TSTP Solution File: ITP070^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP070^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 07:47:35 EDT 2024
% Result : Theorem 74.16s 47.94s
% Output : Refutation 75.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 302
% Syntax : Number of formulae : 548 ( 164 unt; 58 typ; 0 def)
% Number of atoms : 1958 ( 604 equ; 6 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 10378 ( 206 ~; 14 |; 110 &;9214 @)
% ( 0 <=>; 834 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 10 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 494 ( 494 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 15 con; 0-8 aty)
% Number of variables : 2576 ( 92 ^2392 !; 28 ?;2576 :)
% ( 64 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(type_type,type,
type:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_type,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_type,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_type,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(unique1598680935umeral_type,type,
unique1598680935umeral:
!>[TA: $tType] : $o ).
thf(ordere516151231imp_le_type,type,
ordere516151231imp_le:
!>[TA: $tType] : $o ).
thf(bNF_Ca1785829860lChain_type,type,
bNF_Ca1785829860lChain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
thf(unique455577585es_aux_type,type,
unique455577585es_aux:
!>[TA: $tType] : ( ( product_prod @ TA @ TA ) > $o ) ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(heapIm818251801eapify_type,type,
heapIm818251801eapify:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) ) ).
thf(heapIm721255937_empty_type,type,
heapIm721255937_empty:
!>[TA: $tType] : ( ( tree @ TA ) > $o ) ).
thf(heapIm874063447f_list_type,type,
heapIm874063447f_list:
!>[TA: $tType] : ( ( list @ TA ) > ( tree @ TA ) ) ).
thf(heapIm1271749598e_left_type,type,
heapIm1271749598e_left:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) ) ).
thf(heapIm1912108042t_tree_type,type,
heapIm1912108042t_tree:
!>[TA: $tType] : ( ( list @ TA ) > ( tree @ TA ) ) ).
thf(heapIm970386777veLeaf_type,type,
heapIm970386777veLeaf:
!>[TA: $tType] : ( ( tree @ TA ) > ( product_prod @ TA @ ( tree @ TA ) ) ) ).
thf(heapIm1434396069_right_type,type,
heapIm1434396069_right:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) ) ).
thf(heapIm748920189ftDown_type,type,
heapIm748920189ftDown:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) ) ).
thf(heap_type,type,
heap:
!>[TA: $tType,TB: $tType] : ( TB > ( TB > $o ) > ( ( list @ TA ) > TB ) > ( TB > ( multiset @ TA ) ) > ( TB > ( tree @ TA ) ) > ( TB > ( product_prod @ TA @ TB ) ) > $o ) ).
thf(heap_axioms_type,type,
heap_axioms:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( ( list @ TA ) > TB ) > ( TB > ( multiset @ TA ) ) > ( TB > ( tree @ TA ) ) > ( TB > ( product_prod @ TA @ TB ) ) > $o ) ).
thf(e_type,type,
e:
!>[TA: $tType] : ( tree @ TA ) ).
thf(t_type,type,
t:
!>[TA: $tType] : ( TA > ( tree @ TA ) > ( tree @ TA ) > ( tree @ TA ) ) ).
thf(in_tree_type,type,
in_tree:
!>[TA: $tType] : ( TA > ( tree @ TA ) > $o ) ).
thf(is_heap_type,type,
is_heap:
!>[TA: $tType] : ( ( tree @ TA ) > $o ) ).
thf(multiset2_type,type,
multiset2:
!>[TA: $tType] : ( ( tree @ TA ) > ( multiset @ TA ) ) ).
thf(val_type,type,
val:
!>[TA: $tType] : ( ( tree @ TA ) > TA ) ).
thf(lattic929149872er_Max_type,type,
lattic929149872er_Max:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(add_mset_type,type,
add_mset:
!>[TA: $tType] : ( TA > ( multiset @ TA ) > ( multiset @ TA ) ) ).
thf(is_empty_type,type,
is_empty:
!>[TA: $tType] : ( ( multiset @ TA ) > $o ) ).
thf(set_mset_type,type,
set_mset:
!>[TA: $tType] : ( ( multiset @ TA ) > ( set @ TA ) ) ).
thf(subseteq_mset_type,type,
subseteq_mset:
!>[TA: $tType] : ( ( multiset @ TA ) > ( multiset @ TA ) > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(produc2004651681e_prod_type,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ 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(collection_type,type,
collection:
!>[TA: $tType,TB: $tType] : ( TB > ( TB > $o ) > ( ( list @ TA ) > TB ) > ( TB > ( multiset @ TA ) ) > $o ) ).
thf(set2_type,type,
set2:
!>[TA: $tType,TB: $tType] : ( ( TB > ( multiset @ TA ) ) > TB > ( set @ TA ) ) ).
thf(removeMax_type,type,
removeMax:
!>[TA: $tType,TB: $tType] : ( TB > ( TB > $o ) > ( ( list @ TA ) > TB ) > ( TB > ( multiset @ TA ) ) > ( TB > ( product_prod @ TA @ TB ) ) > ( TB > $o ) > $o ) ).
thf(ssort_type,type,
ssort:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > ( product_prod @ TA @ TB ) ) > TB > ( list @ TA ) > ( list @ TA ) ) ).
thf(ssort_dom_type,type,
ssort_dom:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > ( product_prod @ TA @ TB ) ) > ( product_prod @ TB @ ( list @ TA ) ) > $o ) ).
thf(removeMax_axioms_type,type,
removeMax_axioms:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( ( list @ TA ) > TB ) > ( TB > ( multiset @ TA ) ) > ( TB > ( product_prod @ TA @ TB ) ) > ( TB > $o ) > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(l1_type,type,
l1: tree @ a ).
thf(l2_type,type,
l2: tree @ a ).
thf(r1_type,type,
r1: tree @ a ).
thf(r2_type,type,
r2: tree @ a ).
thf(v1_type,type,
v1: a ).
thf(v2_type,type,
v2: a ).
thf(v_type,type,
v: a ).
thf(208,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ D @ E @ F ) ) ) ) @ ( t @ TA @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( t @ TA @ D @ E @ F ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_siftDown_Osimps_I6_J) ).
thf(892,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ D @ E @ F ) ) ) ) @ ( t @ TA @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( t @ TA @ D @ E @ F ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(129,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add__le__imp__le__right) ).
thf(629,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( removeMax_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_RemoveMax_Oaxioms_I2_J) ).
thf(365,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( removeMax_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(37,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_subset__mset_Oorder_Oantisym) ).
thf(347,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(225,axiom,
! [TA: $tType] :
( ( multiset2 @ TA @ ( e @ TA ) )
= ( zero_zero @ ( multiset @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_multiset_Osimps_I1_J) ).
thf(962,plain,
! [TA: $tType] :
( ( multiset2 @ TA @ ( e @ TA ) )
= ( zero_zero @ ( multiset @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(171,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ ( zero_zero @ ( multiset @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_empty__neutral_I1_J) ).
thf(777,plain,
! [TA: $tType,A: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ ( zero_zero @ ( multiset @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(142,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] : ( subseteq_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_mset__subset__eq__add__left) ).
thf(666,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] : ( subseteq_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(83,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_subset__mset_Obot_Oextremum__uniqueI) ).
thf(481,plain,
! [TA: $tType,A: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(39,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_102_prod__cases3) ).
thf(352,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)],[39]) ).
thf(231,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) )
=> ( A
= ( e @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_removeLeaf_Ocases) ).
thf(977,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) )
=> ( A
= ( e @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(154,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add__mset__add__mset__same__iff) ).
thf(730,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(71,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA,D: multiset @ TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ C @ D ) )
= ( ( ( B = D )
& ( A = C ) )
| ? [E: multiset @ TA] :
( ( B
= ( add_mset @ TA @ C @ E ) )
& ( D
= ( add_mset @ TA @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_add__eq__conv__ex) ).
thf(449,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA,D: multiset @ TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ C @ D ) )
= ( ( ( B = D )
& ( A = C ) )
| ? [E: multiset @ TA] :
( ( B
= ( add_mset @ TA @ C @ E ) )
& ( D
= ( add_mset @ TA @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(139,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA] :
( ( subseteq_mset @ TA @ ( add_mset @ TA @ A @ B ) @ ( add_mset @ TA @ C @ ( zero_zero @ ( multiset @ TA ) ) ) )
= ( ( B
= ( zero_zero @ ( multiset @ TA ) ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_add__mset__subseteq__single__iff) ).
thf(655,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA] :
( ( subseteq_mset @ TA @ ( add_mset @ TA @ A @ B ) @ ( add_mset @ TA @ C @ ( zero_zero @ ( multiset @ TA ) ) ) )
= ( ( B
= ( zero_zero @ ( multiset @ TA ) ) )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(146,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_verit__sum__simplify) ).
thf(677,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( product_prod @ TA @ TB ),F: TB > $o,G: product_prod @ TB @ ( list @ TA )] :
( ( removeMax @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( ( ssort_dom @ TB @ TA @ B @ E @ G )
=> ~ ! [H: TB,I: list @ TA] :
( ( G
= ( product_Pair @ TB @ ( list @ TA ) @ H @ I ) )
=> ~ ( ~ ( B @ H )
=> ! [J: TA,K: TB] :
( ( ( product_Pair @ TA @ TB @ J @ K )
= ( E @ H ) )
=> ( ssort_dom @ TB @ TA @ B @ E @ ( product_Pair @ TB @ ( list @ TA ) @ K @ ( cons @ TA @ J @ I ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_RemoveMax_Ossort_H__dom_Ocases) ).
