039,970,457,984,721,569,779,503,605,343,805,921,541,657,1054,1071,530,953,888,906,425,513,1103,856,745,279,444,375,733,819,694,772,579,562,904,572,1090,919,1058,1107,406,599,863,1048,736,377,990,996,362,567,509,880,1043,434,811,758,323,799,483,915,769,494,1080,345,858,848,700,520,912,399,695,780,883,299,653,1076,1034,675,944,663,487,939,355,553,968,617,516,776,1025,282,971,739,993,712,557,1098,310,673,331,441,370,359,544,470,576,951,808,336,727,314,612,450,931,688,524,963,304,390,401,786,896,748,946,1101,1030,290,763,383,832,1045,716,287,999,447,432,835,818,854,790,294,506,437,474,828,960,1065,955,796,928,1093,728,987,464,427,860,1019,908,822,850,1004,691,871,501,607,486,1009,560,1088,364,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM181^1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 16:48:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.05/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.07/1.18 % [INFO] Parsing done (284ms).
% 2.07/1.19 % [INFO] Running in sequential loop mode.
% 2.79/1.42 % [INFO] eprover registered as external prover.
% 2.79/1.42 % [INFO] cvc4 registered as external prover.
% 2.79/1.43 % [INFO] Scanning for conjecture ...
% 3.16/1.54 % [INFO] Found a conjecture and 287 axioms. Running axiom selection ...
% 3.49/1.63 % [INFO] Axiom selection finished. Selected 276 axioms (removed 11 axioms).
% 4.28/1.82 % [INFO] Problem is higher-order (TPTP THF).
% 4.28/1.84 % [INFO] Type checking passed.
% 4.28/1.84 % [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 ...
% 62.97/39.07 % External prover 'e' found a proof!
% 62.97/39.07 % [INFO] Killing All external provers ...
% 62.97/39.07 % Time passed: 38552ms (effective reasoning time: 37882ms)
% 62.97/39.07 % 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)>
% 62.97/39.07 % Axioms used in derivation (276): fact_44_mem__case__prodE, tcon_fun___Orderings_Obot, fact_63_prod__cases6, fact_43_split__paired__Eps, fact_146_singleton__conv, fact_192_finite__Collect__subsets, fact_200_bot_Oextremum__uniqueI, fact_154_ex__in__conv, fact_33_finite__Plus__UNIV__iff, fact_1__092_060open_062finite_Ans_092_060close_062, tcon_HOL_Obool___Orderings_Oord_16, fact_67_Pair__inject, fact_143_empty__Collect__eq, fact_164_Collect__conv__if, tcon_HOL_Obool___Orderings_Oorder_14, fact_39_Finite__Set_Ofinite__set, tcon_fun___Finite__Set_Ofinite, fact_21_old_Oprod_Oinject, fact_70_finite, fact_131_top__conj_I2_J, fact_179_order__refl, fact_235_contra__subsetD, tcon_HOL_Obool___Orderings_Opreorder_12, fact_226_finite__subset, fact_215_linear, fact_176_lset__eq__empty, fact_216_antisym, fact_238_Collect__mono, fact_99_finite_OinsertI, fact_58_prod__induct6, fact_202_dual__order_Oantisym, fact_169_finite__induct, fact_142_Collect__empty__eq, fact_217_eq__iff, fact_239_subset__refl, fact_16_finite__Collect__conjI, fact_60_prod__induct4, fact_248_subsetD, fact_174_Compl__UNIV__eq, fact_94_someI2__bex, fact_25_insert__absorb2, fact_172_infinite__finite__induct, tcon_fun___Orderings_Oord, fact_76_insert__ident, fact_218_ord__le__eq__subst, tcon_HOL_Obool___Finite__Set_Ofinite_13, fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060lbrakk_062finite_Ans_059_Ainfinite_A_Ireachable__via_Agraph_A_I_N_Ainsert_An_Ans_J_An_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_35_finite__compl, fact_113_uminus__apply, tcon_Set_Oset___Groups_Ouminus_9, fact_253_subset__UNIV, fact_209_ord__eq__le__trans, tcon_Set_Oset___Orderings_Obot_8, fact_249_in__mono