TSTP Solution File: ITP066^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP066^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 : Mon May 20 22:22:35 EDT 2024
% Result : Theorem 21.14s 6.36s
% Output : Refutation 21.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 302
% Syntax : Number of formulae : 521 ( 269 unt; 85 typ; 0 def)
% Number of atoms : 1021 ( 752 equ; 4 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 4414 ( 168 ~; 17 |; 112 &;3715 @)
% ( 0 <=>; 402 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 33 ( 32 usr)
% Number of type conns : 303 ( 303 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 17 con; 0-6 aty)
% Number of variables : 1497 ( 88 ^1375 !; 34 ?;1497 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1066112583iset_a_type,type,
set_Pr1066112583iset_a: $tType ).
thf(produc741964647iset_a_type,type,
produc741964647iset_a: $tType ).
thf(set_Pr146455751iset_a_type,type,
set_Pr146455751iset_a: $tType ).
thf(set_Pr295926343Tree_a_type,type,
set_Pr295926343Tree_a: $tType ).
thf(produc558600423iset_a_type,type,
produc558600423iset_a: $tType ).
thf(produc1136638567Tree_a_type,type,
produc1136638567Tree_a: $tType ).
thf(set_Pr1821581383od_a_a_type,type,
set_Pr1821581383od_a_a: $tType ).
thf(set_Pr220561863Tree_a_type,type,
set_Pr220561863Tree_a: $tType ).
thf(produc2061001575od_a_a_type,type,
produc2061001575od_a_a: $tType ).
thf(set_Pr720484615iset_a_type,type,
set_Pr720484615iset_a: $tType ).
thf(produc1254371559Tree_a_type,type,
produc1254371559Tree_a: $tType ).
thf(produc1293660967iset_a_type,type,
produc1293660967iset_a: $tType ).
thf(set_Pr1948701895od_a_a_type,type,
set_Pr1948701895od_a_a: $tType ).
thf(multis782275565iset_a_type,type,
multis782275565iset_a: $tType ).
thf(produc1572603623od_a_a_type,type,
produc1572603623od_a_a: $tType ).
thf(set_Pr158363655iset_a_type,type,
set_Pr158363655iset_a: $tType ).
thf(produc1127127335iset_a_type,type,
produc1127127335iset_a: $tType ).
thf(multis2082063201Tree_a_type,type,
multis2082063201Tree_a: $tType ).
thf(set_Pr1070816379Tree_a_type,type,
set_Pr1070816379Tree_a: $tType ).
thf(set_Pr921883667ee_a_a_type,type,
set_Pr921883667ee_a_a: $tType ).
thf(multis599418605od_a_a_type,type,
multis599418605od_a_a: $tType ).
thf(produc143150363Tree_a_type,type,
produc143150363Tree_a: $tType ).
thf(produc981471411ee_a_a_type,type,
produc981471411ee_a_a: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(multiset_multiset_a_type,type,
multiset_multiset_a: $tType ).
thf(set_multiset_a_type,type,
set_multiset_a: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(multiset_a_type,type,
multiset_a: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(tree_a_type,type,
tree_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(plus_plus_multiset_a_type,type,
plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
thf(zero_zero_multiset_a_type,type,
zero_zero_multiset_a: multiset_a ).
thf(nO_MAT1617603563iset_a_type,type,
nO_MAT1617603563iset_a: multiset_a > multiset_a > $o ).
thf(heapIm970322378pify_a_type,type,
heapIm970322378pify_a: tree_a > tree_a ).
thf(heapIm229596386mpty_a_type,type,
heapIm229596386mpty_a: tree_a > $o ).
thf(heapIm1057938560list_a_type,type,
heapIm1057938560list_a: list_a > tree_a ).
thf(heapIm915766629_max_a_type,type,
heapIm915766629_max_a: tree_a > produc143150363Tree_a ).
thf(heapIm1140443833left_a_type,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(heapIm1637418125tree_a_type,type,
heapIm1637418125tree_a: list_a > tree_a ).
thf(heapIm837449470Leaf_a_type,type,
heapIm837449470Leaf_a: tree_a > produc143150363Tree_a ).
thf(heapIm1257206334ight_a_type,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(heapIm1091024090Down_a_type,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(heap_Tree_a_a_type,type,
heap_Tree_a_a: tree_a > ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > tree_a ) > ( tree_a > produc143150363Tree_a ) > $o ).
thf(heap_axioms_Tree_a_a_type,type,
heap_axioms_Tree_a_a: ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > tree_a ) > ( tree_a > produc143150363Tree_a ) > $o ).
thf(heap_axioms_a_a_type,type,
heap_axioms_a_a: ( a > $o ) > ( list_a > a ) > ( a > multiset_a ) > ( a > tree_a ) > ( a > product_prod_a_a ) > $o ).
thf(e_a_type,type,
e_a: tree_a ).
thf(t_a_type,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(in_tree_a_type,type,
in_tree_a: a > tree_a > $o ).
thf(is_heap_a_type,type,
is_heap_a: tree_a > $o ).
thf(multiset_a2_type,type,
multiset_a2: tree_a > multiset_a ).
thf(val_a_type,type,
val_a: tree_a > a ).
thf(if_Pro1144176865Tree_a_type,type,
if_Pro1144176865Tree_a: $o > produc143150363Tree_a > produc143150363Tree_a > produc143150363Tree_a ).
thf(lattic146396397_Max_a_type,type,
lattic146396397_Max_a: set_a > a ).
thf(add_mset_a_type,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(is_empty_a_type,type,
is_empty_a: multiset_a > $o ).
thf(set_mset_a_type,type,
set_mset_a: multiset_a > set_a ).
thf(ord_le1748873858_a_a_o_type,type,
ord_le1748873858_a_a_o: ( tree_a > a > $o ) > ( tree_a > a > $o ) > $o ).
thf(ord_le864074675ee_a_a_type,type,
ord_le864074675ee_a_a: set_Pr921883667ee_a_a > set_Pr921883667ee_a_a > $o ).
thf(ord_less_eq_a_type,type,
ord_less_eq_a: a > a > $o ).
thf(produc649172771ee_a_a_type,type,
produc649172771ee_a_a: tree_a > a > produc981471411ee_a_a ).
thf(produc686083979Tree_a_type,type,
produc686083979Tree_a: a > tree_a > produc143150363Tree_a ).
thf(product_Pair_a_a_type,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(product_fst_Tree_a_a_type,type,
product_fst_Tree_a_a: produc981471411ee_a_a > tree_a ).
thf(product_fst_a_Tree_a_type,type,
product_fst_a_Tree_a: produc143150363Tree_a > a ).
thf(product_snd_Tree_a_a_type,type,
product_snd_Tree_a_a: produc981471411ee_a_a > a ).
thf(product_snd_a_Tree_a_type,type,
product_snd_a_Tree_a: produc143150363Tree_a > tree_a ).
thf(produc1478296771ee_a_a_type,type,
produc1478296771ee_a_a: produc981471411ee_a_a > produc143150363Tree_a ).
thf(produc1515207979Tree_a_type,type,
produc1515207979Tree_a: produc143150363Tree_a > produc981471411ee_a_a ).
thf(collection_Tree_a_a_type,type,
collection_Tree_a_a: tree_a > ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > $o ).
thf(member1092636252ee_a_a_type,type,
member1092636252ee_a_a: produc981471411ee_a_a > set_Pr921883667ee_a_a > $o ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(l1_type,type,
l1: tree_a ).
thf(l2_type,type,
l2: tree_a ).
thf(r1_type,type,
r1: tree_a ).
thf(r2_type,type,
r2: tree_a ).
thf(t_type,type,
t: tree_a ).
thf(t2_type,type,
t2: tree_a ).
thf(t_a2_type,type,
t_a2: tree_a ).
thf(v1_type,type,
v1: a ).
thf(v2_type,type,
v2: a ).
thf(v_type,type,
v: a ).
thf(v_a_type,type,
v_a: a ).
thf(v3_type,type,
v3: a ).
thf(97,axiom,
! [A: tree_a,B: a] :
( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_snd__conv) ).
thf(606,plain,
! [A: tree_a,B: a] :
( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(205,axiom,
! [A: produc143150363Tree_a,B: a,C: tree_a] :
( ( A
= ( produc686083979Tree_a @ B @ C ) )
=> ( ( product_fst_a_Tree_a @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_fstI) ).
thf(1024,plain,
! [A: produc143150363Tree_a,B: a,C: tree_a] :
( ( A
= ( produc686083979Tree_a @ B @ C ) )
=> ( ( product_fst_a_Tree_a @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(81,axiom,
( produc1478296771ee_a_a
= ( ^ [A: produc981471411ee_a_a] : ( produc686083979Tree_a @ ( product_snd_Tree_a_a @ A ) @ ( product_fst_Tree_a_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_prod_Oswap__def) ).
thf(555,plain,
( produc1478296771ee_a_a
= ( ^ [A: produc981471411ee_a_a] : ( produc686083979Tree_a @ ( product_snd_Tree_a_a @ A ) @ ( product_fst_Tree_a_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(113,axiom,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( A @ ( add_mset_a @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_multiset__induct) ).
thf(666,plain,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( A @ ( add_mset_a @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(39,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ A @ B ) @ C )
= ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_union__assoc) ).
thf(333,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ A @ B ) @ C )
= ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(207,axiom,
! [A: a,B: tree_a] :
( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_fst__conv) ).
thf(1031,plain,
! [A: a,B: tree_a] :
( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(30,axiom,
! [A: tree_a,B: a,C: tree_a] :
( ( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_fst__eqD) ).
thf(308,plain,
! [A: tree_a,B: a,C: tree_a] :
( ( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(10,axiom,
! [A: produc981471411ee_a_a,B: tree_a,C: a] :
( ( A
= ( produc649172771ee_a_a @ B @ C ) )
=> ( ( product_fst_Tree_a_a @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_fstI) ).
thf(247,plain,
! [A: produc981471411ee_a_a,B: tree_a,C: a] :
( ( A
= ( produc649172771ee_a_a @ B @ C ) )
=> ( ( product_fst_Tree_a_a @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(76,axiom,
! [A: a,B: a,C: multiset_a] :
( ( add_mset_a @ A @ ( add_mset_a @ B @ C ) )
= ( add_mset_a @ B @ ( add_mset_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_add__mset__commute) ).
