TSTP Solution File: ITP065^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP065^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 07:47:32 EDT 2024
% Result : Theorem 68.21s 30.46s
% Output : Refutation 68.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 282
% Syntax : Number of formulae : 518 ( 162 unt; 48 typ; 0 def)
% Number of atoms : 2186 ( 653 equ; 2 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 12258 ( 316 ~; 32 |; 120 &;10890 @)
% ( 0 <=>; 900 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 11 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 735 ( 735 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 8 con; 0-8 aty)
% Number of variables : 2907 ( 68 ^2730 !; 44 ?;2907 :)
% ( 65 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
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(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(case_Tree_type,type,
case_Tree:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( tree @ TA ) > ( tree @ TA ) > TB ) > ( tree @ TA ) > TB ) ).
thf(pred_Tree_type,type,
pred_Tree:
!>[TA: $tType] : ( ( TA > $o ) > ( tree @ TA ) > $o ) ).
thf(rec_Tree_type,type,
rec_Tree:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( tree @ TA ) > ( tree @ TA ) > TB > TB > TB ) > ( tree @ TA ) > TB ) ).
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(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(bind_type,type,
bind:
!>[TA: $tType,TB: $tType] : ( ( list @ TB ) > ( TB > ( list @ TA ) ) > ( list @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(lenlex_type,type,
lenlex:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) ) ).
thf(lexord_type,type,
lexord:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(listrel_type,type,
listrel:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) ) ) ).
thf(listrel1_type,type,
listrel1:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) ) ).
thf(product_lists_type,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(subseqs_type,type,
subseqs:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(add_mset_type,type,
add_mset:
!>[TA: $tType] : ( TA > ( multiset @ TA ) > ( multiset @ TA ) ) ).
thf(linorder_part_type,type,
linorder_part:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > TA > ( list @ TB ) > ( product_prod @ ( list @ TB ) @ ( product_prod @ ( list @ TB ) @ ( list @ TB ) ) ) ) ).
thf(set_mset_type,type,
set_mset:
!>[TA: $tType] : ( ( multiset @ TA ) > ( set @ TA ) ) ).
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(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',fact_4_siftDown_Ocases) ).
thf(1036,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)],[220]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',fact_79_is__heap__max) ).
thf(629,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)],[123]) ).
thf(34,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_same__append__eq) ).
thf(333,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(182,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_old_Oprod_Oexhaust) ).
thf(893,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)],[182]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',fact_138_prod__induct6) ).
thf(352,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)],[39]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',fact_81_is__heap_Osimps_I3_J) ).
thf(1083,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)],[229]) ).
thf(200,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_surj__pair) ).
thf(962,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)],[200]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( tree @ TA ) > ( tree @ TA ) > TB > TB > TB,C: TA,D: tree @ TA,E: tree @ TA] :
( ( rec_Tree @ TB @ TA @ A @ B @ ( t @ TA @ C @ D @ E ) )
= ( B @ C @ D @ E @ ( rec_Tree @ TB @ TA @ A @ B @ D ) @ ( rec_Tree @ TB @ TA @ A @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Tree_Osimps_I7_J) ).
thf(977,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( tree @ TA ) > ( tree @ TA ) > TB > TB > TB,C: TA,D: tree @ TA,E: tree @ TA] :
( ( rec_Tree @ TB @ TA @ A @ B @ ( t @ TA @ C @ D @ E ) )
= ( B @ C @ D @ E @ ( rec_Tree @ TB @ TA @ A @ B @ D ) @ ( rec_Tree @ TB @ TA @ A @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(90,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ C ) @ ( listrel1 @ TA @ D ) )
=> ( ! [E: TA] :
( ( C
= ( cons @ TA @ E @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ E ) @ D ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ A @ E ) )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ E ) @ ( listrel1 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_Cons__listrel1E1) ).
thf(523,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ C ) @ ( listrel1 @ TA @ D ) )
=> ( ! [E: TA] :
( ( C
= ( cons @ TA @ E @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ E ) @ D ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ A @ E ) )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ E ) @ ( listrel1 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',fact_82_is__heap_Osimps_I4_J) ).
thf(1005,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)],[213]) ).
thf(16,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_set__eq__subset) ).
thf(276,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ D ) @ ( cons @ TA @ B @ D ) ) @ ( listrel1 @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_listrel1I1) ).
thf(308,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ D ) @ ( cons @ TA @ B @ D ) ) @ ( listrel1 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',fact_19_heapify_Osimps_I2_J) ).
thf(873,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)],[176]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',fact_131_prod__cases4) ).
thf(440,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)],[62]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',fact_98_add__mset__commute) ).
thf(677,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)],[130]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_33_Heap_Oremove__max__is__heap) ).
thf(597,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)],[114]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_subrelI) ).
thf(500,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: set @ ( product_prod @ TB @ TA ),D: ( list @ TB ) > ( list @ TA ) > $o] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: TA,G: list @ TB,H: list @ TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ E @ F ) @ C )
=> ( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ G @ H ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TB @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) )
=> ( D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_listrel_Oinducts) ).
thf(472,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: set @ ( product_prod @ TB @ TA ),D: ( list @ TB ) > ( list @ TA ) > $o] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: TA,G: list @ TB,H: list @ TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ E @ F ) @ C )
=> ( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ G @ H ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TB @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) )
=> ( D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(145,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_successively_Oinduct) ).
thf(747,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',fact_87_Heap__axioms_Ointro) ).
thf(1095,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)],[233]) ).
thf(184,axiom,
! [TA: $tType] :
( ( subseqs @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_subseqs_Osimps_I1_J) ).
thf(898,plain,
! [TA: $tType] :
( ( subseqs @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',fact_243_RemoveMax_Ossort_H__dom_Ocases) ).
thf(301,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)],[24]) ).
thf(9,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_subsetI) ).