, fact_2_finite__branching, fact_69_surj__pair, fact_251_lnull__imp__lfinite, fact_171_finite__ne__induct, fact_12_finite__insert, tcon_Set_Oset___Orderings_Oorder__bot_2, tcon_HOL_Obool___Orderings_Olinorder, fact_136__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_A_123n_125_J_An_J_092_060close_062, tcon_Set_Oset___Orderings_Otop_6, fact_112_add_Oinverse__inverse, fact_90_Collect__neg__eq, fact_148_compl__top__eq, fact_6__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_Ainsert_An_Ans_J_An_J_092_060close_062, fact_106_old_Oprod_Orec, fact_73_insert__commute, fact_208_ord__le__eq__trans, fact_120_equation__minus__iff, fact_72_mk__disjoint__insert, fact_198_bot_Oextremum, fact_56_old_Oprod_Oexhaust, fact_144_singletonI, fact_255_minus__le__iff, fact_156_insert__not__empty, tcon_HOL_Obool___Orderings_Oorder__bot_11, fact_24_finite__code, fact_17_finite__Collect__disjI, fact_193_subset__Compl__singleton, fact_201_lfinite__imp__finite__lset, fact_29_mem__case__prodI2, fact_51_ex__new__if__finite, fact_31_case__prodI2, fact_103_case__prodE_H, fact_46_Collect__mem__eq, fact_190_singleton__insert__inj__eq_H, tcon_Product__Type_Oprod___Finite__Set_Ofinite_21, fact_140_empty__iff, fact_119_fun__Compl__def, fact_240_rev__subsetD, fact_244_equalityD1, fact_55_old_Oprod_Oinducts, fact_122_case__prod__app, fact_254_le__imp__neg__le, fact_165_Collect__conv__if2, fact_227_infinite__super, tcon_HOL_Obool___Orderings_Otop_15, fact_74_insert__eq__iff, fact_127_f__simps_I1_J, fact_168_finite_Osimps, fact_81_double__complement, fact_85_pigeonhole__infinite__rel, fact_78_insertI2, fact_188_Compl__anti__mono, fact_189_lfinite__ltl, fact_187_Compl__subset__Compl__iff, fact_101_case__prod__eta, fact_105_finite__option__UNIV, fact_199_bot_Oextremum__unique, fact_213_le__cases, fact_194_bot__empty__eq2, fact_64_prod__cases5, fact_40_finite__prod, fact_71_finite__set__choice, fact_128_top1I, fact_149_compl__bot__eq, fact_41_finite__Prod__UNIV, fact_30_mem__case__prodI, fact_102_case__prodE2, fact_32_case__prodI, fact_18_ComplI, fact_163_bot__fun__def, fact_65_prod__cases4, fact_0_connected, fact_130_top2I, fact_139_bot__apply, fact_205_dual__order_Orefl, tcon_Option_Ooption___Finite__Set_Ofinite_20, tcon_Set_Oset___Orderings_Oord_7, fact_230_subset__insert, fact_129_ns__def, fact_45_mem__Collect__eq, fact_52_insert__UNIV, fact_141_all__not__in__conv, fact_246_equalityE, fact_175__092_060open_062f_A_In_M_A_123_125_J_A_092_060in_062_Apaths_Agraph_092_060close_062, fact_20_Compl__eq__Compl__iff, fact_124__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_Ainsert_An_Ans_____J_An_J_A_092_060and_062_Afinite_Ans_____092_060close_062, fact_11_case__prod__conv, fact_10_case__prodI2_H, fact_42_finite__fun__UNIVD2, fact_98_old_Oprod_Ocase, fact_180_subset__antisym, fact_59_prod__induct5, tcon_Set_Oset___Orderings_Opreorder_3, fact_204_linorder__wlog, fact_207_order__class_Oorder_Oantisym, fact_108_iso__tuple__UNIV__I, fact_9_LTL__def, fact_212_order_Otrans, fact_121_minus__equation__iff, fact_166_some__in__eq, fact_183_compl__le__compl__iff, fact_50_infinite__UNIV__char__0, fact_34_finite__Collect__not, fact_214_eq__refl, fact_47_Collect__cong, fact_223_le__funI, fact_110_double__compl, fact_133_top__empty__eq, fact_170_finite_Oinducts, fact_191_singleton__insert__inj__eq, tcon_fun___Lattices_Oboolean__algebra, fact_195_bot__empty__eq, fact_132_top__conj_I1_J, tcon_fun___Orderings_Otop, fact_28_Eps__case__prod__eq, fact_109_compl__