thf(511,plain,
! [A: a,B: a,C: multiset_a] :
( ( add_mset_a @ A @ ( add_mset_a @ B @ C ) )
= ( add_mset_a @ B @ ( add_mset_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(17,axiom,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_surj__pair) ).
thf(269,plain,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(94,axiom,
! [A: produc143150363Tree_a,B: a,C: tree_a] :
( ( A
= ( produc686083979Tree_a @ B @ C ) )
=> ( ( product_snd_a_Tree_a @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_sndI) ).
thf(597,plain,
! [A: produc143150363Tree_a,B: a,C: tree_a] :
( ( A
= ( produc686083979Tree_a @ B @ C ) )
=> ( ( product_snd_a_Tree_a @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(131,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) )
= ( plus_plus_multiset_a @ B @ ( plus_plus_multiset_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_add_Oleft__commute) ).
thf(730,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) )
= ( plus_plus_multiset_a @ B @ ( plus_plus_multiset_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(19,axiom,
collection_Tree_a_a @ e_a @ heapIm229596386mpty_a @ heapIm1057938560list_a @ multiset_a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_HS_OCollection__axioms) ).
thf(276,plain,
collection_Tree_a_a @ e_a @ heapIm229596386mpty_a @ heapIm1057938560list_a @ multiset_a2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(54,axiom,
! [A: produc981471411ee_a_a] :
~ ! [B: tree_a,C: a] :
( A
!= ( produc649172771ee_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_old_Oprod_Oexhaust) ).
thf(385,plain,
! [A: produc981471411ee_a_a] :
~ ! [B: tree_a,C: a] :
( A
!= ( produc649172771ee_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(126,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) )
= ( plus_plus_multiset_a @ B @ ( plus_plus_multiset_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_union__lcomm) ).
thf(715,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) )
= ( plus_plus_multiset_a @ B @ ( plus_plus_multiset_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(59,axiom,
! [A: a > multiset_a,B: a > tree_a,C: list_a > a,D: a > $o,E: a > product_prod_a_a] :
( ! [F: a] :
( ( A @ F )
= ( multiset_a2 @ ( B @ F ) ) )
=> ( ! [F: list_a] : ( is_heap_a @ ( B @ ( C @ F ) ) )
=> ( ! [F: a] :
( ( ( B @ F )
= e_a )
= ( D @ F ) )
=> ( ! [F: a,G: a,H: a] :
( ~ ( D @ F )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: a,G: a,H: a] :
( ~ ( D @ F )
=> ( ( is_heap_a @ ( B @ F ) )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( B @ H ) ) ) ) )
=> ( ! [F: a,G: a,H: a] :
( ~ ( D @ F )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( B @ F ) ) ) ) )
=> ( heap_axioms_a_a @ D @ C @ A @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_Heap__axioms_Ointro) ).
thf(404,plain,
! [A: a > multiset_a,B: a > tree_a,C: list_a > a,D: a > $o,E: a > product_prod_a_a] :
( ! [F: a] :
( ( A @ F )
= ( multiset_a2 @ ( B @ F ) ) )
=> ( ! [F: list_a] : ( is_heap_a @ ( B @ ( C @ F ) ) )
=> ( ! [F: a] :
( ( ( B @ F )
= e_a )
= ( D @ F ) )
=> ( ! [F: a,G: a,H: a] :
( ~ ( D @ F )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: a,G: a,H: a] :
( ~ ( D @ F )
=> ( ( is_heap_a @ ( B @ F ) )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( B @ H ) ) ) ) )
=> ( ! [F: a,G: a,H: a] :
( ~ ( D @ F )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( B @ F ) ) ) ) )
=> ( heap_axioms_a_a @ D @ C @ A @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(124,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ ( add_mset_a @ A @ B ) @ C )
= ( add_mset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_union__mset__add__mset__left) ).
thf(709,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ ( add_mset_a @ A @ B ) @ C )
= ( add_mset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(34,axiom,
! [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
& ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_prod_Oexpand) ).
thf(320,plain,
! [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
& ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(60,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_union__left__cancel) ).
thf(436,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(108,axiom,
! [A: produc981471411ee_a_a] :
( ( product_snd_a_Tree_a @ ( produc1478296771ee_a_a @ A ) )
= ( product_fst_Tree_a_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_snd__swap) ).
thf(651,plain,
! [A: produc981471411ee_a_a] :
( ( product_snd_a_Tree_a @ ( produc1478296771ee_a_a @ A ) )
= ( product_fst_Tree_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(13,axiom,
! [A: set_Pr921883667ee_a_a,B: set_Pr921883667ee_a_a] :
( ! [C: tree_a,D: a] :
( ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ A )
=> ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ B ) )
=> ( ord_le864074675ee_a_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_subrelI) ).
thf(257,plain,
! [A: set_Pr921883667ee_a_a,B: set_Pr921883667ee_a_a] :
( ! [C: tree_a,D: a] :
( ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ A )
=> ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ B ) )
=> ( ord_le864074675ee_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(55,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_snd__eqD) ).
thf(389,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(129,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_comm__monoid__add__class_Oadd__0) ).
thf(724,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(50,axiom,
! [A: produc981471411ee_a_a > $o,B: produc981471411ee_a_a] :
( ! [C: tree_a,D: a] : ( A @ ( produc649172771ee_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_old_Oprod_Oinducts) ).
thf(372,plain,
! [A: produc981471411ee_a_a > $o,B: produc981471411ee_a_a] :
( ! [C: tree_a,D: a] : ( A @ ( produc649172771ee_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(138,axiom,
! [A: produc981471411ee_a_a] :
? [B: tree_a,C: a] :
( A
= ( produc649172771ee_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_surj__pair) ).
thf(751,plain,
! [A: produc981471411ee_a_a] :
? [B: tree_a,C: a] :
( A
= ( produc649172771ee_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(154,axiom,
! [A: multiset_a,B: multiset_a,C: a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( add_mset_a @ C @ zero_zero_multiset_a ) )
= ( ( ( A
= ( add_mset_a @ C @ zero_zero_multiset_a ) )
& ( B = zero_zero_multiset_a ) )
| ( ( A = zero_zero_multiset_a )
& ( B
= ( add_mset_a @ C @ zero_zero_multiset_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_union__is__single) ).
thf(802,plain,
! [A: multiset_a,B: multiset_a,C: a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( add_mset_a @ C @ zero_zero_multiset_a ) )
= ( ( ( A
= ( add_mset_a @ C @ zero_zero_multiset_a ) )
& ( B = zero_zero_multiset_a ) )
| ( ( A = zero_zero_multiset_a )
& ( B
= ( add_mset_a @ C @ zero_zero_multiset_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(43,axiom,
! [A: produc981471411ee_a_a,B: tree_a,C: a] :
( ( A
= ( produc649172771ee_a_a @ B @ C ) )
=> ( ( product_snd_Tree_a_a @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_sndI) ).
thf(344,plain,
! [A: produc981471411ee_a_a,B: tree_a,C: a] :
( ( A
= ( produc649172771ee_a_a @ B @ C ) )
=> ( ( product_snd_Tree_a_a @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(149,axiom,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_multiset_Osimps_I1_J) ).
thf(789,plain,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(210,axiom,
! [A: a,B: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
=> ( ( ( t_a @ v1 @ l1 @ r1 )
!= e_a )
=> ( ( plus_plus_multiset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ ( multiset_a2 @ B ) )
= ( multiset_a2 @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9__C4__2_Ohyps_C_I1_J) ).
thf(1040,plain,
! [A: a,B: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
=> ( ( ( t_a @ v1 @ l1 @ r1 )
!= e_a )
=> ( ( plus_plus_multiset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ ( multiset_a2 @ B ) )
= ( multiset_a2 @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(106,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ A @ B ) @ C )
= ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_add_Oassoc) ).
thf(646,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ A @ B ) @ C )
= ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(77,axiom,
! [A: multiset_a,B: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ A @ B ) )
= ( B = zero_zero_multiset_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_add__cancel__right__right) ).
thf(514,plain,
! [A: multiset_a,B: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ A @ B ) )
= ( B = zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(192,axiom,
( ( produc686083979Tree_a @ v @ t2 )
= ( heapIm837449470Leaf_a @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(966,plain,
( ( produc686083979Tree_a @ v @ t2 )
= ( heapIm837449470Leaf_a @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(179,axiom,
( ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) )
!= e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__C4__2_Oprems_C_I2_J) ).
thf(905,plain,
( ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) )
!= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(44,axiom,
! [A: tree_a] :
( ( multiset_a2 @ ( heapIm1091024090Down_a @ A ) )
= ( multiset_a2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_siftDown__multiset) ).
thf(348,plain,
! [A: tree_a] :
( ( multiset_a2 @ ( heapIm1091024090Down_a @ A ) )
= ( multiset_a2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(88,axiom,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Pair__inject) ).
thf(574,plain,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(21,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_old_Oprod_Oinducts) ).
thf(280,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(176,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( val_a @ ( t_a @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_val_Osimps) ).
thf(877,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( val_a @ ( t_a @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(3,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a] :
( ( collection_Tree_a_a @ A @ B @ C @ D )
=> ( ( heap_axioms_Tree_a_a @ B @ C @ D @ E @ F )
=> ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Heap_Ointro) ).
thf(221,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a] :
( ( collection_Tree_a_a @ A @ B @ C @ D )
=> ( ( heap_axioms_Tree_a_a @ B @ C @ D @ E @ F )
=> ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(172,axiom,
! [A: tree_a] :
( ( is_heap_a @ A )
=> ( ( A != e_a )
=> ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_removeLeaf__heap__is__heap) ).
thf(866,plain,
! [A: tree_a] :
( ( is_heap_a @ A )
=> ( ( A != e_a )
=> ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(111,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( if_Pro1144176865Tree_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T) ).
thf(660,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( if_Pro1144176865Tree_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(31,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: list_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( is_heap_a @ ( E @ ( C @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_Heap_Ois__heap__of__list) ).