thf(257,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] : ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( nil @ TA ) @ ( nil @ TB ) ) @ ( listrel @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_listrel_ONil) ).
thf(320,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] : ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( nil @ TA ) @ ( nil @ TB ) ) @ ( listrel @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(102,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_append__Nil2) ).
thf(565,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(51,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ B ) @ ( append @ TA @ A @ C ) ) @ ( lexord @ TA @ D ) )
=> ( ! [E: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ E ) @ D )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ C ) @ ( lexord @ TA @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_lexord__append__leftD) ).
thf(389,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ B ) @ ( append @ TA @ A @ C ) ) @ ( lexord @ TA @ D ) )
=> ( ! [E: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ E ) @ D )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ C ) @ ( lexord @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(141,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_remdups__adj_Oinduct) ).
thf(719,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_241_RemoveMax_Ossort_H__dom_Ointros) ).
thf(372,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)],[46]) ).
thf(120,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( in_tree @ TA )
= ( ^ [A: TA,B: tree @ TA] : ( in_tree @ TA @ A @ ( heapIm748920189ftDown @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_siftDown__in__tree__set) ).
thf(619,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)],[120]) ).
thf(189,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_rev__induct) ).
thf(917,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(193,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_min__list_Oinduct) ).
thf(934,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',fact_6_removeLeaf_Oinduct) ).
thf(1059,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)],[227]) ).
thf(196,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_shuffles_Oinduct) ).
thf(949,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: list @ TA,E: list @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ D @ E ) @ ( listrel @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( cons @ TA @ A @ D ) @ ( cons @ TB @ B @ E ) ) @ ( listrel @ TA @ TB @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_listrel_OCons) ).
thf(284,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: list @ TA,E: list @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ D @ E ) @ ( listrel @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( cons @ TA @ A @ D ) @ ( cons @ TB @ B @ E ) ) @ ( listrel @ TA @ TB @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',fact_235_RemoveMax_Ointro) ).
thf(289,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)],[21]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',fact_134_prod__cases7) ).
thf(448,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)],[65]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',fact_135_prod__induct3) ).
thf(421,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)],[56]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',fact_100_Heap_Oremove__max__multiset_H) ).
thf(870,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)],[175]) ).
thf(79,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_append__Nil) ).
thf(492,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',fact_182_mset__add) ).
thf(756,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)],[148]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',fact_119_ord__le__eq__trans) ).
thf(443,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)],[63]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( listrel1 @ TA @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_Cons__listrel1__Cons) ).
thf(485,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( listrel1 @ TA @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(225,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( tree @ TB ) > ( tree @ TB ) > TA > TA > TA] :
( ( rec_Tree @ TA @ TB @ A @ B @ ( e @ TB ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Tree_Osimps_I6_J) ).
thf(1051,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( tree @ TB ) > ( tree @ TB ) > TA > TA > TA] :
( ( rec_Tree @ TA @ TB @ A @ B @ ( e @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',fact_159_Collection_Ois__empty__empty) ).
thf(480,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)],[74]) ).
thf(142,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_not__Cons__self2) ).
thf(734,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',fact_91_Heap_Ointro) ).
thf(956,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)],[198]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',fact_223_RemoveMax_Oaxioms_I1_J) ).
thf(428,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)],[59]) ).
thf(12,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_subset__antisym) ).
thf(265,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(48,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_append__is__Nil__conv) ).
thf(380,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(14,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_equalityD1) ).
thf(270,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',fact_77_is__heap_Osimps_I5_J) ).
thf(761,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)],[150]) ).
thf(163,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_list_Oinject) ).
thf(810,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)],[163]) ).
thf(92,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ C ) @ ( listrel1 @ TA @ E ) )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_snoc__listrel1__snoc__iff) ).
thf(534,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ C ) @ ( listrel1 @ TA @ E ) )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',fact_180_insert__noteq__member) ).
thf(798,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)],[159]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( ssort @ TA @ TB )
= ( ssort @ TA @ TB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_RemoveMax_Ossort_H_Ocong) ).
thf(910,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(153,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm874063447f_list @ TA )
= ( ^ [A: list @ TA] : ( heapIm818251801eapify @ TA @ ( heapIm1912108042t_tree @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_hs__of__list__def) ).
thf(778,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)],[153]) ).
thf(222,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/sandbox/benchmark/theBenchmark.p',fact_5_removeLeaf_Ocases) ).
thf(1042,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)],[222]) ).
thf(10,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_subset__trans) ).
thf(260,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(165,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_list__nonempty__induct) ).
thf(820,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(42,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lexord @ TA @ B ) )
= ( ? [C: TA,D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_lexord__Nil__left) ).
thf(361,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lexord @ TA @ B ) )
= ( ? [C: TA,D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(33,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_Cons__eq__appendI) ).
thf(329,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
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/sandbox/benchmark/theBenchmark.p',fact_128_prod__cases) ).
thf(889,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(68,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_self__append__conv2) ).
thf(461,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_arg__min__list_Oinduct) ).
thf(682,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',fact_200_RemoveMax_Oremove__max__max) ).
thf(710,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)],[138]) ).
thf(202,axiom,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_sorted__wrt_Ocases) ).
thf(974,plain,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(109,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_sorted__wrt_Oinduct) ).
thf(583,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(167,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_right_Osimps) ).
thf(830,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)],[167]) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',fact_28_siftDown_Osimps_I2_J) ).
thf(1089,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)],[231]) ).
thf(30,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_append_Oleft__neutral) ).
thf(317,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(119,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_list_OdiscI) ).
thf(615,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',fact_198_RemoveMax__axioms__def) ).
thf(980,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)],[204]) ).
thf(207,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_product__lists_Osimps_I1_J) ).
thf(989,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(77,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(488,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(36,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( listrel1 @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_not__listrel1__Nil) ).