thf(523,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( product_prod @ TA @ TB ),F: TB > $o,G: product_prod @ TB @ ( list @ TA )] :
( ( removeMax @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( ( ssort_dom @ TB @ TA @ B @ E @ G )
=> ~ ! [H: TB,I: list @ TA] :
( ( G
= ( product_Pair @ TB @ ( list @ TA ) @ H @ I ) )
=> ~ ( ~ ( B @ H )
=> ! [J: TA,K: TB] :
( ( ( product_Pair @ TA @ TB @ J @ K )
= ( E @ H ) )
=> ( ssort_dom @ TB @ TA @ B @ E @ ( product_Pair @ TB @ ( list @ TA ) @ K @ ( cons @ TA @ J @ I ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA )] :
( ( collection @ TB @ TA @ A @ B @ C @ D )
=> ( ( D @ A )
= ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Collection_Omultiset__empty) ).
thf(582,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA )] :
( ( collection @ TB @ TA @ A @ B @ C @ D )
=> ( ( D @ A )
= ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(164,axiom,
! [TA: $tType] : ( cancel1352612707id_add @ ( multiset @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add) ).
thf(762,plain,
! [TA: $tType] : ( cancel1352612707id_add @ ( multiset @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(53,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(385,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(103,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_zero__le) ).
thf(550,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB] :
( ( collection @ TB @ TA @ A @ B @ C @ D )
=> ( ( B @ E )
=> ( ( D @ E )
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Collection_Ois__empty__as__list) ).
thf(797,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB] :
( ( collection @ TB @ TA @ A @ B @ C @ D )
=> ( ( B @ E )
=> ( ( D @ E )
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(183,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_add__le__same__cancel2) ).
thf(814,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(218,axiom,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( e @ TA ) )
=> ( ! [C: TA,D: tree @ TA,E: tree @ TA] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Tree_Oinduct) ).
thf(930,plain,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( e @ TA ) )
=> ( ! [C: TA,D: tree @ TA,E: tree @ TA] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(242,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
( ( heapIm748920189ftDown @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) )
= ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_siftDown_Osimps_I2_J) ).
thf(1063,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
( ( heapIm748920189ftDown @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) )
= ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_ord__le__eq__trans) ).
thf(340,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(188,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ A )
= ( subseteq_mset @ TA @ B @ ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_subset__mset_Oadd__le__same__cancel1) ).
thf(829,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ A )
= ( subseteq_mset @ TA @ B @ ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(229,axiom,
linorder @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(973,plain,
linorder @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(29,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_ord__eq__le__trans) ).
thf(320,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Collection_Ois__empty__empty) ).
thf(372,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( D @ G )
= ( multiset2 @ TB @ ( E @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Heap_Omultiset) ).
thf(949,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( D @ G )
= ( multiset2 @ TB @ ( E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(75,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( A
!= ( zero_zero @ ( multiset @ TA ) ) )
=> ? [B: multiset @ TA,C: TA] :
( A
= ( add_mset @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_multi__nonempty__split) ).
thf(460,plain,
! [TA: $tType,A: multiset @ TA] :
( ( A
!= ( zero_zero @ ( multiset @ TA ) ) )
=> ? [B: multiset @ TA,C: TA] :
( A
= ( add_mset @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(240,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) )
= ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) @ ( e @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_siftDown_Osimps_I3_J) ).
thf(1055,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) )
= ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) @ ( e @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(152,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( A
!= ( zero_zero @ ( multiset @ TA ) ) )
=> ~ ! [B: TA,C: multiset @ TA] :
( A
!= ( add_mset @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_multiset__cases) ).
thf(724,plain,
! [TA: $tType,A: multiset @ TA] :
( ( A
!= ( zero_zero @ ( multiset @ TA ) ) )
=> ~ ! [B: TA,C: multiset @ TA] :
( A
!= ( add_mset @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(179,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm874063447f_list @ TA )
= ( ^ [A: list @ TA] : ( heapIm818251801eapify @ TA @ ( heapIm1912108042t_tree @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_hs__of__list__def) ).
thf(802,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm874063447f_list @ TA )
= ( ^ [A: list @ TA] : ( heapIm818251801eapify @ TA @ ( heapIm1912108042t_tree @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(36,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_subset__mset_Oantisym) ).
thf(344,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(184,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ B )
= ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_subset__mset_Oadd__le__same__cancel2) ).
thf(817,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ B )
= ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(107,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
= ( subseteq_mset @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_mset__subset__eq__mono__add__left__cancel) ).
thf(559,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
= ( subseteq_mset @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(133,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( zero_zero @ ( multiset @ TA ) ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_subset__mset_Oadd__eq__0__iff__both__eq__0) ).
thf(638,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( zero_zero @ ( multiset @ TA ) ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(62,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
=> ( subseteq_mset @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subset__mset_Oadd__le__imp__le__right) ).
thf(416,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
=> ( subseteq_mset @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(316,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subset__mset_Odual__order_Oantisym) ).
thf(261,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(64,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_linorder__wlog) ).
thf(421,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(200,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_add__le__imp__le__left) ).
thf(870,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(15,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(284,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)],[15]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( tree @ TA ),F: TB > ( product_prod @ TA @ TB ),G: list @ TA] :
( ( heap @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( is_heap @ TA @ ( E @ ( C @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Heap_Ois__heap__of__list) ).
thf(770,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( tree @ TA ),F: TB > ( product_prod @ TA @ TB ),G: list @ TA] :
( ( heap @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( is_heap @ TA @ ( E @ ( C @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(162,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_le__zero__eq) ).
thf(756,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(119,axiom,
! [TA: $tType] :
( ( subseteq_mset @ TA )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
? [C: multiset @ TA] :
( B
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_subset__mset_Ole__iff__add) ).
thf(591,plain,
! [TA: $tType] :
( ( subseteq_mset @ TA )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
? [C: multiset @ TA] :
( B
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(69,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_95_old_Oprod_Oinject) ).
thf(443,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)],[69]) ).
thf(237,axiom,
! [TA: $tType,A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( in_tree @ TA @ A @ ( t @ TA @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree @ TA @ A @ C )
| ( in_tree @ TA @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_in__tree_Osimps_I2_J) ).
thf(1040,plain,
! [TA: $tType,A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( in_tree @ TA @ A @ ( t @ TA @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree @ TA @ A @ C )
| ( in_tree @ TA @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( collection @ TA @ TB @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_RemoveMax_Oaxioms_I1_J) ).
thf(376,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( collection @ TA @ TB @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( set2 @ TA @ TB @ D @ E )
= ( set_mset @ TB @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Collection_Oset__def) ).
thf(253,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( set2 @ TA @ TB @ D @ E )
= ( set_mset @ TB @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( removeMax_axioms @ TA @ TB )
= ( ^ [A: TA > $o,B: ( list @ TB ) > TA,C: TA > ( multiset @ TB ),D: TA > ( product_prod @ TB @ TA ),E: TA > $o] :
( ! [F: list @ TB] : ( E @ ( B @ F ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( E @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( G
= ( lattic929149872er_Max @ TB @ ( set2 @ TA @ TB @ C @ F ) ) ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( E @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( ( add_mset @ TB @ G @ ( C @ H ) )
= ( C @ F ) ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( E @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( E @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_RemoveMax__axioms__def) ).
thf(574,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( removeMax_axioms @ TA @ TB )
= ( ^ [A: TA > $o,B: ( list @ TB ) > TA,C: TA > ( multiset @ TB ),D: TA > ( product_prod @ TB @ TA ),E: TA > $o] :
( ! [F: list @ TB] : ( E @ ( B @ F ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( E @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( G
= ( lattic929149872er_Max @ TB @ ( set2 @ TA @ TB @ C @ F ) ) ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( E @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( ( add_mset @ TB @ G @ ( C @ H ) )
= ( C @ F ) ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( E @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( E @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(211,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( e @ TA ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_siftDown_Osimps_I4_J) ).
thf(905,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( e @ TA ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(81,axiom,
! [TA: $tType,A: TA,B: multiset @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ B ) )
=> ~ ! [C: multiset @ TA] :
( B
!= ( add_mset @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_mset__add) ).
thf(475,plain,
! [TA: $tType,A: TA,B: multiset @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ B ) )
=> ~ ! [C: multiset @ TA] :
( B
!= ( add_mset @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(216,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA,G: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( t @ TA @ E @ F @ G ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ E @ F @ G ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ E @ F @ G ) )
& ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_is__heap_Osimps_I6_J) ).
thf(924,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA,G: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( t @ TA @ E @ F @ G ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ E @ F @ G ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ E @ F @ G ) )
& ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( ( E @ G )
= ( e @ TB ) )
= ( B @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Heap_Oas__tree__empty) ).
thf(397,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( ( E @ G )
= ( e @ TB ) )
= ( B @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: TA,H: TB,I: TA] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( F @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( E @ G ) )
=> ( ( add_mset @ TB @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_RemoveMax_Oremove__max__multiset) ).
thf(877,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: TA,H: TB,I: TA] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( F @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( E @ G ) )
=> ( ( add_mset @ TB @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(245,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm748920189ftDown @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_siftDown_Osimps_I1_J) ).
thf(1072,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm748920189ftDown @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(235,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( tree @ TA ) > $o,B: tree @ TA] :
( ! [C: TA] : ( A @ ( t @ TA @ C @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [C: TA,D: TA,E: tree @ TA,F: tree @ TA] :
( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( A @ ( t @ TA @ C @ ( t @ TA @ D @ E @ F ) @ ( e @ TA ) ) ) ) )
=> ( ! [C: TA,D: TA,E: tree @ TA,F: tree @ TA] :
( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( A @ ( t @ TA @ C @ ( e @ TA ) @ ( t @ TA @ D @ E @ F ) ) ) ) )
=> ( ! [C: TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA,H: tree @ TA,I: tree @ TA] :
( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( A @ ( t @ TA @ C @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ G @ H @ I ) ) ) ) )
=> ( ! [C: TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA,H: tree @ TA,I: tree @ TA] :
( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( A @ ( t @ TA @ C @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ G @ H @ I ) ) ) ) )
=> ( ( A @ ( e @ TA ) )
=> ( A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_removeLeaf_Oinduct) ).