eq__compl__iff, tcon_fun___Orderings_Oorder__bot, fact_123_top__empty__eq2, fact_222_le__fun__def, fact_5_ldistinct_I1_J, fact_88_insert__Collect, fact_150_empty__not__UNIV, fact_153_equals0I, fact_242_set__rev__mp, fact_7_ex__P__I, fact_229_Set_Oinsert__mono, fact_234_Collect__mono__iff, fact_27_insertCI, fact_231_subset__insertI, fact_87_prod_Ocase__distrib, tcon_Set_Oset___Lattices_Oboolean__algebra_1, fact_224_le__funE, fact_3_infinite, fact_38_UNIV__witness, fact_236_set__eq__subset, fact_116_prod_Odisc__eq__case, fact_159_singletonD, fact_197_bot__set__def, fact_158_singleton__iff, fact_26_insert__iff, fact_250_set__mp, fact_49_finite__UNIV, tcon_fun___Orderings_Opreorder, fact_134_pred__equals__eq2, fact_138__092_060open_062n_A_092_060in_062_Alset_A_If_A_In_M_Ans_____J_J_092_060close_062, fact_80_insertE, fact_167_finite_Ocases, tcon_Set_Oset___Orderings_Oorder_5, fact_196_lset__ltl, fact_182_neg__le__iff__le, fact_126_f__simps_I3_J, fact_22_prod_Oinject, fact_184_subset__empty, fact_125_ldistinct_I2_J, fact_225_le__funD, fact_115_split__part, fact_245_subset__eq, fact_241_subset__iff, fact_75_insert__absorb, fact_177__092_060open_062_N_A_123n_125_A_092_060subseteq_062_Areachable__via_Agraph_A_I_N_A_123n_125_J_An_092_060close_062, fact_232_subset__insertI2, fact_114_top__apply, fact_152_equals0D, fact_79_insertI1, fact_173_Compl__empty__eq, fact_135_X, fact_57_prod__induct7, fact_37_UNIV__eq__I, fact_161_finite_OemptyI, fact_54_case__prodD, fact_233_wlog__linorder__le, tcon_fun___Orderings_Oorder, tcon_HOL_Obool___Groups_Ouminus_18, fact_206_order__trans, fact_221_order__subst1, fact_62_prod__cases7, fact_211_le__cases3, fact_66_prod__cases3, tcon_HOL_Obool___Lattices_Oboolean__algebra_10, fact_36_UNIV__def, fact_61_prod__induct3, fact_228_rev__finite__subset, fact_247_subsetCE, fact_185_empty__subsetI, fact_243_equalityD2, fact_91_Compl__eq, fact_237_subset__trans, fact_160_infinite__imp__nonempty, fact_162_empty__def, fact_53_case__prodE, fact_82_ComplD, fact_145_Collect__const, tcon_fun___Groups_Ouminus, fact_107_case__prod__Pair__iden, fact_147_singleton__conv2, fact_178__092_060open_062_092_060not_062_Alfinite_A_If_A_In_M_Ans_____J_J_092_060close_062, fact_252_lfinite__induct, fact_86_not__finite__existsD, fact_77_Set_Oset__insert, fact_68_prod__cases, fact_186_insert__subset, fact_203_dual__order_Otrans, fact_4__092_060open_062_092_060exists_062n_H_O_A_Icase_A_In_M_Ans_J_Aof_A_In_M_Ans_J_A_092_060Rightarrow_062_A_092_060lambda_062n_H_O_Agraph_An_An_H_A_092_060and_062_Ainfinite_A_Ireachable__via_Agraph_A_I_N_Ainsert_An_A_Iinsert_An_H_Ans_J_J_An_H_J_A_092_060and_062_An_H_A_092_060notin_062_Ainsert_An_Ans_J_An_H_092_060close_062, fact_219_ord__eq__le__subst, fact_137_lset, fact_181_subsetI, fact_19_Compl__iff, fact_220_order__subst2, fact_117_top__set__def, tcon_HOL_Obool___Orderings_Obot_17, fact_111_neg__equal__iff__equal, fact_89_insert__compr, fact_100_cond__case__prod__eta, fact_104_case__prodD_H, fact_151_emptyE, fact_23_UNIV__I, fact_157_doubleton__eq__iff, tcon_Set_Oset___Finite__Set_Ofinite_4, tcon_Sum__Type_Osum___Finite__Set_Ofinite_19, fact_210_antisym__conv, fact_118_uminus__set__def, fact_155_singleton__inject
% 62.97/39.07 % No. of inferences in proof: 556
% 62.97/39.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 38552 ms resp. 37882 ms w/o parsing
% 63.65/39.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 63.65/39.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------