thf(339,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( listrel1 @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_142_Heap__def) ).
thf(753,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)],[147]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fact_118_ord__eq__le__trans) ).
thf(537,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)],[93]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',fact_232_RemoveMax_Oremove__max__multiset) ).
thf(669,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)],[127]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',fact_73_siftDown_Osimps_I6_J) ).
thf(901,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)],[185]) ).
thf(78,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_append_Oassoc) ).
thf(489,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(217,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( is_heap @ TA @ ( e @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_is__heap_Osimps_I1_J) ).
thf(1016,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( is_heap @ TA @ ( e @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',fact_186_heap__top__max) ).
thf(1039,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)],[221]) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',fact_139_prod__induct7) ).
thf(547,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)],[96]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',fact_23_siftDown__heap__is__heap) ).
thf(622,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)],[121]) ).
thf(210,axiom,
! [TA: $tType,A: TA > $o] : ( pred_Tree @ TA @ A @ ( e @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Tree_Opred__inject_I1_J) ).
thf(997,plain,
! [TA: $tType,A: TA > $o] : ( pred_Tree @ TA @ A @ ( e @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_list__induct2_H) ).
thf(701,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(87,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( listrel1 @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_not__Nil__listrel1) ).
thf(515,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( listrel1 @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(187,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( val @ TA @ ( t @ TA @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_val_Osimps) ).
thf(911,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)],[187]) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',fact_9_Heap_Oas__tree__empty) ).
thf(1002,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)],[212]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TB,C: list @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ ( cons @ TB @ B @ C ) ) @ ( listrel @ TA @ TB @ D ) )
=> ~ ! [E: TA,F: list @ TA] :
( ( A
= ( cons @ TA @ E @ F ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ B ) @ D )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ C ) @ ( listrel @ TA @ TB @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_listrel__Cons2) ).
thf(503,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TB,C: list @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ ( cons @ TB @ B @ C ) ) @ ( listrel @ TA @ TB @ D ) )
=> ~ ! [E: TA,F: list @ TA] :
( ( A
= ( cons @ TA @ E @ F ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ B ) @ D )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ C ) @ ( listrel @ TA @ TB @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(3,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_subset__iff) ).
thf(237,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( listrel1 @ TA @ A ) @ ( listrel1 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_listrel1__mono) ).
thf(244,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( listrel1 @ TA @ A ) @ ( listrel1 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',fact_88_Heap__axioms__def) ).
thf(1086,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)],[230]) ).
thf(84,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_6) ).
thf(508,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_append__Cons) ).
thf(541,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',fact_75_siftDown_Osimps_I3_J) ).
thf(1054,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)],[226]) ).
thf(99,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ A ) @ ( append @ TA @ D @ B ) ) @ ( lexord @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_lexord__append__leftI) ).
thf(558,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ A ) @ ( append @ TA @ D @ B ) ) @ ( lexord @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',fact_92_add__mset__add__mset__same__iff) ).
thf(674,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)],[129]) ).
thf(197,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_min__list_Ocases) ).
thf(953,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',fact_32_Heap_Oaxioms_I2_J) ).
thf(926,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)],[190]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_123_linorder__wlog) ).
thf(773,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)],[152]) ).
thf(110,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_left_Osimps) ).
thf(586,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)],[110]) ).
thf(17,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_subset__refl) ).
thf(279,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ B ) @ ( listrel @ TA @ TB @ C ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TB ) ) )
| ? [D: TA,E: TB,F: list @ TA,G: list @ TB] :
( ( A
= ( cons @ TA @ D @ F ) )
& ( B
= ( cons @ TB @ E @ G ) )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ G ) @ ( listrel @ TA @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_listrel_Osimps) ).
thf(573,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ B ) @ ( listrel @ TA @ TB @ C ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TB ) ) )
| ? [D: TA,E: TB,F: list @ TA,G: list @ TB] :
( ( A
= ( cons @ TA @ D @ F ) )
& ( B
= ( cons @ TB @ E @ G ) )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ G ) @ ( listrel @ TA @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(201,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_list_Oinducts) ).
thf(965,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(146,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_strict__sorted_Ocases) ).
thf(750,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',fact_102_le__funE) ).
thf(513,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)],[86]) ).
thf(60,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_append__same__eq) ).
thf(430,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(101,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_self__append__conv) ).
thf(562,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_160_Collection_Ois__empty__inj) ).
thf(423,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)],[57]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ B ) @ ( listrel @ TA @ TB @ C ) )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( nil @ TB ) ) )
=> ~ ! [D: TA,E: TB,F: list @ TA] :
( ( A
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TB] :
( ( B
= ( cons @ TB @ E @ G ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ G ) @ ( listrel @ TA @ TB @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_listrel_Ocases) ).
thf(402,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ B ) @ ( listrel @ TA @ TB @ C ) )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( nil @ TB ) ) )
=> ~ ! [D: TA,E: TB,F: list @ TA] :
( ( A
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TB] :
( ( B
= ( cons @ TB @ E @ G ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ G ) @ ( listrel @ TA @ TB @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_104_le__fun__def) ).
thf(286,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)],[20]) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',fact_179_union__single__eq__member) ).
thf(958,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)],[199]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_bind__simps_I2_J) ).
thf(281,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( ssort_dom @ TA @ TB )
= ( ssort_dom @ TA @ TB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_RemoveMax_Ossort_H__dom_Ocong) ).
thf(579,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( lexord @ TA @ E ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( lexord @ TA @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_lexord__cons__cons) ).
thf(291,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( lexord @ TA @ E ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( lexord @ TA @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(52,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( cons @ TA @ B @ C ) ) @ ( listrel1 @ TA @ D ) )
=> ( ! [E: TA] :
( ( A
= ( cons @ TA @ E @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ B ) @ D ) )
=> ~ ! [E: list @ TA] :
( ( A
= ( cons @ TA @ B @ E ) )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ E @ C ) @ ( listrel1 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_Cons__listrel1E2) ).