thf(312,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: list_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( is_heap_a @ ( E @ ( C @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(196,axiom,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_is__heap_Osimps_I2_J) ).
thf(981,plain,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(142,axiom,
! [A: tree_a] : ( is_heap_a @ ( heapIm970322378pify_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_heapify__heap__is__heap) ).
thf(766,plain,
! [A: tree_a] : ( is_heap_a @ ( heapIm970322378pify_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(7,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( collection_Tree_a_a @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_Heap_Oaxioms_I1_J) ).
thf(233,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( collection_Tree_a_a @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(182,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
& ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_prod_Oexpand) ).
thf(925,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
& ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(157,axiom,
! [A: a,B: a,C: multiset_a] :
( ( ( add_mset_a @ A @ zero_zero_multiset_a )
= ( add_mset_a @ B @ C ) )
= ( ( B = A )
& ( C = zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_single__eq__add__mset) ).
thf(810,plain,
! [A: a,B: a,C: multiset_a] :
( ( ( add_mset_a @ A @ zero_zero_multiset_a )
= ( add_mset_a @ B @ C ) )
= ( ( B = A )
& ( C = zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(53,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_multiset_a @ A @ C )
= ( plus_plus_multiset_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_add__mono__thms__linordered__semiring_I4_J) ).
thf(381,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_multiset_a @ A @ C )
= ( plus_plus_multiset_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(48,axiom,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_prod_Oinject) ).
thf(366,plain,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(187,axiom,
( produc1515207979Tree_a
= ( ^ [A: produc143150363Tree_a] : ( produc649172771ee_a_a @ ( product_snd_a_Tree_a @ A ) @ ( product_fst_a_Tree_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_prod_Oswap__def) ).
thf(942,plain,
( produc1515207979Tree_a
= ( ^ [A: produc143150363Tree_a] : ( produc649172771ee_a_a @ ( product_snd_a_Tree_a @ A ) @ ( product_fst_a_Tree_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(61,axiom,
! [A: multiset_a,B: multiset_a] :
( ( zero_zero_multiset_a
= ( plus_plus_multiset_a @ A @ B ) )
= ( ( A = zero_zero_multiset_a )
& ( B = zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_subset__mset_Ozero__eq__add__iff__both__eq__0) ).
thf(439,plain,
! [A: multiset_a,B: multiset_a] :
( ( zero_zero_multiset_a
= ( plus_plus_multiset_a @ A @ B ) )
= ( ( A = zero_zero_multiset_a )
& ( B = zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(212,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_left_Osimps) ).
thf(1047,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(152,axiom,
! [A: a,B: multiset_a,C: a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ zero_zero_multiset_a ) )
= ( ( B = zero_zero_multiset_a )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_add__mset__eq__singleton__iff) ).
thf(798,plain,
! [A: a,B: multiset_a,C: a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ zero_zero_multiset_a ) )
= ( ( B = zero_zero_multiset_a )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(215,axiom,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_removeLeaf_Osimps_I4_J) ).
thf(1057,plain,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(136,axiom,
( add_mset_a
= ( ^ [A: a,B: multiset_a] : ( plus_plus_multiset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_add__mset__add__single) ).
thf(746,plain,
( add_mset_a
= ( ^ [A: a,B: multiset_a] : ( plus_plus_multiset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(146,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_add__mset__add__mset__same__iff) ).
thf(778,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(161,axiom,
! [A: tree_a,B: a,C: a] :
( ( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_snd__eqD) ).
thf(820,plain,
! [A: tree_a,B: a,C: a] :
( ( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(14,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ? [C: multiset_a] :
( B
= ( add_mset_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_multi__member__split) ).
thf(260,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ? [C: multiset_a] :
( B
= ( add_mset_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(171,axiom,
! [A: a,B: tree_a,C: tree_a] :
( e_a
!= ( t_a @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Tree_Odistinct_I1_J) ).
thf(862,plain,
! [A: a,B: tree_a,C: tree_a] :
( e_a
!= ( t_a @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(66,axiom,
! [A: a,B: tree_a] :
( ( in_tree_a @ A @ B )
=> ( ( is_heap_a @ B )
=> ( ord_less_eq_a @ A @ ( val_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_is__heap__max) ).
thf(467,plain,
! [A: a,B: tree_a] :
( ( in_tree_a @ A @ B )
=> ( ( is_heap_a @ B )
=> ( ord_less_eq_a @ A @ ( val_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(11,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ B @ C ) ) )
= ( ( member_a @ A @ ( set_mset_a @ B ) )
| ( member_a @ A @ ( set_mset_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_union__iff) ).
thf(252,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ B @ C ) ) )
= ( ( member_a @ A @ ( set_mset_a @ B ) )
| ( member_a @ A @ ( set_mset_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(170,axiom,
! [A: a > $o,B: a,C: tree_a > $o,D: tree_a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ B @ D ) ) )
& ( C @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_conjI__realizer) ).
thf(852,plain,
! [A: a > $o,B: a,C: tree_a > $o,D: tree_a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ B @ D ) ) )
& ( C @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(64,axiom,
! [A: multiset_a,B: a] :
( ( nO_MAT1617603563iset_a @ zero_zero_multiset_a @ A )
=> ( ( add_mset_a @ B @ A )
= ( plus_plus_multiset_a @ ( add_mset_a @ B @ zero_zero_multiset_a ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_add__mset__replicate__mset__safe) ).
thf(461,plain,
! [A: multiset_a,B: a] :
( ( nO_MAT1617603563iset_a @ zero_zero_multiset_a @ A )
=> ( ( add_mset_a @ B @ A )
= ( plus_plus_multiset_a @ ( add_mset_a @ B @ zero_zero_multiset_a ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(70,axiom,
! [A: a,B: tree_a] :
( ( produc1515207979Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= ( produc649172771ee_a_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_swap__simp) ).
thf(493,plain,
! [A: a,B: tree_a] :
( ( produc1515207979Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= ( produc649172771ee_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(140,axiom,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Pair__inject) ).
thf(757,plain,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(116,axiom,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ C @ zero_zero_multiset_a ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_multi__member__skip) ).
thf(682,plain,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ C @ zero_zero_multiset_a ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(4,axiom,
( heap_Tree_a_a
= ( ^ [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a] :
( ( collection_Tree_a_a @ A @ B @ C @ D )
& ( heap_axioms_Tree_a_a @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Heap__def) ).
thf(224,plain,
( heap_Tree_a_a
= ( ^ [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a] :
( ( collection_Tree_a_a @ A @ B @ C @ D )
& ( heap_axioms_Tree_a_a @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(168,axiom,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ E @ F @ G ) ) @ A )
& ( is_heap_a @ ( t_a @ E @ F @ G ) )
& ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_is__heap_Osimps_I5_J) ).
thf(847,plain,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ E @ F @ G ) ) @ A )
& ( is_heap_a @ ( t_a @ E @ F @ G ) )
& ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(85,axiom,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_siftDown_Osimps_I1_J) ).
thf(566,plain,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(36,axiom,
( ( (=) @ produc981471411ee_a_a )
= ( ^ [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
& ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_prod__eq__iff) ).
thf(324,plain,
( ( (=) @ produc981471411ee_a_a )
= ( ^ [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
& ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(195,axiom,
! [A: a,B: tree_a,C: tree_a,D: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ D @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_siftDown_Osimps_I4_J) ).
thf(974,plain,
! [A: a,B: tree_a,C: tree_a,D: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ D @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(135,axiom,
! [A: a,B: multiset_a] :
( zero_zero_multiset_a
!= ( add_mset_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_empty__not__add__mset) ).
thf(742,plain,
! [A: a,B: multiset_a] :
( zero_zero_multiset_a
!= ( add_mset_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(175,axiom,
! [A: produc143150363Tree_a] :
( ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_prod_Ocollapse) ).
thf(874,plain,
! [A: produc143150363Tree_a] :
( ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(33,axiom,
! [A: tree_a,B: produc981471411ee_a_a] :
( ( A
= ( product_fst_Tree_a_a @ B ) )
= ( ? [C: a] :
( B
= ( produc649172771ee_a_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_eq__fst__iff) ).
thf(317,plain,
! [A: tree_a,B: produc981471411ee_a_a] :
( ( A
= ( product_fst_Tree_a_a @ B ) )
= ( ? [C: a] :
( B
= ( produc649172771ee_a_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(100,axiom,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_prod_Oinject) ).
thf(615,plain,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(47,axiom,
! [A: tree_a > $o,B: tree_a,C: a > $o,D: a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ B @ D ) ) )
& ( C @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_conjI__realizer) ).
thf(356,plain,
! [A: tree_a > $o,B: tree_a,C: a > $o,D: a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ B @ D ) ) )
& ( C @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(173,axiom,
( ( produc686083979Tree_a @ v_a @ t_a2 )
= ( heapIm837449470Leaf_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__C4__2_Oprems_C_I1_J) ).
thf(869,plain,
( ( produc686083979Tree_a @ v_a @ t_a2 )
= ( heapIm837449470Leaf_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(72,axiom,
! [A: tree_a] :
( ( heapIm229596386mpty_a @ A )
=> ( A = e_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_HS_Ois__empty__inj) ).
thf(499,plain,
! [A: tree_a] :
( ( heapIm229596386mpty_a @ A )
=> ( A = e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(199,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ~ ! [B: a,C: tree_a,D: tree_a] :
( A
!= ( t_a @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Tree_Oexhaust) ).
thf(989,plain,
! [A: tree_a] :
( ( A != e_a )
=> ~ ! [B: a,C: tree_a,D: tree_a] :
( A
!= ( t_a @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(103,axiom,
( heap_axioms_a_a
= ( ^ [A: a > $o,B: list_a > a,C: a > multiset_a,D: a > tree_a,E: a > product_prod_a_a] :
( ! [F: a] :
( ( C @ F )
= ( multiset_a2 @ ( D @ F ) ) )
& ! [F: list_a] : ( is_heap_a @ ( D @ ( B @ F ) ) )
& ! [F: a] :
( ( ( D @ F )
= e_a )
= ( A @ F ) )
& ! [F: a,G: a,H: a] :
( ~ ( A @ F )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: a,G: a,H: a] :
( ~ ( A @ F )
=> ( ( is_heap_a @ ( D @ F ) )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( D @ H ) ) ) ) )
& ! [F: a,G: a,H: a] :
( ~ ( A @ F )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( D @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_Heap__axioms__def) ).