thf(988,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( tree @ TA ) > $o,B: tree @ TA] :
( ! [C: TA] : ( A @ ( t @ TA @ C @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [C: TA,D: TA,E: tree @ TA,F: tree @ TA] :
( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( A @ ( t @ TA @ C @ ( t @ TA @ D @ E @ F ) @ ( e @ TA ) ) ) ) )
=> ( ! [C: TA,D: TA,E: tree @ TA,F: tree @ TA] :
( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( A @ ( t @ TA @ C @ ( e @ TA ) @ ( t @ TA @ D @ E @ F ) ) ) ) )
=> ( ! [C: TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA,H: tree @ TA,I: tree @ TA] :
( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( A @ ( t @ TA @ C @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ G @ H @ I ) ) ) ) )
=> ( ! [C: TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA,H: tree @ TA,I: tree @ TA] :
( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( ( A @ ( t @ TA @ D @ E @ F ) )
=> ( A @ ( t @ TA @ C @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ G @ H @ I ) ) ) ) )
=> ( ( A @ ( e @ TA ) )
=> ( A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( heap @ TA @ TB )
= ( ^ [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
& ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Heap__def) ).
thf(602,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( heap @ TA @ TB )
= ( ^ [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
& ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(166,axiom,
! [TA: $tType] :
( ( linorder @ 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_68_le__cases) ).
thf(766,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(23,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_105_prod__cases6) ).
thf(307,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)],[23]) ).
thf(72,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( is_heap @ TA @ ( e @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_is__heap_Osimps_I1_J) ).
thf(452,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( is_heap @ TA @ ( e @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_le__funI) ).
thf(248,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(51,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_subset__mset_Ole__zero__eq) ).
thf(380,plain,
! [TA: $tType,A: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(101,axiom,
! [TA: $tType] :
( ( linorder @ 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_70_linear) ).
thf(546,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(32,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_110_prod__induct6) ).
thf(334,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)],[32]) ).
thf(212,axiom,
ord_less_eq @ a @ v1 @ v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_True) ).
thf(910,plain,
ord_less_eq @ a @ v1 @ v,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(222,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
( ( heapIm970386777veLeaf @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) )
= ( product_Pair @ TA @ ( tree @ TA ) @ A @ ( e @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_removeLeaf_Osimps_I1_J) ).
thf(952,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
( ( heapIm970386777veLeaf @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) )
= ( product_Pair @ TA @ ( tree @ TA ) @ A @ ( e @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(21,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_111_prod__induct7) ).
thf(302,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)],[21]) ).
thf(197,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_union__right__cancel) ).
thf(862,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(185,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_le__add__same__cancel2) ).
thf(820,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(60,axiom,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_subset__mset_Ozero__le) ).
thf(407,plain,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(66,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( subseteq_mset @ TA @ B @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( zero_zero @ ( multiset @ TA ) ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_subset__mset_Oadd__nonpos__eq__0__iff) ).
thf(429,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( subseteq_mset @ TA @ B @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( zero_zero @ ( multiset @ TA ) ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( removeMax_axioms @ TA @ TB @ B @ C @ D @ E @ F )
=> ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_RemoveMax_Ointro) ).
thf(275,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( removeMax_axioms @ TA @ TB @ B @ C @ D @ E @ F )
=> ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(78,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_empty__neutral_I2_J) ).
thf(467,plain,
! [TA: $tType,A: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(42,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_subset__mset_Oorder_Otrans) ).
thf(361,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(207,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_left_Osimps) ).
thf(889,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(110,axiom,
! [TA: $tType,A: TA,B: TA,C: multiset @ TA] :
( ( add_mset @ TA @ A @ ( add_mset @ TA @ B @ C ) )
= ( add_mset @ TA @ B @ ( add_mset @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_add__mset__commute) ).
thf(566,plain,
! [TA: $tType,A: TA,B: TA,C: multiset @ TA] :
( ( add_mset @ TA @ A @ ( add_mset @ TA @ B @ C ) )
= ( add_mset @ TA @ B @ ( add_mset @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(84,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_add__mono__thms__linordered__semiring_I3_J) ).
thf(484,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(30,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_103_prod__cases4) ).
thf(324,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)],[30]) ).
thf(230,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( t @ TA @ B @ C @ D ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_is__heap_Osimps_I3_J) ).
thf(974,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( t @ TA @ B @ C @ D ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(202,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_multi__union__self__other__eq) ).
thf(874,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(232,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] : ( is_heap @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_is__heap_Osimps_I2_J) ).
thf(980,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] : ( is_heap @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: TA,H: TB,I: TA] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( F @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( E @ G ) )
=> ( F @ I ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_RemoveMax_Oremove__max__inv) ).
thf(388,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: TA,H: TB,I: TA] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( F @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( E @ G ) )
=> ( F @ I ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(126,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_add__le__same__cancel1) ).
thf(610,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(173,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_zero__le__double__add__iff__zero__le__single__add) ).
thf(783,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(6,axiom,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_subset__mset_Odual__order_Orefl) ).
thf(256,plain,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(85,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__cases3) ).
thf(488,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(98,axiom,
! [TA: $tType,A: TA,B: TA,C: multiset @ TA] :
( ( ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( add_mset @ TA @ B @ C ) )
= ( ( B = A )
& ( C
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_single__eq__add__mset) ).
thf(537,plain,
! [TA: $tType,A: TA,B: TA,C: multiset @ TA] :
( ( ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( add_mset @ TA @ B @ C ) )
= ( ( B = A )
& ( C
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(209,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_is__heap_Ocases) ).
thf(901,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(105,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_96_prod_Oinject) ).
thf(554,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)],[105]) ).
thf(161,axiom,
! [TA: $tType,A: multiset @ TA,B: TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ A @ ( add_mset @ TA @ B @ C ) )
= ( add_mset @ TA @ B @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_union__mset__add__mset__right) ).
thf(753,plain,
! [TA: $tType,A: multiset @ TA,B: TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ A @ ( add_mset @ TA @ B @ C ) )
= ( add_mset @ TA @ B @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(136,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
=> ( subseteq_mset @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_subset__mset_Oadd__le__imp__le__left) ).
thf(647,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
=> ( subseteq_mset @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(234,axiom,
( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ v )
=> ( ( multiset2 @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v @ ( heapIm1271749598e_left @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) )
= ( multiset2 @ a @ ( t @ a @ v @ ( heapIm1271749598e_left @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__C5__2_Ohyps_C_I2_J) ).
thf(985,plain,
( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ v )
=> ( ( multiset2 @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v @ ( heapIm1271749598e_left @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) )
= ( multiset2 @ a @ ( t @ a @ v @ ( heapIm1271749598e_left @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( product_prod @ TA @ TB ),F: TB > $o,G: TB,H: list @ TA] :
( ( removeMax @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( ! [I: TA,J: TB] :
( ~ ( B @ G )
=> ( ( ( product_Pair @ TA @ TB @ I @ J )
= ( E @ G ) )
=> ( ssort_dom @ TB @ TA @ B @ E @ ( product_Pair @ TB @ ( list @ TA ) @ J @ ( cons @ TA @ I @ H ) ) ) ) )
=> ( ssort_dom @ TB @ TA @ B @ E @ ( product_Pair @ TB @ ( list @ TA ) @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_RemoveMax_Ossort_H__dom_Ointros) ).
thf(515,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( product_prod @ TA @ TB ),F: TB > $o,G: TB,H: list @ TA] :
( ( removeMax @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( ! [I: TA,J: TB] :
( ~ ( B @ G )
=> ( ( ( product_Pair @ TA @ TB @ I @ J )
= ( E @ G ) )
=> ( ssort_dom @ TB @ TA @ B @ E @ ( product_Pair @ TB @ ( list @ TA ) @ J @ ( cons @ TA @ I @ H ) ) ) ) )
=> ( ssort_dom @ TB @ TA @ B @ E @ ( product_Pair @ TB @ ( list @ TA ) @ G @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(157,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_add__left__mono) ).
thf(738,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(213,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( A
= ( t @ TA @ B @ C @ D ) )
=> ? [E: tree @ TA,F: TA,G: tree @ TA] :
( ( ( heapIm748920189ftDown @ TA @ A )
= ( t @ TA @ F @ E @ G ) )
& ( ord_less_eq @ TA @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_siftDown__Node) ).
thf(911,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( A
= ( t @ TA @ B @ C @ D ) )
=> ? [E: tree @ TA,F: TA,G: tree @ TA] :
( ( ( heapIm748920189ftDown @ TA @ A )
= ( t @ TA @ F @ E @ G ) )
& ( ord_less_eq @ TA @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(151,axiom,
! [TA: $tType,A: TA,B: multiset @ TA] :
( ( zero_zero @ ( multiset @ TA ) )
!= ( add_mset @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_empty__not__add__mset) ).
thf(721,plain,
! [TA: $tType,A: TA,B: multiset @ TA] :
( ( zero_zero @ ( multiset @ TA ) )
!= ( add_mset @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(111,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___HOL_Otype) ).
thf(569,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( collection @ TA @ TB @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Heap_Oaxioms_I1_J) ).
thf(605,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( collection @ TA @ TB @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(241,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( val @ TA @ ( t @ TA @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_val_Osimps) ).