thf(391,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( cons @ TA @ B @ C ) ) @ ( listrel1 @ TA @ D ) )
=> ( ! [E: TA] :
( ( A
= ( cons @ TA @ E @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ B ) @ D ) )
=> ~ ! [E: list @ TA] :
( ( A
= ( cons @ TA @ B @ E ) )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ E @ C ) @ ( listrel1 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(28,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( cons @ TA @ D @ B ) ) @ ( listrel1 @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_listrel1I2) ).
thf(313,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( cons @ TA @ D @ B ) ) @ ( listrel1 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(156,axiom,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ( ! [B: TA > TA > $o,C: TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_successively_Ocases) ).
thf(787,plain,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ( ! [B: TA > TA > $o,C: TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(139,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_append1__eq__conv) ).
thf(713,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1,conjecture,
heapIm721255937_empty @ b @ ( e @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( heapIm721255937_empty @ b @ ( e @ b ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(236,plain,
~ ( heapIm721255937_empty @ b @ ( e @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',fact_157_internal__case__prod__conv) ).
thf(804,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)],[161]) ).
thf(136,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_splice_Oinduct) ).
thf(704,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',fact_141_old_Oprod_Oinducts) ).
thf(672,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)],[128]) ).
thf(70,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_append__eq__append__conv2) ).
thf(466,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( tree @ TB ) > ( tree @ TB ) > TA] :
( ( case_Tree @ TA @ TB @ A @ B @ ( e @ TB ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Tree_Osimps_I4_J) ).
thf(1092,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( tree @ TB ) > ( tree @ TB ) > TA] :
( ( case_Tree @ TA @ TB @ A @ B @ ( e @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(151,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_strict__sorted_Oinduct) ).
thf(764,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(15,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_3) ).
thf(274,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',fact_97_add__eq__conv__ex) ).
thf(784,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)],[155]) ).
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/sandbox/benchmark/theBenchmark.p',fact_30_siftDown__in__tree) ).
thf(1048,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(47,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_Nil__is__append__conv) ).
thf(377,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',fact_108_ord__le__eq__subst) ).
thf(451,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)],[66]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) )] :
( ! [B: TB > TA,C: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ C ) ) )
=> ~ ! [B: TB > TA,C: TB,D: list @ TB,E: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( cons @ TB @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_map__tailrec__rev_Ocases) ).
thf(737,plain,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) )] :
( ! [B: TB > TA,C: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ C ) ) )
=> ~ ! [B: TB > TA,C: TB,D: list @ TB,E: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( cons @ TB @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(85,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_eq__Nil__appendI) ).
thf(509,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',fact_31_of__list__tree_Osimps_I2_J) ).
thf(1011,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)],[215]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_137_prod__induct5) ).
thf(419,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)],[55]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',fact_244_RemoveMax_Ossort_H__dom_Osimps) ).
thf(477,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)],[73]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_214_RemoveMax_Oaxioms_I2_J) ).
thf(387,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)],[50]) ).
thf(228,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm748920189ftDown @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_siftDown_Osimps_I1_J) ).
thf(1080,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm748920189ftDown @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',fact_197_RemoveMax__axioms_Ointro) ).
thf(631,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)],[124]) ).
thf(117,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_remdups__adj_Ocases) ).
thf(609,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_list_Odistinct_I1_J) ).
thf(594,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',fact_13_Tree_Oinject) ).
thf(848,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)],[171]) ).
thf(4,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_subsetD) ).
thf(240,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( D @ G )
= ( multiset2 @ TB @ ( E @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Heap_Omultiset) ).
thf(626,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)],[122]) ).
thf(38,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA] :
( ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ A )
| ( D = E )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ A ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ C ) @ ( lexord @ TA @ A ) )
| ( B = C )
| ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ B ) @ ( lexord @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_lexord__linear) ).
thf(345,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA] :
( ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ A )
| ( D = E )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ A ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ C ) @ ( lexord @ TA @ A ) )
| ( B = C )
| ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ B ) @ ( lexord @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(44,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_append__self__conv) ).
thf(367,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(98,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ~ ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ C )
=> ! [F: list @ TA,G: list @ TA] :
( ( A
= ( append @ TA @ F @ ( cons @ TA @ D @ G ) ) )
=> ( B
!= ( append @ TA @ F @ ( cons @ TA @ E @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_listrel1E) ).
thf(552,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ~ ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ C )
=> ! [F: list @ TA,G: list @ TA] :
( ( A
= ( append @ TA @ F @ ( cons @ TA @ D @ G ) ) )
=> ( B
!= ( append @ TA @ F @ ( cons @ TA @ E @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(205,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_append__eq__Cons__conv) ).
thf(983,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(53,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_append_Oright__neutral) ).
thf(399,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(166,axiom,
! [TA: $tType,A: multiset @ TA,B: TA] :
( A
!= ( add_mset @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_multi__self__add__other__not__self) ).
thf(827,plain,
! [TA: $tType,A: multiset @ TA,B: TA] :
( A
!= ( add_mset @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(178,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_neq__Nil__conv) ).
thf(883,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',fact_74_Heap_Oremove__max__val) ).
thf(851,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)],[172]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',fact_115_le__cases3) ).
thf(685,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)],[133]) ).
thf(89,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA] :
( ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ A )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ B ) @ ( lexord @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_lexord__irreflexive) ).
thf(521,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA] :
( ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ A )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ B ) @ ( lexord @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(206,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_list_Oexhaust) ).
thf(986,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',fact_103_le__funI) ).
thf(306,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)],[25]) ).
thf(58,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( lexord @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_lexord__Nil__right) ).