thf(637,plain,
( heap_axioms_a_a
= ( ^ [A: a > $o,B: list_a > a,C: a > multiset_a,D: a > tree_a,E: a > product_prod_a_a] :
( ! [F: a] :
( ( C @ F )
= ( multiset_a2 @ ( D @ F ) ) )
& ! [F: list_a] : ( is_heap_a @ ( D @ ( B @ F ) ) )
& ! [F: a] :
( ( ( D @ F )
= e_a )
= ( A @ F ) )
& ! [F: a,G: a,H: a] :
( ~ ( A @ F )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: a,G: a,H: a] :
( ~ ( A @ F )
=> ( ( is_heap_a @ ( D @ F ) )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( D @ H ) ) ) ) )
& ! [F: a,G: a,H: a] :
( ~ ( A @ F )
=> ( ( ( product_Pair_a_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( D @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(69,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_add__left__imp__eq) ).
thf(489,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(115,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_add__right__cancel) ).
thf(679,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(123,axiom,
! [A: multiset_a,B: multiset_a] :
( ( zero_zero_multiset_a
= ( plus_plus_multiset_a @ A @ B ) )
= ( ( A = zero_zero_multiset_a )
& ( B = zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_empty__eq__union) ).
thf(706,plain,
! [A: multiset_a,B: multiset_a] :
( ( zero_zero_multiset_a
= ( plus_plus_multiset_a @ A @ B ) )
= ( ( A = zero_zero_multiset_a )
& ( B = zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(56,axiom,
! [A: tree_a > a > $o,B: tree_a,C: a,D: produc981471411ee_a_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc649172771ee_a_a @ B @ C ) )
=> ( A @ ( product_fst_Tree_a_a @ D ) @ ( product_snd_Tree_a_a @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(393,plain,
! [A: tree_a > a > $o,B: tree_a,C: a,D: produc981471411ee_a_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc649172771ee_a_a @ B @ C ) )
=> ( A @ ( product_fst_Tree_a_a @ D ) @ ( product_snd_Tree_a_a @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(109,axiom,
! [A: a,B: multiset_a,C: a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ zero_zero_multiset_a ) )
= ( ( A = C )
& ( B = zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_add__mset__eq__single) ).
thf(654,plain,
! [A: a,B: multiset_a,C: a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ zero_zero_multiset_a ) )
= ( ( A = C )
& ( B = zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(128,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( ( is_heap_a @ A )
=> ( ( val_a @ A )
= ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_heap__top__max) ).
thf(721,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( ( is_heap_a @ A )
=> ( ( val_a @ A )
= ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(216,axiom,
( t_a2
= ( t_a @ v3 @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062t_H_A_061_AT_Av_A_Isnd_A_IremoveLeaf_A_IT_Av1_Al1_Ar1_J_J_J_A_IT_Av2_Al2_Ar2_J_092_060close_062) ).
thf(1060,plain,
( t_a2
= ( t_a @ v3 @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(213,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ A @ B @ C ) )
= ( heapIm1091024090Down_a @ ( t_a @ A @ ( heapIm970322378pify_a @ B ) @ ( heapIm970322378pify_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_heapify_Osimps_I2_J) ).
thf(1050,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ A @ B @ C ) )
= ( heapIm1091024090Down_a @ ( t_a @ A @ ( heapIm970322378pify_a @ B ) @ ( heapIm970322378pify_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(16,axiom,
! [A: tree_a,B: a] :
( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_fst__conv) ).
thf(266,plain,
! [A: tree_a,B: a] :
( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(155,axiom,
! [A: multiset_a,B: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= zero_zero_multiset_a )
= ( ( A = zero_zero_multiset_a )
& ( B = zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_subset__mset_Oadd__eq__0__iff__both__eq__0) ).
thf(805,plain,
! [A: multiset_a,B: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= zero_zero_multiset_a )
= ( ( A = zero_zero_multiset_a )
& ( B = zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(75,axiom,
! [A: produc143150363Tree_a] :
? [B: a,C: tree_a] :
( A
= ( produc686083979Tree_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_surj__pair) ).
thf(508,plain,
! [A: produc143150363Tree_a] :
? [B: a,C: tree_a] :
( A
= ( produc686083979Tree_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(110,axiom,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a] :
( ! [C: a,D: tree_a] : ( A @ ( produc686083979Tree_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_old_Oprod_Oinducts) ).
thf(657,plain,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a] :
( ! [C: a,D: tree_a] : ( A @ ( produc686083979Tree_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(57,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_add__left__cancel) ).
thf(398,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(151,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add__right__imp__eq) ).
thf(794,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(127,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_verit__sum__simplify) ).
thf(718,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(101,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_empty__neutral_I2_J) ).
thf(618,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(162,axiom,
( heapIm229596386mpty_a
= ( ^ [A: tree_a] : ( A = e_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_hs__is__empty__def) ).
thf(824,plain,
( heapIm229596386mpty_a
= ( ^ [A: tree_a] : ( A = e_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(26,axiom,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_old_Oprod_Oexhaust) ).
thf(296,plain,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(95,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_add_Oleft__neutral) ).
thf(601,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(51,axiom,
! [A: tree_a] :
( ( multiset_a2 @ ( heapIm970322378pify_a @ A ) )
= ( multiset_a2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_multiset__heapify) ).
thf(375,plain,
! [A: tree_a] :
( ( multiset_a2 @ ( heapIm970322378pify_a @ A ) )
= ( multiset_a2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(132,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( if_Pro1144176865Tree_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T) ).
thf(733,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( if_Pro1144176865Tree_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(160,axiom,
heapIm229596386mpty_a @ e_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_HS_Ois__empty__empty) ).
thf(819,plain,
heapIm229596386mpty_a @ e_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(203,axiom,
! [A: tree_a] :
( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) )
=> ( A = e_a ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_removeLeaf_Ocases) ).
thf(1007,plain,
! [A: tree_a] :
( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) )
=> ( A = e_a ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(23,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ B )
= C )
=> ( member_a @ A @ ( set_mset_a @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_union__single__eq__member) ).
thf(286,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ B )
= C )
=> ( member_a @ A @ ( set_mset_a @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(163,axiom,
! [A: a,B: tree_a,C: tree_a,D: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) )
= ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1091024090Down_a @ ( t_a @ D @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) @ e_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_siftDown_Osimps_I3_J) ).
thf(826,plain,
! [A: a,B: tree_a,C: tree_a,D: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) )
= ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1091024090Down_a @ ( t_a @ D @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) @ e_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(87,axiom,
( plus_plus_multiset_a
= ( ^ [A: multiset_a,B: multiset_a] : ( plus_plus_multiset_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_union__commute) ).
thf(572,plain,
( plus_plus_multiset_a
= ( ^ [A: multiset_a,B: multiset_a] : ( plus_plus_multiset_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(8,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ( D @ G )
= ( multiset_a2 @ ( E @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_Heap_Omultiset) ).
thf(236,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ( D @ G )
= ( multiset_a2 @ ( E @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(189,axiom,
! [A: produc143150363Tree_a] :
( ( product_snd_Tree_a_a @ ( produc1515207979Tree_a @ A ) )
= ( product_fst_a_Tree_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_snd__swap) ).
thf(947,plain,
! [A: produc143150363Tree_a] :
( ( product_snd_Tree_a_a @ ( produc1515207979Tree_a @ A ) )
= ( product_fst_a_Tree_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(63,axiom,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ D ) )
=> ( ord_less_eq_a @ C @ E ) )
=> ( A @ ( add_mset_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_multiset__induct__min) ).
thf(445,plain,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ D ) )
=> ( ord_less_eq_a @ C @ E ) )
=> ( A @ ( add_mset_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(185,axiom,
! [A: a,B: produc143150363Tree_a] :
( ( A
= ( product_fst_a_Tree_a @ B ) )
= ( ? [C: tree_a] :
( B
= ( produc686083979Tree_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_eq__fst__iff) ).
thf(936,plain,
! [A: a,B: produc143150363Tree_a] :
( ( A
= ( product_fst_a_Tree_a @ B ) )
= ( ? [C: tree_a] :
( B
= ( produc686083979Tree_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1,conjecture,
( v_a
= ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( v_a
!= ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(219,plain,
( v_a
!= ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(204,axiom,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a,G: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1257206334ight_a @ ( t_a @ D @ E @ F ) ) ) ) @ ( t_a @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( t_a @ D @ E @ F ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_siftDown_Osimps_I6_J) ).
thf(1011,plain,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a,G: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1257206334ight_a @ ( t_a @ D @ E @ F ) ) ) ) @ ( t_a @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( t_a @ D @ E @ F ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(133,axiom,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_old_Oprod_Oinject) ).
thf(736,plain,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(201,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ e_a ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_is__heap_Osimps_I4_J) ).
thf(996,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ e_a ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(6,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a] :
( ( collection_Tree_a_a @ A @ B @ C @ D )
=> ( ( D @ A )
= zero_zero_multiset_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Collection_Omultiset__empty) ).
thf(230,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a] :
( ( collection_Tree_a_a @ A @ B @ C @ D )
=> ( ( D @ A )
= zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
nO_MAT1617603563iset_a = nO_MAT1617603563iset_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_NO__MATCH__cong) ).
thf(303,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(141,axiom,
( is_empty_a
= ( ^ [A: multiset_a] : ( A = zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Multiset_Ois__empty__def) ).
thf(764,plain,
( is_empty_a
= ( ^ [A: multiset_a] : ( A = zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(96,axiom,
( ( heapIm970322378pify_a @ e_a )
= e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_heapify_Osimps_I1_J) ).
thf(604,plain,
( ( heapIm970322378pify_a @ e_a )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(177,axiom,
! [A: produc143150363Tree_a] :
( A
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_prod_Oexhaust__sel) ).