thf(1060,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( val @ TA @ ( t @ TA @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: product_prod @ TA @ ( list @ TB )] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( ssort_dom @ TA @ TB @ B @ E @ G )
= ( ? [H: TA,I: list @ TB] :
( ( G
= ( product_Pair @ TA @ ( list @ TB ) @ H @ I ) )
& ! [J: TB,K: TA] :
( ~ ( B @ H )
=> ( ( ( product_Pair @ TB @ TA @ J @ K )
= ( E @ H ) )
=> ( ssort_dom @ TA @ TB @ B @ E @ ( product_Pair @ TA @ ( list @ TB ) @ K @ ( cons @ TB @ J @ I ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_RemoveMax_Ossort_H__dom_Osimps) ).
thf(457,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: product_prod @ TA @ ( list @ TB )] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( ssort_dom @ TA @ TB @ B @ E @ G )
= ( ? [H: TA,I: list @ TB] :
( ( G
= ( product_Pair @ TA @ ( list @ TB ) @ H @ I ) )
& ! [J: TB,K: TA] :
( ~ ( B @ H )
=> ( ( ( product_Pair @ TB @ TA @ J @ K )
= ( E @ H ) )
=> ( ssort_dom @ TA @ TB @ B @ E @ ( product_Pair @ TA @ ( list @ TB ) @ K @ ( cons @ TB @ J @ I ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(131,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_subset__mset_Oadd__right__mono) ).
thf(633,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(180,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_113_old_Oprod_Oinducts) ).
thf(805,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)],[180]) ).
thf(88,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add__decreasing2) ).
thf(508,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(215,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( heap_axioms @ TA @ TB )
= ( ^ [A: TA > $o,B: ( list @ TB ) > TA,C: TA > ( multiset @ TB ),D: TA > ( tree @ TB ),E: TA > ( product_prod @ TB @ TA )] :
( ! [F: TA] :
( ( C @ F )
= ( multiset2 @ TB @ ( D @ F ) ) )
& ! [F: list @ TB] : ( is_heap @ TB @ ( D @ ( B @ F ) ) )
& ! [F: TA] :
( ( ( D @ F )
= ( e @ TB ) )
= ( A @ F ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( ( add_mset @ TB @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( is_heap @ TB @ ( D @ F ) )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( is_heap @ TB @ ( D @ H ) ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( G
= ( val @ TB @ ( D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Heap__axioms__def) ).
thf(921,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( heap_axioms @ TA @ TB )
= ( ^ [A: TA > $o,B: ( list @ TB ) > TA,C: TA > ( multiset @ TB ),D: TA > ( tree @ TB ),E: TA > ( product_prod @ TB @ TA )] :
( ! [F: TA] :
( ( C @ F )
= ( multiset2 @ TB @ ( D @ F ) ) )
& ! [F: list @ TB] : ( is_heap @ TB @ ( D @ ( B @ F ) ) )
& ! [F: TA] :
( ( ( D @ F )
= ( e @ TB ) )
= ( A @ F ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( ( add_mset @ TB @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( is_heap @ TB @ ( D @ F ) )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( is_heap @ TB @ ( D @ H ) ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( G
= ( val @ TB @ ( D @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(145,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( zero_zero @ ( multiset @ TA ) ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_union__eq__empty) ).
thf(674,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( zero_zero @ ( multiset @ TA ) ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(95,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_le__numeral__extra_I3_J) ).
thf(530,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(176,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) )
= ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_subset__mset_Ole__add__same__cancel1) ).
thf(794,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) )
= ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(150,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_99_surj__pair) ).
thf(718,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)],[150]) ).
thf(20,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( B = C )
=> ( subseteq_mset @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_subset__mset_Oord__le__eq__trans) ).
thf(298,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( B = C )
=> ( subseteq_mset @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(90,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( set_mset @ TA @ ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_multi__member__last) ).
thf(513,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( set_mset @ TA @ ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ord__le__eq__subst) ).
thf(264,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(194,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_internal__case__prod__conv) ).
thf(856,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(13,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_109_prod__induct5) ).
thf(279,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)],[13]) ).
thf(19,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ord @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oord) ).
thf(296,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ord @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(155,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(733,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(226,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: list @ TA] :
( ( heapIm1912108042t_tree @ TA @ ( cons @ TA @ A @ B ) )
= ( t @ TA @ A @ ( heapIm1912108042t_tree @ TA @ B ) @ ( e @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_of__list__tree_Osimps_I2_J) ).
thf(965,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: list @ TA] :
( ( heapIm1912108042t_tree @ TA @ ( cons @ TA @ A @ B ) )
= ( t @ TA @ A @ ( heapIm1912108042t_tree @ TA @ B ) @ ( e @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(160,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_le__add__same__cancel1) ).
thf(750,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(58,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
= ( subseteq_mset @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_mset__subset__eq__mono__add__right__cancel) ).
thf(402,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
= ( subseteq_mset @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(169,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_add__mono__thms__linordered__semiring_I2_J) ).
thf(772,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( product_prod @ TA @ TB ),F: TB > $o,G: TB,H: TB > ( list @ TA ) > $o,I: list @ TA] :
( ( removeMax @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( ( F @ G )
=> ( ( H @ G @ I )
=> ( ! [J: TB,K: list @ TA,L: TA,M: TB] :
( ~ ( B @ J )
=> ( ( F @ J )
=> ( ( ( product_Pair @ TA @ TB @ L @ M )
= ( E @ J ) )
=> ( ( H @ J @ K )
=> ( H @ M @ ( cons @ TA @ L @ K ) ) ) ) ) )
=> ( H @ A @ ( ssort @ TB @ TA @ B @ E @ G @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_RemoveMax_Ossort_HInduct) ).
thf(743,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( product_prod @ TA @ TB ),F: TB > $o,G: TB,H: TB > ( list @ TA ) > $o,I: list @ TA] :
( ( removeMax @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( ( F @ G )
=> ( ( H @ G @ I )
=> ( ! [J: TB,K: list @ TA,L: TA,M: TB] :
( ~ ( B @ J )
=> ( ( F @ J )
=> ( ( ( product_Pair @ TA @ TB @ L @ M )
= ( E @ J ) )
=> ( ( H @ J @ K )
=> ( H @ M @ ( cons @ TA @ L @ K ) ) ) ) ) )
=> ( H @ A @ ( ssort @ TB @ TA @ B @ E @ G @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_le__fun__def) ).
thf(281,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F )
=> ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Heap_Ointro) ).
thf(562,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F )
=> ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(210,axiom,
ord_less_eq @ a @ v2 @ v1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062v2_A_092_060le_062_Av1_092_060close_062) ).
thf(904,plain,
ord_less_eq @ a @ v2 @ v1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(187,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_add__nonneg__eq__0__iff) ).
thf(826,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(114,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( ( zero_zero @ ( multiset @ TA ) )
= ( plus_plus @ ( multiset @ TA ) @ A @ B ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_empty__eq__union) ).
thf(577,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( ( zero_zero @ ( multiset @ TA ) )
= ( plus_plus @ ( multiset @ TA ) @ A @ B ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(134,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( ( zero_zero @ ( multiset @ TA ) )
= ( plus_plus @ ( multiset @ TA ) @ A @ B ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_subset__mset_Ozero__eq__add__iff__both__eq__0) ).
thf(641,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( ( zero_zero @ ( multiset @ TA ) )
= ( plus_plus @ ( multiset @ TA ) @ A @ B ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_le__funD) ).
thf(313,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(148,axiom,
! [TA: $tType,A: TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) @ B )
= ( member @ TA @ A @ ( set_mset @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_single__subset__iff) ).
thf(713,plain,
! [TA: $tType,A: TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) @ B )
= ( member @ TA @ A @ ( set_mset @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( ssort_dom @ TA @ TB )
= ( ssort_dom @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_RemoveMax_Ossort_H__dom_Ocong) ).
thf(466,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(38,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_108_prod__induct4) ).
thf(350,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)],[38]) ).
thf(99,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_112_old_Oprod_Oexhaust) ).
thf(540,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)],[99]) ).
thf(165,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] : ( subseteq_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_mset__subset__eq__add__right) ).
thf(764,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] : ( subseteq_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(156,axiom,
! [TA: $tType,A: TA] :
~ ( in_tree @ TA @ A @ ( e @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_in__tree_Osimps_I1_J) ).
thf(736,plain,
! [TA: $tType,A: TA] :
~ ( in_tree @ TA @ A @ ( e @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(28,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_subset__mset_Oorder__trans) ).
thf(318,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( A = B )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_subset__mset_Oord__eq__le__trans) ).
thf(271,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( A = B )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( is_heap @ TB @ ( E @ G ) )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( is_heap @ TB @ ( E @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Heap_Oremove__max__is__heap) ).
thf(599,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( is_heap @ TB @ ( E @ G ) )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( is_heap @ TB @ ( E @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(204,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( e @ TA )
!= ( t @ TA @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Tree_Odistinct_I1_J) ).
thf(880,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( e @ TA )
!= ( t @ TA @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(137,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
= ( subseteq_mset @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_subset__mset_Oadd__le__cancel__right) ).
thf(649,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ C @ B ) )
= ( subseteq_mset @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(238,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ D @ E @ F ) ) ) ) @ ( t @ TA @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( t @ TA @ D @ E @ F ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_siftDown_Osimps_I5_J) ).
thf(1043,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ D @ E @ F ) ) ) ) @ ( t @ TA @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( t @ TA @ D @ E @ F ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(182,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_add__nonpos__eq__0__iff) ).
thf(811,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(130,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_subset__mset_Oadd__decreasing2) ).
thf(631,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(97,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__nonpos__nonpos) ).
thf(535,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(120,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( set_mset @ TA @ A ) )
=> ( member @ TA @ C @ ( set_mset @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_mset__subset__eqD) ).