thf(426,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( lexord @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(111,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: tree @ TA,D: tree @ TA] :
( ( pred_Tree @ TA @ A @ ( t @ TA @ B @ C @ D ) )
= ( ( A @ B )
& ( pred_Tree @ TA @ A @ C )
& ( pred_Tree @ TA @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Tree_Opred__inject_I2_J) ).
thf(589,plain,
! [TA: $tType,A: TA > $o,B: TA,C: tree @ TA,D: tree @ TA] :
( ( pred_Tree @ TA @ A @ ( t @ TA @ B @ C @ D ) )
= ( ( A @ B )
& ( pred_Tree @ TA @ A @ C )
& ( pred_Tree @ TA @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',fact_76_siftDown_Osimps_I4_J) ).
thf(1018,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)],[218]) ).
thf(67,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lenlex @ TA @ B ) )
= ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Nil__lenlex__iff1) ).
thf(458,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lenlex @ TA @ B ) )
= ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',fact_72_siftDown_Osimps_I5_J) ).
thf(836,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)],[169]) ).
thf(91,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_append__self__conv2) ).
thf(531,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(194,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_linear) ).
thf(944,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)],[194]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',fact_143_old_Oprod_Orec) ).
thf(795,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)],[158]) ).
thf(131,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( tree @ TA ) > $o ) @ ( pred_Tree @ TA @ A ) @ ( pred_Tree @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Tree_Opred__mono) ).
thf(680,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( tree @ TA ) > $o ) @ ( pred_Tree @ TA @ A ) @ ( pred_Tree @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(108,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( multiset2 @ TA @ ( heapIm748920189ftDown @ TA @ A ) )
= ( multiset2 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_siftDown__multiset) ).
thf(580,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( multiset2 @ TA @ ( heapIm748920189ftDown @ TA @ A ) )
= ( multiset2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( tree @ TA ) > ( tree @ TA ) > TB,C: TA,D: tree @ TA,E: tree @ TA] :
( ( case_Tree @ TB @ TA @ A @ B @ ( t @ TA @ C @ D @ E ) )
= ( B @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Tree_Osimps_I5_J) ).
thf(707,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( tree @ TA ) > ( tree @ TA ) > TB,C: TA,D: tree @ TA,E: tree @ TA] :
( ( case_Tree @ TB @ TA @ A @ B @ ( t @ TA @ C @ D @ E ) )
= ( B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ ( nil @ TB ) ) @ ( listrel @ TA @ TB @ B ) )
=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_listrel__Nil2) ).
thf(310,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ ( nil @ TB ) ) @ ( listrel @ TA @ TB @ B ) )
=> ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',fact_101_le__funD) ).
thf(370,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)],[45]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_bind__simps_I1_J) ).
thf(576,plain,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA,F: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ ( cons @ TA @ A @ E ) ) @ ( append @ TA @ D @ ( cons @ TA @ B @ F ) ) ) @ ( lexord @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_lexord__append__left__rightI) ).
thf(359,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA,F: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ ( cons @ TA @ A @ E ) ) @ ( append @ TA @ D @ ( cons @ TA @ B @ F ) ) ) @ ( lexord @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_187_Collection_Oset__def) ).
thf(544,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)],[95]) ).
thf(35,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_predicate1I) ).
thf(336,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',fact_26_Tree_Oinduct) ).
thf(1023,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)],[219]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',fact_78_is__heap_Osimps_I6_J) ).
thf(600,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)],[115]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',fact_24_is__heap_Ocases) ).
thf(1008,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)],[214]) ).
thf(104,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_rev__predicate1D) ).
thf(571,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(118,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_transpose_Ocases) ).
thf(612,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',fact_130_prod__cases3) ).
thf(497,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)],[81]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',fact_35_siftDown__Node) ).
thf(876,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)],[177]) ).
thf(170,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_Cons__eq__append__conv) ).
thf(845,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(8,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_equalityE) ).
thf(250,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > TB,B: TB] :
( ( linorder_part @ TA @ TB @ A @ B @ ( nil @ TA ) )
= ( product_Pair @ ( list @ TA ) @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( nil @ TA ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_part__code_I1_J) ).
thf(931,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > TB,B: TB] :
( ( linorder_part @ TA @ TB @ A @ B @ ( nil @ TA ) )
= ( product_Pair @ ( list @ TA ) @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( nil @ TA ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',fact_236_RemoveMax__def) ).
thf(482,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)],[75]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(495,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(149,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] : ( is_heap @ TA @ ( heapIm818251801eapify @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_heapify__heap__is__heap) ).
thf(759,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] : ( is_heap @ TA @ ( heapIm818251801eapify @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',fact_20_Heap_Ois__heap__of__list) ).
thf(891,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)],[181]) ).
thf(234,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm818251801eapify @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_heapify_Osimps_I1_J) ).
thf(1126,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm818251801eapify @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',fact_99_Heap_Oaxioms_I1_J) ).
thf(699,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)],[134]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',fact_252_RemoveMax_Ossort_HInduct) ).
thf(813,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)],[164]) ).
thf(88,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ? [D: TA,E: list @ TA] :
( A
= ( cons @ TA @ D @ E ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( append @ TA @ B @ A ) ) @ ( lexord @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_lexord__append__rightI) ).
thf(517,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ? [D: TA,E: list @ TA] :
( A
= ( cons @ TA @ D @ E ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( append @ TA @ B @ A ) ) @ ( lexord @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',fact_178_heap__top__geq) ).
thf(896,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)],[183]) ).
thf(195,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_insert__Nil) ).
thf(946,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(154,axiom,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: list @ TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_shuffles_Ocases) ).
thf(781,plain,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: list @ TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(209,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] : ( is_heap @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_is__heap_Osimps_I2_J) ).
thf(995,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)],[209]) ).
thf(103,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_append__assoc) ).
thf(568,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(188,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_rev__exhaust) ).