thf(880,plain,
! [A: produc143150363Tree_a] :
( A
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(107,axiom,
( heap_axioms_Tree_a_a
= ( ^ [A: tree_a > $o,B: list_a > tree_a,C: tree_a > multiset_a,D: tree_a > tree_a,E: tree_a > produc143150363Tree_a] :
( ! [F: tree_a] :
( ( C @ F )
= ( multiset_a2 @ ( D @ F ) ) )
& ! [F: list_a] : ( is_heap_a @ ( D @ ( B @ F ) ) )
& ! [F: tree_a] :
( ( ( D @ F )
= e_a )
= ( A @ F ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( is_heap_a @ ( D @ F ) )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( D @ H ) ) ) ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( D @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_Heap__axioms__def) ).
thf(649,plain,
( heap_axioms_Tree_a_a
= ( ^ [A: tree_a > $o,B: list_a > tree_a,C: tree_a > multiset_a,D: tree_a > tree_a,E: tree_a > produc143150363Tree_a] :
( ! [F: tree_a] :
( ( C @ F )
= ( multiset_a2 @ ( D @ F ) ) )
& ! [F: list_a] : ( is_heap_a @ ( D @ ( B @ F ) ) )
& ! [F: tree_a] :
( ( ( D @ F )
= e_a )
= ( A @ F ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( is_heap_a @ ( D @ F ) )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( D @ H ) ) ) ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( D @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(211,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ~ ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_siftDown_Ocases) ).
thf(1043,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ~ ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(80,axiom,
! [A: multiset_a,B: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= zero_zero_multiset_a )
= ( ( A = zero_zero_multiset_a )
& ( B = zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_union__eq__empty) ).
thf(552,plain,
! [A: multiset_a,B: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= zero_zero_multiset_a )
= ( ( A = zero_zero_multiset_a )
& ( B = zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(159,axiom,
! [A: multiset_a,B: a,C: multiset_a] :
( ( plus_plus_multiset_a @ A @ ( add_mset_a @ B @ C ) )
= ( add_mset_a @ B @ ( plus_plus_multiset_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_union__mset__add__mset__right) ).
thf(816,plain,
! [A: multiset_a,B: a,C: multiset_a] :
( ( plus_plus_multiset_a @ A @ ( add_mset_a @ B @ C ) )
= ( add_mset_a @ B @ ( plus_plus_multiset_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(98,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( is_heap_a @ ( E @ G ) )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( is_heap_a @ ( E @ I ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Heap_Oremove__max__is__heap) ).
thf(609,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( is_heap_a @ ( E @ G ) )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( is_heap_a @ ( E @ I ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(35,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T) ).
thf(323,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(93,axiom,
! [A: multiset_a,B: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ B @ A ) )
= ( B = zero_zero_multiset_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_add__cancel__right__left) ).
thf(594,plain,
! [A: multiset_a,B: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ B @ A ) )
= ( B = zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(102,axiom,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ D ) )
=> ( ord_less_eq_a @ E @ C ) )
=> ( A @ ( add_mset_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_multiset__induct__max) ).
thf(621,plain,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ D ) )
=> ( ord_less_eq_a @ E @ C ) )
=> ( A @ ( add_mset_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(9,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Pair__inject) ).
thf(240,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(206,axiom,
! [A: tree_a > a > $o,B: tree_a,C: a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ C @ B ) ) @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_exI__realizer) ).
thf(1029,plain,
! [A: tree_a > a > $o,B: tree_a,C: a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ C @ B ) ) @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(38,axiom,
! [A: a > tree_a > $o,B: produc981471411ee_a_a] :
( ( A @ ( product_snd_Tree_a_a @ B ) @ ( product_fst_Tree_a_a @ B ) )
=> ~ ! [C: tree_a,D: a] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_exE__realizer_H) ).
thf(330,plain,
! [A: a > tree_a > $o,B: produc981471411ee_a_a] :
( ( A @ ( product_snd_Tree_a_a @ B ) @ ( product_fst_Tree_a_a @ B ) )
=> ~ ! [C: tree_a,D: a] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(117,axiom,
! [A: a,B: a] :
( ( A = B )
| ~ ( ord_less_eq_a @ A @ B )
| ~ ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_verit__la__disequality) ).
thf(685,plain,
! [A: a,B: a] :
( ( A = B )
| ~ ( ord_less_eq_a @ A @ B )
| ~ ( ord_less_eq_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(197,axiom,
! [A: produc143150363Tree_a] :
( A
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_surjective__pairing) ).
thf(983,plain,
! [A: produc143150363Tree_a] :
( A
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(143,axiom,
! [A: multiset_a,B: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= B )
= ( A = zero_zero_multiset_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_add__cancel__left__left) ).
thf(768,plain,
! [A: multiset_a,B: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= B )
= ( A = zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(178,axiom,
! [A: tree_a > $o,B: tree_a] :
( ! [C: a] : ( A @ ( t_a @ C @ e_a @ e_a ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ e_a ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ e_a @ ( t_a @ D @ E @ F ) ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a,G: a,H: tree_a,I: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ ( t_a @ G @ H @ I ) ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a,G: a,H: tree_a,I: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ ( t_a @ G @ H @ I ) ) ) ) )
=> ( ( A @ e_a )
=> ( A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_removeLeaf_Oinduct) ).
thf(883,plain,
! [A: tree_a > $o,B: tree_a] :
( ! [C: a] : ( A @ ( t_a @ C @ e_a @ e_a ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ e_a ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ e_a @ ( t_a @ D @ E @ F ) ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a,G: a,H: tree_a,I: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ ( t_a @ G @ H @ I ) ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a,G: a,H: tree_a,I: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ ( t_a @ G @ H @ I ) ) ) ) )
=> ( ( A @ e_a )
=> ( A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(198,axiom,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ E @ F @ G ) ) @ A )
& ( is_heap_a @ ( t_a @ E @ F @ G ) )
& ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_is__heap_Osimps_I6_J) ).
thf(986,plain,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ E @ F @ G ) ) @ A )
& ( is_heap_a @ ( t_a @ E @ F @ G ) )
& ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(84,axiom,
! [A: set_Pr921883667ee_a_a,B: set_Pr921883667ee_a_a] :
( ( ord_le1748873858_a_a_o
@ ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ A )
@ ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ B ) )
= ( ord_le864074675ee_a_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_pred__subset__eq2) ).
thf(563,plain,
! [A: set_Pr921883667ee_a_a,B: set_Pr921883667ee_a_a] :
( ( ord_le1748873858_a_a_o
@ ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ A )
@ ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ B ) )
= ( ord_le864074675ee_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(5,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a] :
( ( collection_Tree_a_a @ A @ B @ C @ D )
=> ( ( B @ E )
=> ( ( D @ E )
= zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Collection_Ois__empty__as__list) ).
thf(226,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a] :
( ( collection_Tree_a_a @ A @ B @ C @ D )
=> ( ( B @ E )
=> ( ( D @ E )
= zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(74,axiom,
! [A: produc981471411ee_a_a] :
( A
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_surjective__pairing) ).
thf(505,plain,
! [A: produc981471411ee_a_a] :
( A
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(181,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_right_Osimps) ).
thf(922,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(208,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
=> ( ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_prod__eqI) ).
thf(1034,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
=> ( ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(188,axiom,
! [A: tree_a] :
( ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) )
!= e_a )
=> ( ( A != e_a )
=> ( ( val_a @ A )
= ( val_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_removeLeaf__val__val) ).
thf(944,plain,
! [A: tree_a] :
( ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) )
!= e_a )
=> ( ( A != e_a )
=> ( ( val_a @ A )
= ( val_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(112,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_siftDown__in__tree) ).
thf(663,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(12,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( heap_axioms_Tree_a_a @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_Heap_Oaxioms_I2_J) ).
thf(255,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( heap_axioms_Tree_a_a @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(68,axiom,
! [A: a,B: multiset_a] : ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_multi__member__this) ).
thf(487,plain,
! [A: a,B: multiset_a] : ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(186,axiom,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a] :
( ( ( t_a @ A @ B @ C )
= ( t_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Tree_Oinject) ).
thf(939,plain,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a] :
( ( ( t_a @ A @ B @ C )
= ( t_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(139,axiom,
! [A: produc981471411ee_a_a] :
( A
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_prod_Oexhaust__sel) ).
thf(754,plain,
! [A: produc981471411ee_a_a] :
( A
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(193,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ e_a @ ( t_a @ B @ C @ D ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ e_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_removeLeaf_Osimps_I3_J) ).
thf(968,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ e_a @ ( t_a @ B @ C @ D ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ e_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(165,axiom,
! [A: a,B: tree_a,C: a] :
( ( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_fst__eqD) ).
thf(836,plain,
! [A: a,B: tree_a,C: a] :
( ( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(194,axiom,
! [A: a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ e_a @ e_a ) )
= ( produc686083979Tree_a @ A @ e_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_removeLeaf_Osimps_I1_J) ).
thf(971,plain,
! [A: a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ e_a @ e_a ) )
= ( produc686083979Tree_a @ A @ e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(134,axiom,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a] :
( ! [C: a,D: tree_a] : ( A @ ( produc686083979Tree_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_prod__cases) ).
thf(739,plain,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a] :
( ! [C: a,D: tree_a] : ( A @ ( produc686083979Tree_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(15,axiom,
! [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
=> ( ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_prod__eqI) ).
thf(263,plain,
! [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
=> ( ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(200,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( is_heap_a @ ( t_a @ A @ e_a @ ( t_a @ B @ C @ D ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_is__heap_Osimps_I3_J) ).
thf(993,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( is_heap_a @ ( t_a @ A @ e_a @ ( t_a @ B @ C @ D ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(125,axiom,
! [A: a,B: tree_a] :
( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_snd__conv) ).
thf(712,plain,
! [A: a,B: tree_a] :
( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(82,axiom,
! [A: produc981471411ee_a_a] :
( ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_prod_Ocollapse) ).
thf(557,plain,
! [A: produc981471411ee_a_a] :
( ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(214,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ~ ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_is__heap_Ocases) ).
thf(1053,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ~ ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(150,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_empty__neutral_I1_J) ).
thf(791,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(90,axiom,
! [A: multiset_a,B: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= A )
= ( B = zero_zero_multiset_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_add__cancel__left__right) ).