thf(594,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( set_mset @ TA @ A ) )
=> ( member @ TA @ C @ ( set_mset @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: TA,H: TB,I: TA] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( F @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( E @ G ) )
=> ( H
= ( lattic929149872er_Max @ TB @ ( set2 @ TA @ TB @ D @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_RemoveMax_Oremove__max__max) ).
thf(626,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: TA,H: TB,I: TA] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( F @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( E @ G ) )
=> ( H
= ( lattic929149872er_Max @ TB @ ( set2 @ TA @ TB @ D @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(219,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( e @ TA ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_is__heap_Osimps_I4_J) ).
thf(943,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( e @ TA ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(143,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ A ) )
= ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_subset__mset_Ole__add__same__cancel2) ).
thf(668,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ A ) )
= ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(45,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( add_mset @ TA @ A @ B ) @ ( add_mset @ TA @ A @ C ) )
= ( subseteq_mset @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_mset__subset__eq__add__mset__cancel) ).
thf(367,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( add_mset @ TA @ A @ B ) @ ( add_mset @ TA @ A @ C ) )
= ( subseteq_mset @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(104,axiom,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_empty__le) ).
thf(552,plain,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(191,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_union__left__cancel) ).
thf(848,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_relChain__def) ).
thf(520,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(224,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( in_tree @ TA @ ( val @ TA @ ( heapIm748920189ftDown @ TA @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_siftDown__in__tree) ).
thf(959,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( in_tree @ TA @ ( val @ TA @ ( heapIm748920189ftDown @ TA @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(167,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_100_prod__cases) ).
thf(768,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)],[167]) ).
thf(243,axiom,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ~ ! [B: TA,C: tree @ TA,D: tree @ TA] :
( A
!= ( t @ TA @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Tree_Oexhaust) ).
thf(1066,plain,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ~ ! [B: TA,C: tree @ TA,D: tree @ TA] :
( A
!= ( t @ TA @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(172,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ~ ! [C: multiset @ TA] :
( B
!= ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_subset__mset_Oless__eqE) ).
thf(780,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ~ ! [C: multiset @ TA] :
( B
!= ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(205,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ~ ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_siftDown_Ocases) ).
thf(883,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ~ ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(55,axiom,
! [TA: $tType,A: TA,B: multiset @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ B ) )
=> ? [C: multiset @ TA] :
( B
= ( add_mset @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_multi__member__split) ).
thf(394,plain,
! [TA: $tType,A: TA,B: multiset @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ B ) )
=> ? [C: multiset @ TA] :
( B
= ( add_mset @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(192,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_list_Oinject) ).
thf(851,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(87,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ C @ ( zero_zero @ ( multiset @ TA ) ) ) )
= ( ( A = C )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_add__mset__eq__single) ).
thf(505,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ C @ ( zero_zero @ ( multiset @ TA ) ) ) )
= ( ( A = C )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(140,axiom,
! [TA: $tType,TB: $tType,A: ( multiset @ TB ) > ( multiset @ TA ) > $o,B: multiset @ TB,C: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TB ) ) @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [D: TB,E: multiset @ TB,F: multiset @ TA] :
( ( A @ E @ F )
=> ( A @ ( add_mset @ TB @ D @ E ) @ F ) )
=> ( ! [D: TA,E: multiset @ TB,F: multiset @ TA] :
( ( A @ E @ F )
=> ( A @ E @ ( add_mset @ TA @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_multiset__induct2) ).
thf(658,plain,
! [TA: $tType,TB: $tType,A: ( multiset @ TB ) > ( multiset @ TA ) > $o,B: multiset @ TB,C: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TB ) ) @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [D: TB,E: multiset @ TB,F: multiset @ TA] :
( ( A @ E @ F )
=> ( A @ ( add_mset @ TB @ D @ E ) @ F ) )
=> ( ! [D: TA,E: multiset @ TB,F: multiset @ TA] :
( ( A @ E @ F )
=> ( A @ E @ ( add_mset @ TA @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(80,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA,D: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ C @ D )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) @ ( plus_plus @ ( multiset @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_mset__subset__eq__mono__add) ).
thf(473,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA,D: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ C @ D )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) @ ( plus_plus @ ( multiset @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(65,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_add__le__cancel__left) ).
thf(426,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > $o,B: ( list @ TB ) > TA,C: TA > $o,D: TA > ( product_prod @ TB @ TA ),E: TA > ( multiset @ TB )] :
( ! [F: list @ TB] : ( A @ ( B @ F ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( C @ F )
=> ( ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( G
= ( lattic929149872er_Max @ TB @ ( set2 @ TA @ TB @ E @ F ) ) ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( C @ F )
=> ( ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( ( add_mset @ TB @ G @ ( E @ H ) )
= ( E @ F ) ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( C @ F )
=> ( ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( A @ H ) ) ) )
=> ( removeMax_axioms @ TA @ TB @ C @ B @ E @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_RemoveMax__axioms_Ointro) ).
thf(680,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > $o,B: ( list @ TB ) > TA,C: TA > $o,D: TA > ( product_prod @ TB @ TA ),E: TA > ( multiset @ TB )] :
( ! [F: list @ TB] : ( A @ ( B @ F ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( C @ F )
=> ( ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( G
= ( lattic929149872er_Max @ TB @ ( set2 @ TA @ TB @ E @ F ) ) ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( C @ F )
=> ( ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( ( add_mset @ TB @ G @ ( E @ H ) )
= ( E @ F ) ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( C @ F )
=> ( ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( D @ F ) )
=> ( A @ H ) ) ) )
=> ( removeMax_axioms @ TA @ TB @ C @ B @ E @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(40,axiom,
! [TA: $tType] :
( ( (=) @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ B @ A )
& ( subseteq_mset @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_subset__mset_Odual__order_Oeq__iff) ).
thf(355,plain,
! [TA: $tType] :
( ( (=) @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ B @ A )
& ( subseteq_mset @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(141,axiom,
! [TA: $tType,A: multiset @ TA,B: TA] :
( A
!= ( add_mset @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_multi__self__add__other__not__self) ).
thf(663,plain,
! [TA: $tType,A: multiset @ TA,B: TA] :
( A
!= ( add_mset @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(102,axiom,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_subset__mset_Obot_Oextremum) ).
thf(548,plain,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(217,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( multiset2 @ TA @ ( t @ TA @ A @ B @ C ) )
= ( plus_plus @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) @ ( multiset2 @ TA @ B ) @ ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) ) @ ( multiset2 @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_multiset_Osimps_I2_J) ).
thf(927,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( multiset2 @ TA @ ( t @ TA @ A @ B @ C ) )
= ( plus_plus @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) @ ( multiset2 @ TA @ B ) @ ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) ) @ ( multiset2 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(48,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ C @ A )
=> ( subseteq_mset @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_subset__mset_Odual__order_Otrans) ).
thf(374,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ C @ A )
=> ( subseteq_mset @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(227,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( in_tree @ TA )
= ( ^ [A: TA,B: tree @ TA] : ( in_tree @ TA @ A @ ( heapIm748920189ftDown @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_siftDown__in__tree__set) ).
thf(968,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( in_tree @ TA )
= ( ^ [A: TA,B: tree @ TA] : ( in_tree @ TA @ A @ ( heapIm748920189ftDown @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(186,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_not__Cons__self2) ).
thf(823,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(170,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(776,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Heap_Oaxioms_I2_J) ).
thf(557,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(115,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ B @ ( plus_plus @ ( multiset @ TA ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_subset__mset_Oadd__increasing2) ).
thf(580,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ B @ ( plus_plus @ ( multiset @ TA ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(201,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA,D: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ C @ D )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) @ ( plus_plus @ ( multiset @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_subset__mset_Oadd__mono) ).
thf(872,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA,D: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ C @ D )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) @ ( plus_plus @ ( multiset @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(228,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ ( multiset2 @ TA @ B ) ) )
=> ( ( is_heap @ TA @ B )
=> ( ord_less_eq @ TA @ A @ ( val @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_heap__top__geq) ).
thf(971,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ ( multiset2 @ TA @ B ) ) )
=> ( ( is_heap @ TA @ B )
=> ( ord_less_eq @ TA @ A @ ( val @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ord__eq__le__subst) ).
thf(327,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: product_prod @ TA @ ( list @ TB ),H: ( product_prod @ TA @ ( list @ TB ) ) > $o] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( ssort_dom @ TA @ TB @ B @ E @ G )
=> ( ! [I: TA,J: list @ TB] :
( ! [K: TB,L: TA] :
( ~ ( B @ I )
=> ( ( ( product_Pair @ TB @ TA @ K @ L )
= ( E @ I ) )
=> ( ssort_dom @ TA @ TB @ B @ E @ ( product_Pair @ TA @ ( list @ TB ) @ L @ ( cons @ TB @ K @ J ) ) ) ) )
=> ( ! [K: TB,L: TA] :
( ~ ( B @ I )
=> ( ( ( product_Pair @ TB @ TA @ K @ L )
= ( E @ I ) )
=> ( H @ ( product_Pair @ TA @ ( list @ TB ) @ L @ ( cons @ TB @ K @ J ) ) ) ) )
=> ( H @ ( product_Pair @ TA @ ( list @ TB ) @ I @ J ) ) ) )
=> ( H @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_RemoveMax_Ossort_H__dom_Oinducts) ).