thf(914,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(7,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_equalityD2) ).
thf(246,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_107_ord__eq__le__subst) ).
thf(433,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)],[61]) ).
thf(126,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_le__cases) ).
thf(667,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)],[126]) ).
thf(49,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA,F: list @ TA,G: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( ( D
= ( append @ TA @ E @ ( cons @ TA @ A @ F ) ) )
=> ( ( G
= ( append @ TA @ E @ ( cons @ TA @ B @ F ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ G ) @ ( listrel1 @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_listrel1I) ).
thf(383,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA,F: list @ TA,G: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( ( D
= ( append @ TA @ E @ ( cons @ TA @ A @ F ) ) )
=> ( ( G
= ( append @ TA @ E @ ( cons @ TA @ B @ F ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ G ) @ ( listrel1 @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',fact_132_prod__cases5) ).
thf(549,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)],[97]) ).
thf(223,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm1912108042t_tree @ TA @ ( nil @ TA ) )
= ( e @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_of__list__tree_Osimps_I1_J) ).
thf(1045,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm1912108042t_tree @ TA @ ( nil @ TA ) )
= ( e @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(140,axiom,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_subset__eq__mset__impl_Ocases) ).
thf(716,plain,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',fact_25_Tree_Oexhaust) ).
thf(999,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)],[211]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( set2 @ TA @ TB )
= ( set2 @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_Collection_Oset_Ocong) ).
thf(447,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',fact_222_RemoveMax_Oof__list__inv) ).
thf(315,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)],[29]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',fact_17_in__tree_Osimps_I2_J) ).
thf(833,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)],[168]) ).
thf(11,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_subset__eq) ).
thf(262,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(173,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_induct__list012) ).
thf(854,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Pair__inject) ).
thf(790,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(174,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( multiset2 @ TA @ ( heapIm818251801eapify @ TA @ A ) )
= ( multiset2 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_multiset__heapify) ).
thf(867,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( multiset2 @ TA @ ( heapIm818251801eapify @ TA @ A ) )
= ( multiset2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_221_RemoveMax_Oremove__max__inv) ).
thf(603,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)],[116]) ).
thf(5,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_in__mono) ).
thf(242,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_append__eq__appendI) ).
thf(341,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) ) @ ( listrel @ TA @ TB @ A ) @ ( listrel @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_listrel__mono) ).
thf(268,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) ) @ ( listrel @ TA @ TB @ A ) @ ( listrel @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_map__tailrec__rev_Oinduct) ).
thf(807,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',fact_84_old_Oprod_Oinject) ).
thf(664,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)],[125]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',fact_240_RemoveMax_Ossort_H__dom_Oinducts) ).
thf(294,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)],[23]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',fact_181_multi__member__split) ).
thf(801,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)],[160]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',fact_85_prod_Oinject) ).
thf(886,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)],[179]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: product_prod @ ( TA > TB ) @ ( list @ TA )] :
( ! [B: TA > TB,C: TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [B: TA > TB,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ~ ! [B: TA > TB] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_arg__min__list_Ocases) ).
thf(928,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: product_prod @ ( TA > TB ) @ ( list @ TA )] :
( ! [B: TA > TB,C: TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [B: TA > TB,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ~ ! [B: TA > TB] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(144,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_rev__nonempty__induct) ).
thf(740,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(69,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_predicate1D) ).
thf(464,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(235,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( e @ TA )
!= ( t @ TA @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Tree_Odistinct_I1_J) ).
thf(1129,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)],[235]) ).
thf(208,axiom,
! [TA: $tType] :
( ( heapIm721255937_empty @ TA )
= ( ^ [A: tree @ TA] :
( A
= ( e @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_hs__is__empty__def) ).
thf(992,plain,
! [TA: $tType] :
( ( heapIm721255937_empty @ TA )
= ( ^ [A: tree @ TA] :
( A
= ( e @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(32,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
& ( D = E ) )
| ( ( A = B )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ E ) @ ( listrel1 @ TA @ C ) ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ D ) @ ( append @ TA @ B @ E ) ) @ ( listrel1 @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_append__listrel1I) ).
thf(322,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
& ( D = E ) )
| ( ( A = B )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ E ) @ ( listrel1 @ TA @ C ) ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ D ) @ ( append @ TA @ B @ E ) ) @ ( listrel1 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_133_prod__cases6) ).
thf(469,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)],[71]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: list @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( cons @ TA @ A @ B ) @ C ) @ ( listrel @ TA @ TB @ D ) )
=> ~ ! [E: TB,F: list @ TB] :
( ( C
= ( cons @ TB @ E @ F ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ E ) @ D )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ B @ F ) @ ( listrel @ TA @ TB @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_listrel__Cons1) ).
thf(354,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: list @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( cons @ TA @ A @ B ) @ C ) @ ( listrel @ TA @ TB @ D ) )
=> ~ ! [E: TB,F: list @ TB] :
( ( C
= ( cons @ TB @ E @ F ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ E ) @ D )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ B @ F ) @ ( listrel @ TA @ TB @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',fact_136_prod__induct4) ).
thf(560,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)],[100]) ).
thf(112,axiom,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_list__ex1__simps_I1_J) ).
thf(592,plain,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ A ) @ ( listrel @ TB @ TA @ B ) )
=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_listrel__Nil1) ).
thf(364,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ A ) @ ( listrel @ TB @ TA @ B ) )
=> ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(216,axiom,
! [TA: $tType,A: TA] :
~ ( in_tree @ TA @ A @ ( e @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_in__tree_Osimps_I1_J) ).