thf(585,plain,
! [A: multiset_a,B: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= A )
= ( B = zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(73,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_add_Oright__neutral) ).
thf(502,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(166,axiom,
! [A: a > tree_a > $o,B: a,C: tree_a,D: produc143150363Tree_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc686083979Tree_a @ B @ C ) )
=> ( A @ ( product_fst_a_Tree_a @ D ) @ ( product_snd_a_Tree_a @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(840,plain,
! [A: a > tree_a > $o,B: a,C: tree_a,D: produc143150363Tree_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc686083979Tree_a @ B @ C ) )
=> ( A @ ( product_fst_a_Tree_a @ D ) @ ( product_snd_a_Tree_a @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(41,axiom,
! [A: produc981471411ee_a_a] :
( ( produc1515207979Tree_a @ ( produc1478296771ee_a_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_swap__swap) ).
thf(338,plain,
! [A: produc981471411ee_a_a] :
( ( produc1515207979Tree_a @ ( produc1478296771ee_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(156,axiom,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ C @ B ) ) @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_exI__realizer) ).
thf(808,plain,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ C @ B ) ) @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(105,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ A @ B ) @ C )
= ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(643,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ A @ B ) @ C )
= ( plus_plus_multiset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(40,axiom,
( plus_plus_multiset_a
= ( ^ [A: multiset_a,B: multiset_a] : ( plus_plus_multiset_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_add_Ocommute) ).
thf(336,plain,
( plus_plus_multiset_a
= ( ^ [A: multiset_a,B: multiset_a] : ( plus_plus_multiset_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(122,axiom,
! [A: produc143150363Tree_a] :
( ( produc1478296771ee_a_a @ ( produc1515207979Tree_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_swap__swap) ).
thf(703,plain,
! [A: produc143150363Tree_a] :
( ( produc1478296771ee_a_a @ ( produc1515207979Tree_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(99,axiom,
! [A: a,B: tree_a] :
( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ B ) ) )
=> ( ( is_heap_a @ B )
=> ( ord_less_eq_a @ A @ ( val_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_heap__top__geq) ).
thf(613,plain,
! [A: a,B: tree_a] :
( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ B ) ) )
=> ( ( is_heap_a @ B )
=> ( ord_less_eq_a @ A @ ( val_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(130,axiom,
! [A: tree_a] :
( ( heapIm229596386mpty_a @ A )
=> ( ( multiset_a2 @ A )
= zero_zero_multiset_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_HS_Ois__empty__as__list) ).
thf(727,plain,
! [A: tree_a] :
( ( heapIm229596386mpty_a @ A )
=> ( ( multiset_a2 @ A )
= zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(167,axiom,
( heapIm915766629_max_a
= ( ^ [A: tree_a] :
( if_Pro1144176865Tree_a
@ ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) )
= e_a )
@ ( produc686083979Tree_a @ ( val_a @ A ) @ e_a )
@ ( produc686083979Tree_a @ ( val_a @ A ) @ ( heapIm1091024090Down_a @ ( t_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) @ ( heapIm1140443833left_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) @ ( heapIm1257206334ight_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_hs__remove__max__def) ).
thf(845,plain,
( heapIm915766629_max_a
= ( ^ [A: tree_a] :
( if_Pro1144176865Tree_a
@ ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) )
= e_a )
@ ( produc686083979Tree_a @ ( val_a @ A ) @ e_a )
@ ( produc686083979Tree_a @ ( val_a @ A ) @ ( heapIm1091024090Down_a @ ( t_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) @ ( heapIm1140443833left_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) @ ( heapIm1257206334ight_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(65,axiom,
( heapIm1057938560list_a
= ( ^ [A: list_a] : ( heapIm970322378pify_a @ ( heapIm1637418125tree_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_hs__of__list__def) ).
thf(465,plain,
( heapIm1057938560list_a
= ( ^ [A: list_a] : ( heapIm970322378pify_a @ ( heapIm1637418125tree_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(184,axiom,
! [A: tree_a,B: tree_a,C: tree_a,D: a] :
( ( is_heap_a @ A )
=> ( ( is_heap_a @ B )
=> ( ( C
= ( t_a @ D @ A @ B ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_siftDown__heap__is__heap) ).
thf(931,plain,
! [A: tree_a,B: tree_a,C: tree_a,D: a] :
( ( is_heap_a @ A )
=> ( ( is_heap_a @ B )
=> ( ( C
= ( t_a @ D @ A @ B ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(118,axiom,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ? [B: multiset_a,C: a] :
( A
= ( add_mset_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_multi__nonempty__split) ).
thf(688,plain,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ? [B: multiset_a,C: a] :
( A
= ( add_mset_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(89,axiom,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ~ ! [B: a,C: multiset_a] :
( A
!= ( add_mset_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_multiset__cases) ).
thf(581,plain,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ~ ! [B: a,C: multiset_a] :
( A
!= ( add_mset_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(144,axiom,
! [A: multiset_a,B: a] :
( A
!= ( add_mset_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_multi__self__add__other__not__self) ).
thf(771,plain,
! [A: multiset_a,B: a] :
( A
!= ( add_mset_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(158,axiom,
! [A: produc981471411ee_a_a > $o,B: produc981471411ee_a_a] :
( ! [C: tree_a,D: a] : ( A @ ( produc649172771ee_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_prod__cases) ).
thf(813,plain,
! [A: produc981471411ee_a_a > $o,B: produc981471411ee_a_a] :
( ! [C: tree_a,D: a] : ( A @ ( produc649172771ee_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(137,axiom,
! [A: a,B: produc981471411ee_a_a] :
( ( A
= ( product_snd_Tree_a_a @ B ) )
= ( ? [C: tree_a] :
( B
= ( produc649172771ee_a_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_eq__snd__iff) ).
thf(748,plain,
! [A: a,B: produc981471411ee_a_a] :
( ( A
= ( product_snd_Tree_a_a @ B ) )
= ( ? [C: tree_a] :
( B
= ( produc649172771ee_a_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(29,axiom,
! [A: a,B: multiset_a,C: a,D: multiset_a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ D ) )
=> ( ( A != C )
=> ( member_a @ C @ ( set_mset_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_insert__noteq__member) ).
thf(304,plain,
! [A: a,B: multiset_a,C: a,D: multiset_a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ D ) )
=> ( ( A != C )
=> ( member_a @ C @ ( set_mset_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(217,axiom,
! [A: produc981471411ee_a_a] :
( ( product_fst_a_Tree_a @ ( produc1478296771ee_a_a @ A ) )
= ( product_snd_Tree_a_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_fst__swap) ).
thf(1062,plain,
! [A: produc981471411ee_a_a] :
( ( product_fst_a_Tree_a @ ( produc1478296771ee_a_a @ A ) )
= ( product_snd_Tree_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(45,axiom,
! [A: tree_a,B: produc143150363Tree_a] :
( ( A
= ( product_snd_a_Tree_a @ B ) )
= ( ? [C: a] :
( B
= ( produc686083979Tree_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_eq__snd__iff) ).
thf(351,plain,
! [A: tree_a,B: produc143150363Tree_a] :
( ( A
= ( product_snd_a_Tree_a @ B ) )
= ( ? [C: a] :
( B
= ( produc686083979Tree_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(58,axiom,
! [A: tree_a,B: a] :
( ( produc1478296771ee_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= ( produc686083979Tree_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_swap__simp) ).
thf(401,plain,
! [A: tree_a,B: a] :
( ( produc1478296771ee_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= ( produc686083979Tree_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(148,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_union__right__cancel) ).
thf(786,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(147,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ B @ C ) )
=> ( ( plus_plus_multiset_a @ A @ D )
= ( plus_plus_multiset_a @ B @ ( plus_plus_multiset_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_group__cancel_Oadd1) ).
thf(781,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ B @ C ) )
=> ( ( plus_plus_multiset_a @ A @ D )
= ( plus_plus_multiset_a @ B @ ( plus_plus_multiset_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(91,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_multi__union__self__other__eq) ).
thf(588,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ( plus_plus_multiset_a @ A @ B )
= ( plus_plus_multiset_a @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(121,axiom,
! [A: produc143150363Tree_a] :
~ ! [B: a,C: tree_a] :
( A
!= ( produc686083979Tree_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_old_Oprod_Oexhaust) ).
thf(699,plain,
! [A: produc143150363Tree_a] :
~ ! [B: a,C: tree_a] :
( A
!= ( produc686083979Tree_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(191,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( in_tree_a @ A @ ( t_a @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree_a @ A @ C )
| ( in_tree_a @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_in__tree_Osimps_I2_J) ).
thf(963,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( in_tree_a @ A @ ( t_a @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree_a @ A @ C )
| ( in_tree_a @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(78,axiom,
! [A: tree_a > multiset_a,B: tree_a > tree_a,C: list_a > tree_a,D: tree_a > $o,E: tree_a > produc143150363Tree_a] :
( ! [F: tree_a] :
( ( A @ F )
= ( multiset_a2 @ ( B @ F ) ) )
=> ( ! [F: list_a] : ( is_heap_a @ ( B @ ( C @ F ) ) )
=> ( ! [F: tree_a] :
( ( ( B @ F )
= e_a )
= ( D @ F ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( is_heap_a @ ( B @ F ) )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( B @ H ) ) ) ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( B @ F ) ) ) ) )
=> ( heap_axioms_Tree_a_a @ D @ C @ A @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Heap__axioms_Ointro) ).
thf(517,plain,
! [A: tree_a > multiset_a,B: tree_a > tree_a,C: list_a > tree_a,D: tree_a > $o,E: tree_a > produc143150363Tree_a] :
( ! [F: tree_a] :
( ( A @ F )
= ( multiset_a2 @ ( B @ F ) ) )
=> ( ! [F: list_a] : ( is_heap_a @ ( B @ ( C @ F ) ) )
=> ( ! [F: tree_a] :
( ( ( B @ F )
= e_a )
= ( D @ F ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( is_heap_a @ ( B @ F ) )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( B @ H ) ) ) ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( B @ F ) ) ) ) )
=> ( heap_axioms_Tree_a_a @ D @ C @ A @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(86,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( H
= ( val_a @ ( E @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Heap_Oremove__max__val) ).