thf(409,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o,G: product_prod @ TA @ ( list @ TB ),H: ( product_prod @ TA @ ( list @ TB ) ) > $o] :
( ( removeMax @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( ssort_dom @ TA @ TB @ B @ E @ G )
=> ( ! [I: TA,J: list @ TB] :
( ! [K: TB,L: TA] :
( ~ ( B @ I )
=> ( ( ( product_Pair @ TB @ TA @ K @ L )
= ( E @ I ) )
=> ( ssort_dom @ TA @ TB @ B @ E @ ( product_Pair @ TA @ ( list @ TB ) @ L @ ( cons @ TB @ K @ J ) ) ) ) )
=> ( ! [K: TB,L: TA] :
( ~ ( B @ I )
=> ( ( ( product_Pair @ TB @ TA @ K @ L )
= ( E @ I ) )
=> ( H @ ( product_Pair @ TA @ ( list @ TB ) @ L @ ( cons @ TB @ K @ J ) ) ) ) )
=> ( H @ ( product_Pair @ TA @ ( list @ TB ) @ I @ J ) ) ) )
=> ( H @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(24,axiom,
! [TA: $tType] :
( ( (=) @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
& ( subseteq_mset @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_subset__mset_Oorder_Oeq__iff) ).
thf(310,plain,
! [TA: $tType] :
( ( (=) @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
& ( subseteq_mset @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(175,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_less__eqE) ).
thf(791,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(68,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_add__nonneg__nonneg) ).
thf(441,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(86,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_verit__la__disequality) ).
thf(502,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( add_mset @ TA @ B @ ( zero_zero @ ( multiset @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_single__eq__single) ).
thf(463,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( add_mset @ TA @ B @ ( zero_zero @ ( multiset @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(79,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_add__le__cancel__right) ).
thf(470,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(117,axiom,
! [TA: $tType] :
( ( heapIm721255937_empty @ TA )
= ( ^ [A: tree @ TA] :
( A
= ( e @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_hs__is__empty__def) ).
thf(585,plain,
! [TA: $tType] :
( ( heapIm721255937_empty @ TA )
= ( ^ [A: tree @ TA] :
( A
= ( e @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(46,axiom,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_subset__mset_Oorder__refl) ).
thf(370,plain,
! [TA: $tType,A: multiset @ TA] : ( subseteq_mset @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(33,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_6) ).
thf(336,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(127,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_mset @ TA @ D ) )
=> ( ord_less_eq @ TA @ C @ E ) )
=> ( A @ ( add_mset @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_multiset__induct__min) ).
thf(613,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_mset @ TA @ D ) )
=> ( ord_less_eq @ TA @ C @ E ) )
=> ( A @ ( add_mset @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(239,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA,G: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( t @ TA @ E @ F @ G ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ E @ F @ G ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ E @ F @ G ) )
& ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_is__heap_Osimps_I5_J) ).
thf(1052,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA,G: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( t @ TA @ E @ F @ G ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ E @ F @ G ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ E @ F @ G ) )
& ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(153,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_double__add__le__zero__iff__single__add__le__zero) ).
thf(727,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( ssort @ TA @ TB )
= ( ssort @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_RemoveMax_Ossort_H_Ocong) ).
thf(859,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) )
= ( ( member @ TA @ A @ ( set_mset @ TA @ B ) )
| ( member @ TA @ A @ ( set_mset @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_union__iff) ).
thf(446,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) )
= ( ( member @ TA @ A @ ( set_mset @ TA @ B ) )
| ( member @ TA @ A @ ( set_mset @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA,D: multiset @ TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ C @ D ) )
=> ( ( A != C )
=> ( member @ TA @ C @ ( set_mset @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_insert__noteq__member) ).
thf(571,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA,D: multiset @ TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ C @ D ) )
=> ( ( A != C )
=> ( member @ TA @ C @ ( set_mset @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(190,axiom,
! [TA: $tType] :
( ( plus_plus @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] : ( plus_plus @ ( multiset @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_union__commute) ).
thf(845,plain,
! [TA: $tType] :
( ( plus_plus @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] : ( plus_plus @ ( multiset @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( B @ E )
=> ( E = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Collection_Ois__empty__inj) ).
thf(250,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( B @ E )
=> ( E = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,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_107_prod__induct3) ).
thf(363,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)],[43]) ).
thf(144,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) )
= ( plus_plus @ ( multiset @ TA ) @ B @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_union__lcomm) ).
thf(671,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) )
= ( plus_plus @ ( multiset @ TA ) @ B @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(163,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: multiset @ TA] :
( A
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Multiset_Ois__empty__def) ).
thf(759,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: multiset @ TA] :
( A
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(118,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A )
=> ( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ B )
=> ( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( zero_zero @ ( multiset @ TA ) ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_subset__mset_Oadd__nonneg__eq__0__iff) ).
thf(588,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A )
=> ( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ B )
=> ( ( ( plus_plus @ ( multiset @ TA ) @ A @ B )
= ( zero_zero @ ( multiset @ TA ) ) )
= ( ( A
= ( zero_zero @ ( multiset @ TA ) ) )
& ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( removeMax @ TA @ TB )
= ( ^ [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
& ( removeMax_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_RemoveMax__def) ).
thf(304,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( removeMax @ TA @ TB )
= ( ^ [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( product_prod @ TB @ TA ),F: TA > $o] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
& ( removeMax_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(138,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
= ( subseteq_mset @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_subset__mset_Oadd__le__cancel__left) ).
thf(652,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) )
= ( subseteq_mset @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(220,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ( is_heap @ TA @ A )
=> ( ( val @ TA @ A )
= ( lattic929149872er_Max @ TA @ ( set_mset @ TA @ ( multiset2 @ TA @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_heap__top__max) ).
thf(946,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ( is_heap @ TA @ A )
=> ( ( val @ TA @ A )
= ( lattic929149872er_Max @ TA @ ( set_mset @ TA @ ( multiset2 @ TA @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(7,axiom,
! [TA: $tType] :
( ( (=) @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
& ( subseteq_mset @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_subset__mset_Oeq__iff) ).
thf(258,plain,
! [TA: $tType] :
( ( (=) @ ( multiset @ TA ) )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
& ( subseteq_mset @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(63,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_le__iff__add) ).
thf(418,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(174,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_101_Pair__inject) ).
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)],[174]) ).
thf(1,conjecture,
( ( multiset2 @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) )
= ( multiset2 @ a @ ( t @ a @ v @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( multiset2 @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) )
!= ( multiset2 @ a @ ( t @ a @ v @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(246,plain,
( ( multiset2 @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) )
!= ( multiset2 @ a @ ( t @ a @ v @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(89,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm818251801eapify @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_heapify_Osimps_I1_J) ).
thf(510,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm818251801eapify @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(82,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( A
!= ( zero_zero @ ( multiset @ TA ) ) )
=> ~ ! [B: TA] :
~ ( member @ TA @ B @ ( set_mset @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_multiset__nonemptyE) ).
thf(478,plain,
! [TA: $tType,A: multiset @ TA] :
( ( A
!= ( zero_zero @ ( multiset @ TA ) ) )
=> ~ ! [B: TA] :
~ ( member @ TA @ B @ ( set_mset @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(52,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_add__increasing2) ).
thf(383,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(189,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_mset @ TA @ D ) )
=> ( ord_less_eq @ TA @ E @ C ) )
=> ( A @ ( add_mset @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_multiset__induct__max) ).
thf(832,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_mset @ TA @ D ) )
=> ( ord_less_eq @ TA @ E @ C ) )
=> ( A @ ( add_mset @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(17,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( A = B )
=> ( subseteq_mset @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_subset__mset_Oeq__refl) ).
thf(290,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( A = B )
=> ( subseteq_mset @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(50,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_subset__mset_Oadd__decreasing) ).
thf(378,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(149,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_add__mono) ).
thf(716,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(178,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( subseteq_mset @ TA @ B @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_subset__mset_Oadd__nonpos__nonpos) ).
thf(800,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ( subseteq_mset @ TA @ B @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(16,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_106_prod__cases7) ).
thf(287,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)],[16]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType] :
( ( set2 @ TA @ TB )
= ( set2 @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Collection_Oset_Ocong) ).
thf(315,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(67,axiom,
! [TA: $tType,A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( A @ ( add_mset @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_multiset__induct) ).
thf(432,plain,
! [TA: $tType,A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( A @ ( add_mset @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(59,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] : ( is_heap @ TA @ ( heapIm818251801eapify @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_heapify__heap__is__heap) ).
thf(405,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] : ( is_heap @ TA @ ( heapIm818251801eapify @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(193,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add__mono__thms__linordered__semiring_I1_J) ).
thf(854,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(199,axiom,
! [TA: $tType] :
( ( subseteq_mset @ TA )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
? [C: multiset @ TA] :
( B
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_mset__subset__eq__exists__conv) ).
thf(867,plain,
! [TA: $tType] :
( ( subseteq_mset @ TA )
= ( ^ [A: multiset @ TA,B: multiset @ TA] :
? [C: multiset @ TA] :
( B
= ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(198,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA] :
( ( in_tree @ TA @ A @ B )
=> ( ( is_heap @ TA @ B )
=> ( ord_less_eq @ TA @ A @ ( val @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_is__heap__max) ).
thf(865,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA] :
( ( in_tree @ TA @ A @ B )
=> ( ( is_heap @ TA @ B )
=> ( ord_less_eq @ TA @ A @ ( val @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(109,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A )
=> ( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ B )
=> ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_subset__mset_Oadd__nonneg__nonneg) ).
thf(564,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A )
=> ( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ B )
=> ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(57,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ C @ A ) @ ( plus_plus @ ( multiset @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_subset__mset_Oadd__left__mono) ).
thf(400,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( subseteq_mset @ TA @ ( plus_plus @ ( multiset @ TA ) @ C @ A ) @ ( plus_plus @ ( multiset @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( ( add_mset @ TB @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_Heap_Oremove__max__multiset_H) ).
thf(635,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( ( add_mset @ TB @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(96,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_subset__mset_Obot_Oextremum__unique) ).
thf(532,plain,
! [TA: $tType,A: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(223,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( is_heap @ TA @ A )
=> ( ( is_heap @ TA @ B )
=> ( ( C
= ( t @ TA @ D @ A @ B ) )
=> ( is_heap @ TA @ ( heapIm748920189ftDown @ TA @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_siftDown__heap__is__heap) ).