thf(1014,plain,
! [TA: $tType,A: TA] :
~ ( in_tree @ TA @ A @ ( e @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(2390,plain,
$false,
inference(cvc4,[status(thm)],[1036,629,333,893,352,1083,962,977,523,1005,276,308,873,440,677,597,500,472,747,1095,898,301,257,320,565,389,719,372,619,917,934,1059,949,284,289,448,421,870,492,756,443,485,1051,480,734,956,428,265,380,270,761,810,534,798,910,778,1042,260,820,361,329,889,461,682,710,974,583,830,1089,317,615,980,989,488,339,753,537,669,901,489,1016,1039,547,622,997,701,515,911,1002,503,237,244,1086,508,541,1054,558,674,953,926,773,586,279,573,965,750,513,430,562,423,402,286,958,281,579,291,391,313,787,713,236,804,704,672,466,1092,764,274,784,1048,377,451,737,509,1011,419,477,387,1080,631,609,594,848,240,626,345,367,552,983,399,827,883,851,685,521,986,306,426,589,1018,458,836,531,944,795,680,580,707,310,370,576,359,544,336,1023,600,1008,571,612,497,876,845,250,931,482,495,759,891,1126,699,813,517,896,946,781,995,568,914,246,433,667,383,549,1045,716,999,447,315,833,262,854,790,867,603,242,341,268,807,664,294,801,886,928,740,464,1129,992,322,469,354,560,592,364,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP065^2 : TPTP v8.1.2. Released v7.5.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 6 14:43:09 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.06/1.17 % [INFO] Parsing done (317ms).
% 2.06/1.18 % [INFO] Running in sequential loop mode.
% 2.81/1.40 % [INFO] eprover registered as external prover.
% 2.81/1.40 % [INFO] cvc4 registered as external prover.
% 2.81/1.40 % [INFO] Scanning for conjecture ...
% 3.15/1.51 % [INFO] Found a conjecture and 268 axioms. Running axiom selection ...
% 3.62/1.63 % [INFO] Axiom selection finished. Selected 233 axioms (removed 35 axioms).
% 4.57/1.91 % [INFO] Problem is higher-order (TPTP THF).
% 4.57/1.94 % [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 ...
% 68.21/30.46 % External prover 'cvc4' found a proof!
% 68.21/30.46 % [INFO] Killing All external provers ...
% 68.21/30.46 % Time passed: 29947ms (effective reasoning time: 29278ms)
% 68.21/30.46 % 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)>
% 68.21/30.46 % Axioms used in derivation (233): fact_220_rev__induct, fact_198_RemoveMax__axioms__def, fact_113_le__cases, fact_28_siftDown_Osimps_I2_J, fact_75_siftDown_Osimps_I3_J, fact_84_old_Oprod_Oinject, fact_196_listrel1I1, fact_92_add__mset__add__mset__same__iff, fact_94_predicate1I, fact_5_removeLeaf_Ocases, fact_39_list_Oinject, fact_241_RemoveMax_Ossort_H__dom_Ointros, fact_150_listrel__Nil1, fact_49_map__tailrec__rev_Ocases, fact_137_prod__induct5, fact_36_left_Osimps, fact_244_RemoveMax_Ossort_H__dom_Osimps, fact_115_le__cases3, fact_213_append1__eq__conv, fact_78_is__heap_Osimps_I6_J, fact_206_append__self__conv, fact_101_le__funD, fact_144_product__lists_Osimps_I1_J, fact_161_subset__antisym, fact_200_RemoveMax_Oremove__max__max, fact_20_Heap_Ois__heap__of__list, fact_89_subset__eq__mset__impl_Ocases, fact_73_siftDown_Osimps_I6_J, fact_38_Heap_Omultiset, fact_181_multi__member__split, fact_102_le__funE, fact_10_Tree_Opred__inject_I1_J, fact_216_rev__nonempty__induct, tcon_fun___Orderings_Oord, fact_43_arg__min__list_Ocases, fact_40_shuffles_Ocases, fact_16_Tree_Osimps_I5_J, fact_231_append__listrel1I, fact_14_Tree_Opred__inject_I2_J, fact_204_same__append__eq, fact_135_prod__induct3, fact_223_RemoveMax_Oaxioms_I1_J, fact_185_lexord__Nil__right, fact_71_Tree_Opred__mono, fact_226_eq__Nil__appendI, fact_138_prod__induct6, fact_25_Tree_Oexhaust, tcon_HOL_Obool___Orderings_Olinorder, fact_146_part__code_I1_J, fact_127_surj__pair, fact_186_heap__top__max, fact_218_Cons__eq__append__conv, fact_245_bind__simps_I2_J, fact_79_is__heap__max, fact_42_sorted__wrt_Ocases, fact_187_Collection_Oset__def, fact_191_not__Nil__listrel1, fact_199_snoc__listrel1__snoc__iff, fact_76_siftDown_Osimps_I4_J, fact_12_is__heap_Osimps_I1_J, fact_233_lexord__append__leftD, fact_29_hs__of__list__def, fact_225_append__eq__append__conv2, fact_160_Collection_Ois__empty__inj, fact_176_lexord__Nil__left, fact_96_predicate1D, fact_22_siftDown__in__tree__set, fact_129_Pair__inject, fact_70_list_Odistinct_I1_J, fact_159_Collection_Ois__empty__empty, fact_11_of__list__tree_Osimps_I1_J, fact_239_lexord__append__left__rightI, fact_207_self__append__conv, fact_182_mset__add, fact_142_Heap__def, fact_133_prod__cases6, fact_214_RemoveMax_Oaxioms_I2_J, fact_184_lexord__irreflexive, fact_63_induct__list012, fact_222_RemoveMax_Oof__list__inv, fact_238_listrel1I, fact_104_le__fun__def, fact_234_lexord__append__rightI, fact_67_list_Oinducts, fact_118_ord__eq__le__trans, fact_98_add__mset__commute, fact_32_Heap_Oaxioms_I2_J, fact_88_Heap__axioms__def, fact_252_RemoveMax_Ossort_HInduct, fact_35_siftDown__Node, fact_208_append__self__conv2, fact_224_append__eq__appendI, fact_156_listrel_Osimps, fact_152_listrel__Cons2, fact_183_lexord__linear, fact_168_equalityD1, fact_74_Heap_Oremove__max__val, fact_34_multiset__heapify, fact_59_remdups__adj_Ocases, fact_31_of__list__tree_Osimps_I2_J, fact_167_subset__eq, fact_77_is__heap_Osimps_I5_J, fact_65_list__induct2_H, fact_100_Heap_Oremove__max__multiset_H, fact_188_Cons__listrel1__Cons, fact_173_subset__trans, fact_97_add__eq__conv__ex, fact_157_internal__case__prod__conv, fact_217_append__eq__Cons__conv, fact_236_RemoveMax__def, fact_19_heapify_Osimps_I2_J, fact_247_bind__simps_I1_J, fact_21_heapify__heap__is__heap, fact_58_sorted__wrt_Oinduct, fact_99_Heap_Oaxioms_I1_J, fact_149_listrel_ONil, fact_41_transpose_Ocases, fact_80_val_Osimps, fact_180_insert__noteq__member, fact_24_is__heap_Ocases, fact_69_list_OdiscI, fact_243_RemoveMax_Ossort_H__dom_Ocases, fact_128_prod__cases, fact_139_prod__induct7, fact_50_not__Cons__self2, fact_193_listrel1__mono, fact_17_in__tree_Osimps_I2_J, fact_95_rev__predicate1D, fact_27_Tree_Odistinct_I1_J, fact_83_siftDown__multiset, fact_103_le__funI, fact_132_prod__cases5, fact_33_Heap_Oremove__max__is__heap, fact_162_subsetI, fact_145_subseqs_Osimps_I1_J, fact_60_shuffles_Oinduct, fact_201_append_Oassoc, fact_235_RemoveMax_Ointro, fact_93_multi__self__add__other__not__self, fact_205_append__Nil2, fact_194_Cons__listrel1E2, fact_253_Nil__lenlex__iff1, fact_230_append__Cons, fact_203_append__same__eq, fact_56_arg__min__list_Oinduct, fact_151_listrel__Nil2, fact_165_subsetD, fact_107_ord__eq__le__subst, fact_212_append_Oright__neutral, fact_90_insert__Nil, fact_131_prod__cases4, fact_8_Tree_Osimps_I6_J, fact_170_subset__iff, fact_164_in__mono, fact_57_remdups__adj_Oinduct, fact_51_strict__sorted_Oinduct, fact_26_Tree_Oinduct, tcon_Set_Oset___Orderings_Oord_3, fact_53_map__tailrec__rev_Oinduct, fact_13_Tree_Oinject, fact_155_listrel_Ocases, fact_85_prod_Oinject, fact_242_RemoveMax_Ossort_H__dom_Ocong, fact_72_siftDown_Osimps_I5_J, fact_134_prod__cases7, fact_237_listrel1E, fact_192_not__listrel1__Nil, fact_30_siftDown__in__tree, fact_163_subrelI, fact_211_append__is__Nil__conv, fact_178_heap__top__geq, fact_171_subset__refl, fact_108_ord__le__eq__subst, fact_23_siftDown__heap__is__heap, fact_2_siftDown_Osimps_I1_J, fact_143_old_Oprod_Orec, fact_174_set__eq__subset, fact_140_old_Oprod_Oexhaust, fact_123_linorder__wlog, fact_227_append__Nil, fact_111_linear, fact_136_prod__induct4, fact_54_list__nonempty__induct, fact_64_splice_Oinduct, fact_158_list__ex1__simps_I1_J, fact_87_Heap__axioms_Ointro, fact_0_hs__is__empty__def, fact_7_in__tree_Osimps_I1_J, fact_81_is__heap_Osimps_I3_J, fact_240_RemoveMax_Ossort_H__dom_Oinducts, fact_91_Heap_Ointro, fact_228_append_Oleft__neutral, fact_215_lexord__append__leftI, fact_37_right_Osimps, fact_52_strict__sorted_Ocases, fact_4_siftDown_Ocases, fact_119_ord__le__eq__trans, fact_66_neq__Nil__conv, fact_9_Heap_Oas__tree__empty, fact_177_lexord__cons__cons, fact_166_equalityE, fact_48_successively_Ocases, fact_15_Tree_Osimps_I7_J, fact_153_listrel__Cons1, fact_148_listrel__mono, fact_179_union__single__eq__member, tcon_HOL_Obool___Orderings_Oord_6, fact_169_equalityD2, fact_1_heapify_Osimps_I1_J, fact_55_successively_Oinduct, fact_202_append__assoc, fact_209_self__append__conv2, fact_18_is__heap_Osimps_I2_J, fact_62_min__list_Ocases, fact_190_listrel1I2, fact_141_old_Oprod_Oinducts, fact_197_RemoveMax__axioms_Ointro, fact_254_RemoveMax_Ossort_H_Ocong, fact_147_listrel_Oinducts, fact_82_is__heap_Osimps_I4_J, fact_130_prod__cases3, fact_232_RemoveMax_Oremove__max__multiset, fact_195_Cons__listrel1E1, fact_68_list_Oexhaust, fact_61_min__list_Oinduct, fact_3_Tree_Osimps_I4_J, fact_189_Collection_Oset_Ocong, fact_6_removeLeaf_Oinduct, fact_210_Nil__is__append__conv, fact_221_RemoveMax_Oremove__max__inv, fact_154_listrel_OCons, fact_229_Cons__eq__appendI, fact_219_rev__exhaust
% 68.21/30.46 % No. of inferences in proof: 470
% 68.21/30.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 29947 ms resp. 29278 ms w/o parsing
% 68.96/30.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 68.96/30.65 % [INFO] Killing All external provers ...
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