thf(568,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( H
= ( val_a @ ( E @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(18,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ( ( E @ G )
= e_a )
= ( B @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_Heap_Oas__tree__empty) ).
thf(272,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ( ( E @ G )
= e_a )
= ( B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(79,axiom,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_old_Oprod_Oinject) ).
thf(549,plain,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(24,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ~ ! [C: multiset_a] :
( B
!= ( add_mset_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_mset__add) ).
thf(290,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ~ ! [C: multiset_a] :
( B
!= ( add_mset_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(52,axiom,
! [A: a,B: a] :
( ( ( add_mset_a @ A @ zero_zero_multiset_a )
= ( add_mset_a @ B @ zero_zero_multiset_a ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_single__eq__single) ).
thf(378,plain,
! [A: a,B: a] :
( ( ( add_mset_a @ A @ zero_zero_multiset_a )
= ( add_mset_a @ B @ zero_zero_multiset_a ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(27,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_old_Oprod_Oinject) ).
thf(300,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(202,axiom,
! [A: tree_a,B: a,C: tree_a,D: tree_a] :
( ( A
= ( t_a @ B @ C @ D ) )
=> ? [E: tree_a,F: a,G: tree_a] :
( ( ( heapIm1091024090Down_a @ A )
= ( t_a @ F @ E @ G ) )
& ( ord_less_eq_a @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_siftDown__Node) ).
thf(999,plain,
! [A: tree_a,B: a,C: tree_a,D: tree_a] :
( ( A
= ( t_a @ B @ C @ D ) )
=> ? [E: tree_a,F: a,G: tree_a] :
( ( ( heapIm1091024090Down_a @ A )
= ( t_a @ F @ E @ G ) )
& ( ord_less_eq_a @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(32,axiom,
( nO_MAT1617603563iset_a
= ( ^ [A: multiset_a,B: multiset_a] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_NO__MATCH__def) ).
thf(315,plain,
( nO_MAT1617603563iset_a
= ( ^ [A: multiset_a,B: multiset_a] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(164,axiom,
! [A: a] :
( ( heapIm1091024090Down_a @ ( t_a @ A @ e_a @ e_a ) )
= ( t_a @ A @ e_a @ e_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_siftDown_Osimps_I2_J) ).
thf(833,plain,
! [A: a] :
( ( heapIm1091024090Down_a @ ( t_a @ A @ e_a @ e_a ) )
= ( t_a @ A @ e_a @ e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(190,axiom,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a,G: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1257206334ight_a @ ( t_a @ D @ E @ F ) ) ) ) @ ( t_a @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( t_a @ D @ E @ F ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_siftDown_Osimps_I5_J) ).
thf(950,plain,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a,G: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1257206334ight_a @ ( t_a @ D @ E @ F ) ) ) ) @ ( t_a @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( t_a @ D @ E @ F ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(37,axiom,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ~ ! [B: a] :
~ ( member_a @ B @ ( set_mset_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_multiset__nonemptyE) ).
thf(326,plain,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ~ ! [B: a] :
~ ( member_a @ B @ ( set_mset_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(42,axiom,
! [A: a,B: multiset_a,C: a,D: multiset_a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ D ) )
= ( ( ( B = D )
& ( A = C ) )
| ? [E: multiset_a] :
( ( B
= ( add_mset_a @ C @ E ) )
& ( D
= ( add_mset_a @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_add__eq__conv__ex) ).
thf(341,plain,
! [A: a,B: multiset_a,C: a,D: multiset_a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ D ) )
= ( ( ( B = D )
& ( A = C ) )
| ? [E: multiset_a] :
( ( B
= ( add_mset_a @ C @ E ) )
& ( D
= ( add_mset_a @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(218,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( multiset_a2 @ ( t_a @ A @ B @ C ) )
= ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_multiset_Osimps_I2_J) ).
thf(1065,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( multiset_a2 @ ( t_a @ A @ B @ C ) )
= ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(120,axiom,
! [A: set_Pr921883667ee_a_a,B: set_Pr921883667ee_a_a] :
( ( ( ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ A ) )
= ( ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_pred__equals__eq2) ).
thf(696,plain,
! [A: set_Pr921883667ee_a_a,B: set_Pr921883667ee_a_a] :
( ( ( ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ A ) )
= ( ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(22,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_prod__cases) ).
thf(283,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(183,axiom,
! [A: tree_a > a > $o,B: produc143150363Tree_a] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ~ ! [C: a,D: tree_a] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_exE__realizer_H) ).
thf(928,plain,
! [A: tree_a > a > $o,B: produc143150363Tree_a] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ~ ! [C: a,D: tree_a] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(25,axiom,
! [A: a] : ( member_a @ A @ ( set_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_multi__member__last) ).
thf(294,plain,
! [A: a] : ( member_a @ A @ ( set_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(153,axiom,
is_heap_a @ e_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_is__heap_Osimps_I1_J) ).
thf(801,plain,
is_heap_a @ e_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(180,axiom,
! [A: tree_a > $o,B: tree_a] :
( ( A @ e_a )
=> ( ! [C: a,D: tree_a,E: tree_a] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t_a @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Tree_Oinduct) ).
thf(908,plain,
! [A: tree_a > $o,B: tree_a] :
( ( A @ e_a )
=> ( ! [C: a,D: tree_a,E: tree_a] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t_a @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(169,axiom,
( ( (=) @ produc143150363Tree_a )
= ( ^ [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
& ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_prod__eq__iff) ).
thf(850,plain,
( ( (=) @ produc143150363Tree_a )
= ( ^ [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
& ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(62,axiom,
t != e_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_assms_I2_J) ).
thf(442,plain,
t != e_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(174,axiom,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_removeLeaf_Osimps_I5_J) ).
thf(871,plain,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(49,axiom,
! [A: produc143150363Tree_a] :
( ( product_fst_Tree_a_a @ ( produc1515207979Tree_a @ A ) )
= ( product_snd_a_Tree_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_fst__swap) ).
thf(369,plain,
! [A: produc143150363Tree_a] :
( ( product_fst_Tree_a_a @ ( produc1515207979Tree_a @ A ) )
= ( product_snd_a_Tree_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(20,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_prod_Oinject) ).
thf(277,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(119,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ B @ C ) )
=> ( ( plus_plus_multiset_a @ D @ A )
= ( plus_plus_multiset_a @ B @ ( plus_plus_multiset_a @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_group__cancel_Oadd2) ).
thf(691,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ B @ C ) )
=> ( ( plus_plus_multiset_a @ D @ A )
= ( plus_plus_multiset_a @ B @ ( plus_plus_multiset_a @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(67,axiom,
! [A: multiset_a > multiset_a > $o,B: multiset_a,C: multiset_a] :
( ( A @ zero_zero_multiset_a @ zero_zero_multiset_a )
=> ( ! [D: a,E: multiset_a,F: multiset_a] :
( ( A @ E @ F )
=> ( A @ ( add_mset_a @ D @ E ) @ F ) )
=> ( ! [D: a,E: multiset_a,F: multiset_a] :
( ( A @ E @ F )
=> ( A @ E @ ( add_mset_a @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_multiset__induct2) ).
thf(469,plain,
! [A: multiset_a > multiset_a > $o,B: multiset_a,C: multiset_a] :
( ( A @ zero_zero_multiset_a @ zero_zero_multiset_a )
=> ( ! [D: a,E: multiset_a,F: multiset_a] :
( ( A @ E @ F )
=> ( A @ ( add_mset_a @ D @ E ) @ F ) )
=> ( ! [D: a,E: multiset_a,F: multiset_a] :
( ( A @ E @ F )
=> ( A @ E @ ( add_mset_a @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(46,axiom,
( in_tree_a
= ( ^ [A: a,B: tree_a] : ( in_tree_a @ A @ ( heapIm1091024090Down_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_siftDown__in__tree__set) ).
thf(354,plain,
( in_tree_a
= ( ^ [A: a,B: tree_a] : ( in_tree_a @ A @ ( heapIm1091024090Down_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(104,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( ( add_mset_a @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Heap_Oremove__max__multiset_H) ).
thf(639,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( ( add_mset_a @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(114,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ zero_zero_multiset_a )
= ( plus_plus_multiset_a @ B @ C ) )
= ( ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
= B )
& ( C = zero_zero_multiset_a ) )
| ( ( B = zero_zero_multiset_a )
& ( ( add_mset_a @ A @ zero_zero_multiset_a )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_single__is__union) ).
thf(676,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ zero_zero_multiset_a )
= ( plus_plus_multiset_a @ B @ C ) )
= ( ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
= B )
& ( C = zero_zero_multiset_a ) )
| ( ( B = zero_zero_multiset_a )
& ( ( add_mset_a @ A @ zero_zero_multiset_a )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(92,axiom,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_HS_Omultiset__empty) ).
thf(592,plain,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(71,axiom,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_in__tree_Osimps_I1_J) ).
thf(496,plain,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(209,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ e_a ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ e_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_removeLeaf_Osimps_I2_J) ).
thf(1037,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ e_a ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ e_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(145,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_add_Ocomm__neutral) ).
thf(775,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(83,axiom,
! [A: multiset_a] :
( ( zero_zero_multiset_a = A )
= ( A = zero_zero_multiset_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_zero__reorient) ).
thf(560,plain,
! [A: multiset_a] :
( ( zero_zero_multiset_a = A )
= ( A = zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1403,plain,
$false,
inference(cvc4,[status(thm)],[606,1024,555,666,333,1031,308,247,511,269,597,730,276,385,715,404,709,320,436,651,257,389,724,372,751,802,344,789,1040,646,514,966,905,348,574,280,877,221,866,660,312,981,766,233,925,810,381,366,942,439,1047,798,1057,746,778,820,260,862,467,252,852,461,493,757,682,224,847,566,324,974,742,874,317,615,356,869,499,989,637,489,679,706,393,654,721,1060,1050,266,805,508,657,398,794,718,618,824,296,601,375,733,819,1007,286,826,572,236,947,445,936,219,1011,736,996,230,303,764,604,880,649,1043,552,816,609,323,594,621,240,1029,330,685,983,768,883,986,563,226,505,922,1034,944,663,255,487,939,754,968,836,971,739,263,993,712,557,1053,791,585,502,840,338,808,643,336,703,613,727,845,465,931,688,581,771,813,748,304,1062,351,401,786,781,588,699,963,517,568,272,549,290,378,300,999,315,833,950,326,341,1065,696,283,928,294,801,908,850,442,871,369,277,691,469,354,639,676,592,496,1037,775,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP066^1 : TPTP v8.2.0. Released v7.5.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 15:46:39 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.89/1.10 % [INFO] Parsing done (242ms).