thf(955,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( is_heap @ TA @ A )
=> ( ( is_heap @ TA @ B )
=> ( ( C
= ( t @ TA @ D @ A @ B ) )
=> ( is_heap @ TA @ ( heapIm748920189ftDown @ TA @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(206,axiom,
( ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ v )
=> ( ( multiset2 @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) )
= ( multiset2 @ a @ ( t @ a @ v @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__C5__2_Ohyps_C_I1_J) ).
thf(886,plain,
( ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ v )
=> ( ( multiset2 @ a @ ( heapIm748920189ftDown @ a @ ( t @ a @ v @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) )
= ( multiset2 @ a @ ( t @ a @ v @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( product_prod @ TA @ TB ),F: TB > $o,G: list @ TA] :
( ( removeMax @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( F @ ( C @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_RemoveMax_Oof__list__inv) ).
thf(294,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( product_prod @ TA @ TB ),F: TB > $o,G: list @ TA] :
( ( removeMax @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( F @ ( C @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(214,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA] :
( ( ( t @ TA @ A @ B @ C )
= ( t @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Tree_Oinject) ).
thf(918,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA] :
( ( ( t @ TA @ A @ B @ C )
= ( t @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(41,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_subset__mset_Oantisym__conv) ).
thf(358,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA] :
( ( subseteq_mset @ TA @ A @ B )
=> ( ( subseteq_mset @ TA @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(181,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( add_mset @ TA @ A @ B )
= C )
=> ( member @ TA @ A @ ( set_mset @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_union__single__eq__member) ).
thf(807,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( ( add_mset @ TA @ A @ B )
= C )
=> ( member @ TA @ A @ ( set_mset @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(158,axiom,
! [TA: $tType] :
( ( unique1598680935umeral @ TA )
=> ! [A: TA,B: TA] :
( ( unique455577585es_aux @ TA @ ( product_Pair @ TA @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_divides__aux__eq) ).
thf(740,plain,
! [TA: $tType] :
( ( unique1598680935umeral @ TA )
=> ! [A: TA,B: TA] :
( ( unique455577585es_aux @ TA @ ( product_Pair @ TA @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(196,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_add__right__mono) ).
thf(860,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(121,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_118_old_Oprod_Orec) ).
thf(596,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)],[121]) ).
thf(94,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ B @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_subset__mset_Oadd__increasing) ).
thf(528,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( subseteq_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) @ A )
=> ( ( subseteq_mset @ TA @ B @ C )
=> ( subseteq_mset @ TA @ B @ ( plus_plus @ ( multiset @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(135,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ C @ ( zero_zero @ ( multiset @ TA ) ) ) )
= ( ( B
= ( zero_zero @ ( multiset @ TA ) ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_add__mset__eq__singleton__iff) ).
thf(644,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: TA] :
( ( ( add_mset @ TA @ A @ B )
= ( add_mset @ TA @ C @ ( zero_zero @ ( multiset @ TA ) ) ) )
= ( ( B
= ( zero_zero @ ( multiset @ TA ) ) )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(233,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_right_Osimps) ).
thf(982,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__funE) ).
thf(277,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(125,axiom,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ ( add_mset @ TA @ A @ B ) @ C )
= ( add_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_union__mset__add__mset__left) ).
thf(607,plain,
! [TA: $tType,A: TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ ( add_mset @ TA @ A @ B ) @ C )
= ( add_mset @ TA @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(34,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_104_prod__cases5) ).
thf(337,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)],[34]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > ( multiset @ TB ),B: TA > ( tree @ TB ),C: ( list @ TB ) > TA,D: TA > $o,E: TA > ( product_prod @ TB @ TA )] :
( ! [F: TA] :
( ( A @ F )
= ( multiset2 @ TB @ ( B @ F ) ) )
=> ( ! [F: list @ TB] : ( is_heap @ TB @ ( B @ ( C @ F ) ) )
=> ( ! [F: TA] :
( ( ( B @ F )
= ( e @ TB ) )
= ( D @ F ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( ( add_mset @ TB @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( is_heap @ TB @ ( B @ F ) )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( is_heap @ TB @ ( B @ H ) ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( G
= ( val @ TB @ ( B @ F ) ) ) ) )
=> ( heap_axioms @ TA @ TB @ D @ C @ A @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Heap__axioms_Ointro) ).
thf(1009,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > ( multiset @ TB ),B: TA > ( tree @ TB ),C: ( list @ TB ) > TA,D: TA > $o,E: TA > ( product_prod @ TB @ TA )] :
( ! [F: TA] :
( ( A @ F )
= ( multiset2 @ TB @ ( B @ F ) ) )
=> ( ! [F: list @ TB] : ( is_heap @ TB @ ( B @ ( C @ F ) ) )
=> ( ! [F: TA] :
( ( ( B @ F )
= ( e @ TB ) )
= ( D @ F ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( ( add_mset @ TB @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( is_heap @ TB @ ( B @ F ) )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( is_heap @ TB @ ( B @ H ) ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( G
= ( val @ TB @ ( B @ F ) ) ) ) )
=> ( heap_axioms @ TA @ TB @ D @ C @ A @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( H
= ( val @ TB @ ( E @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Heap_Oremove__max__val) ).
thf(543,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( H
= ( val @ TB @ ( E @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(73,axiom,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ C )
= ( plus_plus @ ( multiset @ TA ) @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_union__assoc) ).
thf(454,plain,
! [TA: $tType,A: multiset @ TA,B: multiset @ TA,C: multiset @ TA] :
( ( plus_plus @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) @ A @ B ) @ C )
= ( plus_plus @ ( multiset @ TA ) @ A @ ( plus_plus @ ( multiset @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(244,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm818251801eapify @ TA @ ( t @ TA @ A @ B @ C ) )
= ( heapIm748920189ftDown @ TA @ ( t @ TA @ A @ ( heapIm818251801eapify @ TA @ B ) @ ( heapIm818251801eapify @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_heapify_Osimps_I2_J) ).
thf(1069,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm818251801eapify @ TA @ ( t @ TA @ A @ B @ C ) )
= ( heapIm748920189ftDown @ TA @ ( t @ TA @ A @ ( heapIm818251801eapify @ TA @ B ) @ ( heapIm818251801eapify @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1075,plain,
$false,
inference(cvc4,[status(thm)],[892,629,365,347,962,777,666,481,352,977,730,449,655,677,523,582,762,385,550,797,814,930,1063,340,829,973,320,372,949,460,1055,724,802,344,817,559,638,416,316,261,421,870,284,770,756,591,443,1040,376,253,574,905,475,924,397,877,1072,988,602,766,307,452,248,380,546,334,910,952,302,862,820,407,429,275,467,361,889,566,484,324,974,874,980,388,610,783,256,488,537,901,554,753,647,985,515,738,911,721,569,605,1060,457,633,805,508,921,674,530,794,718,298,513,264,856,279,296,733,965,750,402,772,743,281,562,904,826,577,641,313,713,466,350,540,764,736,318,271,599,880,649,1043,811,631,535,594,626,943,668,367,552,848,520,959,768,1066,780,883,394,851,505,658,473,426,680,355,663,548,927,374,968,823,776,557,580,872,971,327,409,310,791,441,502,463,470,585,370,336,613,1052,727,859,446,571,845,250,363,671,759,588,304,652,946,258,418,786,246,510,478,383,832,290,378,716,800,287,315,432,405,854,867,865,564,400,635,532,955,886,294,918,358,807,740,860,596,528,644,982,277,607,337,1009,543,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP070^2 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n026.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 6 14:19:54 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.68/1.16 % [INFO] Parsing done (280ms).
% 2.14/1.17 % [INFO] Running in sequential loop mode.
% 2.92/1.41 % [INFO] eprover registered as external prover.
% 2.92/1.41 % [INFO] cvc4 registered as external prover.
% 2.92/1.42 % [INFO] Scanning for conjecture ...
% 3.22/1.53 % [INFO] Found a conjecture and 276 axioms. Running axiom selection ...
% 3.60/1.65 % [INFO] Axiom selection finished. Selected 243 axioms (removed 33 axioms).
% 4.57/1.91 % [INFO] Problem is higher-order (TPTP THF).
% 4.57/1.93 % [INFO] Type checking passed.
% 4.57/1.94 % [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 ...
% 74.16/47.93 % External prover 'cvc4' found a proof!
% 74.16/47.93 % [INFO] Killing All external provers ...
% 74.16/47.94 % Time passed: 47392ms (effective reasoning time: 46762ms)
% 74.16/47.94 % 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)>
% 74.16/47.94 % Axioms used in derivation (243): fact_12_siftDown_Osimps_I1_J, fact_159_RemoveMax_Ossort_H__dom_Oinducts, fact_134_multiset__cases, fact_50_le__funE, fact_190_add__mset__subseteq__single__iff, fact_66_le__cases3, fact_225_add__mono__thms__linordered__semiring_I3_J, fact_86_Collection_Ois__empty__empty, fact_101_Pair__inject, fact_152_le__numeral__extra_I3_J, fact_10_right_Osimps, tfree_0, fact_23_Heap_Oas__tree__empty, fact_145_RemoveMax_Oaxioms_I1_J, fact_253_add__nonneg__nonneg, fact_197_subset__mset_Oantisym, tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add, fact_146_multi__member__last, fact_233_add__le__imp__le__left, fact_21_heapify_Osimps_I1_J, fact_62_ord__le__eq__trans, fact_185_zero__le__double__add__iff__zero__le__single__add, fact_24_Heap_Ois__heap__of__list, fact_85_Collection_Ois__empty__inj, fact_77_Heap__def, fact_111_prod__induct7, fact_255_add__decreasing2, fact_13_Heap_Omultiset, fact_179_union__mset__add__mset__left, fact_230_less__eqE, fact_1_True, fact_137_empty__not__add__mset, fact_3__C5__2_Ohyps_C_I1_J, fact_119_internal__case__prod__conv, fact_178_union__mset__add__mset__right, fact_110_prod__induct6, fact_201_subset__mset_Ole__iff__add, fact_166_add__le__cancel__left, fact_222_mset__subset__eqD, fact_208_subset__mset_Oorder_Oeq__iff, fact_107_prod__induct3, fact_204_subset__mset_Oorder_Otrans, fact_214_subset__mset_Oord__eq__le__trans, fact_195_subset__mset_Oeq__iff, fact_182_le__add__same__cancel1, fact_161_multiset_Osimps_I2_J, fact_202_mset__subset__eq__add__left, fact_135_multiset__induct, fact_116_union__single__eq__member, tcon_fun___Orderings_Oord, fact_219_subset__mset_Odual__order_Oantisym, fact_163_single__subset__iff, fact_128_add__mset__eq__singleton__iff, fact_235_empty__neutral_I2_J, fact_191_union__assoc, fact_75_heap__top__max, fact_212_mset__subset__eq__exists__conv, fact_112_old_Oprod_Oexhaust, fact_123_Collection_Oset_Ocong, fact_169_subset__mset_Ole__zero__eq, tcon_HOL_Obool___Orderings_Olinorder, fact_28_Tree_Oexhaust, fact_103_prod__cases4, fact_165_subset__mset_Odual__order_Orefl, fact_136_multiset__induct2, fact_131_single__eq__single, fact_36_in__tree_Osimps_I2_J, fact_148_multiset_Osimps_I1_J, fact_205_subset__mset_Oorder__trans, fact_30_Tree_Odistinct_I1_J, fact_164_subset__mset_Oorder__refl, fact_115_add__mset__commute, fact_229_add__left__mono, fact_172_mset__subset__eq__mono__add__left__cancel, fact_58_linorder__wlog, fact_0__092_060open_062v2_A_092_060le_062_Av1_092_060close_062, fact_224_mset__subset__eq__add__mset__cancel, fact_245_subset__mset_Oadd__nonpos__nonpos, fact_244_subset__mset_Oadd__nonneg__nonneg, fact_9_left_Osimps, fact_118_old_Oprod_Orec, fact_19_is__heap_Osimps_I2_J, fact_189_subset__mset_Ole__add__same__cancel2, fact_82_verit__la__disequality, fact_151_Multiset_Ois__empty__def, fact_49_le__funD, fact_46_Collect__mem__eq, fact_94_add__mset__add__mset__same__iff, fact_139_multiset__nonemptyE, fact_140_RemoveMax_Oof__list__inv, fact_104_prod__cases5, fact_154_RemoveMax_Ossort_HInduct, fact_120_Collection_Oset__def, fact_106_prod__cases7, fact_226_add__mono__thms__linordered__semiring_I2_J, fact_68_le__cases, fact_192_union__lcomm, fact_130_add__mset__eq__single, fact_198_subset__mset_Oeq__refl, fact_250_add__nonpos__eq__0__iff, fact_231_add__right__mono, fact_34_siftDown_Osimps_I5_J, fact_129_single__eq__add__mset, fact_228_add__mono, fact_251_add__nonneg__eq__0__iff, fact_22_is__heap__max, fact_63_ord__eq__le__trans, fact_184_double__add__le__zero__iff__single__add__le__zero, fact_122_removeLeaf_Osimps_I1_J, fact_88_Heap__axioms__def, fact_91_Heap_Oremove__max__val, fact_147_RemoveMax_Oremove__max__multiset, fact_167_add__le__cancel__right, fact_32_siftDown_Osimps_I4_J, fact_27_is__heap_Ocases, fact_173_mset__subset__eq__mono__add__right__cancel, fact_141_RemoveMax_Oaxioms_I2_J, fact_100_prod__cases, fact_188_subset__mset_Ole__add__same__cancel1, fact_248_subset__mset_Obot_Oextremum__uniqueI, fact_5_Tree_Oinject, fact_157_RemoveMax_Ossort_H__dom_Ocong, fact_209_multi__union__self__other__eq, fact_210_subset__mset_Oadd__left__mono, fact_87_not__Cons__self2, fact_52_le__fun__def, fact_96_prod_Oinject, fact_29_Tree_Oinduct, fact_45_mem__Collect__eq, fact_108_prod__induct4, fact_102_prod__cases3, fact_6_heapify_Osimps_I2_J, fact_180_add__le__same__cancel1, fact_220_subset__mset_Oadd__le__imp__le__right, fact_20_is__heap_Osimps_I1_J, fact_168_subset__mset_Obot_Oextremum__unique, fact_215_subset__mset_Oord__le__eq__trans, fact_156_RemoveMax_Ossort_H__dom_Osimps, fact_153_zero__le, fact_162_divides__aux__eq, fact_234_add__le__imp__le__right, fact_37_removeLeaf_Oinduct, fact_213_subset__mset_Oadd__right__mono, fact_199_subset__mset_Oadd__mono, fact_211_subset__mset_Oorder_Oantisym, fact_105_prod__cases6, fact_216_subset__mset_Odual__order_Otrans, fact_144_Collection_Omultiset__empty, fact_93_multi__self__add__other__not__self, fact_206_mset__subset__eq__add__right, fact_2__C5__2_Ohyps_C_I2_J, fact_73_ord__le__eq__subst, fact_254_add__increasing2, fact_218_subset__mset_Oadd__le__imp__le__left, fact_7_siftDown__heap__is__heap, fact_194_union__left__cancel, fact_155_RemoveMax_Ossort_H__dom_Ocases, fact_193_union__commute, fact_89_Heap__axioms_Ointro, fact_47_Collect__cong, fact_99_surj__pair, fact_84_list_Oinject, fact_247_subset__mset_Oadd__nonpos__eq__0__iff, fact_158_RemoveMax_Ossort_H_Ocong, fact_138_multi__nonempty__split, fact_171_subset__mset_Oadd__le__cancel__right, fact_17_is__heap_Osimps_I4_J, fact_26_siftDown__in__tree, fact_4_siftDown__Node, fact_124_RemoveMax__axioms__def, fact_31_siftDown_Osimps_I3_J, fact_132_RemoveMax__def, fact_133_RemoveMax_Ointro, fact_246_subset__mset_Oadd__nonneg__eq__0__iff, fact_241_subset__mset_Oadd__increasing, subcl_Orderings_Olinorder___Orderings_Oord, fact_76_Heap_Ointro, fact_16_is__heap_Osimps_I5_J, fact_149_multiset__induct__min, fact_74_ord__eq__le__subst, fact_176_union__eq__empty, fact_249_verit__sum__simplify, fact_240_subset__mset_Oadd__decreasing, fact_150_le__zero__eq, fact_183_le__add__same__cancel2, fact_252_add__nonpos__nonpos, fact_181_add__le__same__cancel2, fact_221_union__iff, fact_109_prod__induct5, fact_174_subset__mset_Ozero__eq__add__iff__both__eq__0, fact_200_subset__mset_Oless__eqE, fact_236_empty__neutral_I1_J, fact_11_siftDown_Osimps_I2_J, fact_114_add__eq__conv__ex, fact_38_removeLeaf_Ocases, fact_127_multiset__induct__max, fact_203_mset__subset__eq__mono__add, fact_40_hs__is__empty__def, fact_186_subset__mset_Oadd__le__same__cancel1, fact_51_le__funI, fact_39_siftDown_Ocases, fact_142_RemoveMax_Oremove__max__inv, fact_14_in__tree_Osimps_I1_J, fact_170_subset__mset_Oadd__le__cancel__left, fact_78_of__list__tree_Osimps_I2_J, fact_238_subset__mset_Ozero__le, fact_95_old_Oprod_Oinject, fact_97_mset__add, fact_83_Heap_Oaxioms_I1_J, fact_160_RemoveMax_Ossort_H__dom_Ointros, fact_70_linear, fact_92_Heap_Oremove__max__is__heap, fact_175_subset__mset_Oadd__eq__0__iff__both__eq__0, fact_42_heap__top__geq, fact_25_heapify__heap__is__heap, fact_239_subset__mset_Obot_Oextremum, fact_125_RemoveMax__axioms_Ointro, tcon_HOL_Obool___Orderings_Oord_6, fact_18_is__heap_Osimps_I3_J, fact_126_RemoveMax_Oremove__max__max, subcl_Orderings_Olinorder___HOL_Otype, fact_217_subset__mset_Odual__order_Oeq__iff, fact_243_subset__mset_Oadd__increasing2, fact_8_siftDown__in__tree__set, fact_242_subset__mset_Oadd__decreasing2, fact_207_subset__mset_Oantisym__conv, fact_43_Heap_Oaxioms_I2_J, fact_196_union__right__cancel, fact_121_relChain__def, fact_90_Heap_Oremove__max__multiset_H, fact_113_old_Oprod_Oinducts, fact_98_multi__member__split, fact_187_subset__mset_Oadd__le__same__cancel2, fact_237_empty__le, fact_143_Collection_Ois__empty__as__list, fact_227_add__mono__thms__linordered__semiring_I1_J, fact_117_insert__noteq__member, fact_33_val_Osimps, fact_15_is__heap_Osimps_I6_J, fact_232_le__iff__add, fact_44_hs__of__list__def, fact_177_empty__eq__union, fact_35_siftDown_Osimps_I6_J
% 74.16/47.94 % No. of inferences in proof: 490
% 74.16/47.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 47392 ms resp. 46762 ms w/o parsing
% 75.07/48.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 75.07/48.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------