% 1.89/1.11 % [INFO] Running in sequential loop mode.
% 2.68/1.31 % [INFO] eprover registered as external prover.
% 2.68/1.32 % [INFO] cvc4 registered as external prover.
% 2.68/1.32 % [INFO] Scanning for conjecture ...
% 2.83/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 356 axioms. Running axiom selection ...
% 3.19/1.50 % [INFO] Axiom selection finished. Selected 216 axioms (removed 140 axioms).
% 3.67/1.65 % [INFO] Problem is higher-order (TPTP THF).
% 3.67/1.66 % [INFO] Type checking passed.
% 3.67/1.66 % [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 ...
% 21.14/6.35 % External prover 'cvc4' found a proof!
% 21.14/6.35 % [INFO] Killing All external provers ...
% 21.14/6.35 % Time passed: 5831ms (effective reasoning time: 5243ms)
% 21.14/6.35 % 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)>
% 21.14/6.36 % Axioms used in derivation (216): fact_138_add__mset__commute, fact_98_removeLeaf_Ocases, fact_65_old_Oprod_Oexhaust, fact_261_pred__subset__eq2, fact_165_exE__realizer_H, fact_54_prod__cases, fact_178_HS_Ois__empty__empty, fact_195_snd__swap, fact_177_add__mset__replicate__mset__safe, fact_107_add__mset__eq__singleton__iff, fact_96_Tree_Odistinct_I1_J, fact_219_Heap_Omultiset, fact_128_group__cancel_Oadd2, fact_243_heapify_Osimps_I1_J, fact_189_swap__swap, fact_60_Pair__inject, fact_142_empty__neutral_I1_J, fact_120_add__cancel__left__left, fact_131_ab__semigroup__add__class_Oadd__ac_I1_J, fact_8_right_Osimps, fact_228_siftDown_Osimps_I3_J, fact_70_HS_Omultiset__empty, fact_250_Collection_Omultiset__empty, fact_180_HS_Ois__empty__inj, fact_197_fst__swap, fact_79_prod__eq__iff, fact_134_union__left__cancel, fact_229_siftDown_Osimps_I5_J, fact_148_multiset__cases, fact_151_single__is__union, fact_176_HS_Ois__empty__as__list, fact_300_multiset__nonemptyE, fact_14_fstI, fact_23_assms_I2_J, fact_140_add_Ocomm__neutral, fact_104_single__eq__single, fact_155_exI__realizer, fact_4_Tree_Oinject, fact_112_add_Oleft__neutral, fact_5_removeLeaf_Osimps_I5_J, fact_103_union__mset__add__mset__right, fact_77_prod_Oexhaust__sel, fact_295_union__iff, fact_125_add_Oleft__commute, fact_280_insert__noteq__member, fact_239_in__tree_Osimps_I1_J, fact_185_removeLeaf__heap__is__heap, fact_44_snd__eqD, fact_144_multi__nonempty__split, fact_110_subset__mset_Oadd__eq__0__iff__both__eq__0, fact_99_siftDown_Ocases, fact_275_union__single__eq__member, fact_315_multi__member__skip, fact_194_snd__swap, fact_21_fst__conv, fact_204_Heap__axioms_Ointro, fact_242_heapify_Osimps_I2_J, fact_83_prod__eqI, fact_159_conjI__realizer, fact_143_empty__neutral_I2_J, fact_26_prod_Oinject, fact_1_assms_I1_J, fact_34_prod_Ocollapse, fact_173_eq__fst__iff, fact_252_hs__of__list__def, fact_48_snd__conv, fact_198_is__heap_Osimps_I1_J, fact_85_is__heap_Ocases, fact_146_multiset__induct2, fact_249_HS_OCollection__axioms, fact_137_union__assoc, fact_106_single__eq__add__mset, fact_232_siftDown__Node, fact_50_surj__pair, help_If_3_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T, fact_7_left_Osimps, fact_179_hs__is__empty__def, fact_341_heap__top__max, fact_66_old_Oprod_Oinducts, fact_22_fst__conv, fact_270_multi__member__last, fact_132_multi__union__self__other__eq, fact_56_prod__cases, fact_230_siftDown_Osimps_I1_J, fact_205_val_Osimps, fact_196_fst__swap, fact_40_sndI, fact_113_add__right__cancel, fact_82_prod_Oexpand, fact_253_pred__equals__eq2, fact_10_removeLeaf_Osimps_I1_J, fact_13_fstI, help_If_1_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T, fact_3__092_060open_062t_H_A_061_AT_Av_A_Isnd_A_IremoveLeaf_A_IT_Av1_Al1_Ar1_J_J_J_A_IT_Av2_Al2_Ar2_J_092_060close_062, fact_265_heap__top__geq, fact_206_is__heap_Osimps_I4_J, fact_135_union__commute, fact_227_siftDown_Osimps_I4_J, fact_240_siftDown__in__tree__set, fact_233_siftDown_Osimps_I2_J, fact_285_multi__member__split, fact_231_siftDown__multiset, fact_41_sndI, fact_117_add__cancel__right__right, fact_310_multiset__induct__max, fact_78_prod_Oexhaust__sel, fact_73_surjective__pairing, fact_28_old_Oprod_Oinject, fact_170_eq__snd__iff, fact_210_verit__la__disequality, fact_58_Pair__inject, fact_17_fst__eqD, fact_220_Heap_Oaxioms_I2_J, fact_183_prod_Oswap__def, fact_115_multi__self__add__other__not__self, fact_74_surjective__pairing, fact_68_old_Oprod_Oinducts, fact_309_multiset__induct__min, fact_53_surj__pair, fact_244_heapify__heap__is__heap, fact_320_multi__member__this, fact_61_Pair__inject, fact_166_exE__realizer_H, fact_248_Heap_Oaxioms_I1_J, fact_184_prod_Oswap__def, fact_192_swap__simp, fact_64_old_Oprod_Oexhaust, fact_101_removeLeaf_Osimps_I3_J, fact_18_fst__eqD, fact_241_hs__remove__max__def, fact_24_prod_Oinject, fact_199_is__heap_Osimps_I2_J, fact_31_old_Oprod_Oinject, fact_52_surj__pair, fact_37_multiset_Osimps_I1_J, fact_126_add_Ocommute, fact_147_multiset__induct, fact_127_add_Oassoc, fact_124_add__left__imp__eq, fact_237_is__heap__max, fact_136_union__lcomm, fact_6_removeLeaf_Osimps_I4_J, fact_116_add__mset__add__mset__same__iff, fact_251_Collection_Ois__empty__as__list, fact_234_siftDown__heap__is__heap, fact_150_union__is__single, fact_49_snd__conv, fact_221_is__heap_Osimps_I6_J, fact_105_add__mset__eq__single, fact_145_empty__not__add__mset, fact_2__C4__2_Oprems_C_I2_J, fact_119_add__cancel__left__right, fact_57_prod__cases, fact_245_multiset__heapify, fact_175_verit__sum__simplify, fact_0__C4__2_Oprems_C_I1_J, fact_290_mset__add, fact_69_old_Oprod_Oinducts, fact_257_subrelI, fact_130_add__mono__thms__linordered__semiring_I4_J, fact_129_group__cancel_Oadd1, fact_100_removeLeaf_Osimps_I2_J, fact_202_Heap__axioms__def, fact_102_union__mset__add__mset__left, fact_45_snd__eqD, fact_149_add__mset__add__single, fact_95_Tree_Oinduct, fact_111_subset__mset_Ozero__eq__add__iff__both__eq__0, fact_246_Heap__def, fact_224_Heap_Oremove__max__multiset_H, fact_123_add__right__imp__eq, fact_84_prod__eqI, fact_222_is__heap_Osimps_I5_J, fact_81_prod_Oexpand, fact_236_siftDown__in__tree, fact_80_prod__eq__iff, fact_200_removeLeaf__val__val, fact_118_add__cancel__right__left, fact_139_add__eq__conv__ex, fact_35_prod_Ocollapse, fact_9__C4__2_Ohyps_C_I1_J, fact_27_prod_Oinject, fact_238_in__tree_Osimps_I2_J, fact_186_NO__MATCH__cong, fact_30_old_Oprod_Oinject, fact_108_empty__eq__union, fact_235_siftDown_Osimps_I6_J, fact_154_exI__realizer, fact_226_Heap_Oremove__max__val, fact_133_union__right__cancel, fact_141_comm__monoid__add__class_Oadd__0, fact_169_eq__snd__iff, fact_218_Heap_Ois__heap__of__list, fact_94_Tree_Oexhaust, fact_109_union__eq__empty, fact_164_Multiset_Ois__empty__def, fact_203_Heap__axioms_Ointro, help_If_2_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T, fact_122_zero__reorient, fact_188_swap__swap, fact_158_conjI__realizer, fact_163_BNF__Greatest__Fixpoint_Osubst__Pair, fact_201_Heap__axioms__def, fact_162_BNF__Greatest__Fixpoint_Osubst__Pair, fact_114_add__left__cancel, fact_121_add_Oright__neutral, fact_36_multiset_Osimps_I2_J, fact_62_old_Oprod_Oexhaust, fact_207_is__heap_Osimps_I3_J, fact_193_swap__simp, fact_187_NO__MATCH__def, fact_217_Heap_Oas__tree__empty, fact_209_Heap_Oremove__max__is__heap, fact_174_eq__fst__iff, fact_97_removeLeaf_Oinduct, fact_247_Heap_Ointro
% 21.14/6.36 % No. of inferences in proof: 436
% 21.14/6.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5831 ms resp. 5243 ms w/o parsing
% 21.14/6.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.14/6.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------