%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP069^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:39 AM UTC 2026
% Result : Theorem 10.77s 4.00s
% Output : Refutation 11.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 134
% Syntax : Number of formulae : 270 ( 144 unt; 0 typ; 0 def)
% Number of atoms : 721 ( 375 equ; 6 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 3120 ( 102 ~; 18 |; 84 &;2621 @)
% ( 0 <=>; 295 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 7 con; 0-3 aty)
% Number of variables : 828 ( 28 ^; 784 !; 16 ?; 828 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr158363655iset_a_type,type,
set_Pr158363655iset_a: $tType ).
thf(produc1127127335iset_a_type,type,
produc1127127335iset_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(tree_a_type,type,
tree_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(minus_1649712171iset_a_decl,type,
minus_1649712171iset_a: multiset_a > multiset_a > multiset_a ).
thf(plus_plus_multiset_a_decl,type,
plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
thf(zero_zero_multiset_a_decl,type,
zero_zero_multiset_a: multiset_a ).
thf(nO_MAT1617603563iset_a_decl,type,
nO_MAT1617603563iset_a: multiset_a > multiset_a > $o ).
thf(heapIm970322378pify_a_decl,type,
heapIm970322378pify_a: tree_a > tree_a ).
thf(heapIm1140443833left_a_decl,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(heapIm1257206334ight_a_decl,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(heapIm1091024090Down_a_decl,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(e_a_decl,type,
e_a: tree_a ).
thf(t_a_decl,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(in_tree_a_decl,type,
in_tree_a: a > tree_a > $o ).
thf(is_heap_a_decl,type,
is_heap_a: tree_a > $o ).
thf(multiset_a2_decl,type,
multiset_a2: tree_a > multiset_a ).
thf(val_a_decl,type,
val_a: tree_a > a ).
thf(lattic146396397_Max_a_decl,type,
lattic146396397_Max_a: set_a > a ).
thf(add_mset_a_decl,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(comm_m315775925iset_a_decl,type,
comm_m315775925iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
thf(fold_m382157835iset_a_decl,type,
fold_m382157835iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
thf(fold_m364285649iset_a_decl,type,
fold_m364285649iset_a: ( a > multiset_a > multiset_a ) > multiset_a > multiset_a > multiset_a ).
thf(is_empty_a_decl,type,
is_empty_a: multiset_a > $o ).
thf(set_mset_multiset_a_decl,type,
set_mset_multiset_a: multiset_multiset_a > set_multiset_a ).
thf(set_mset_a_decl,type,
set_mset_a: multiset_a > set_a ).
thf(ord_le1199012836iset_a_decl,type,
ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
thf(ord_less_eq_a_decl,type,
ord_less_eq_a: a > a > $o ).
thf(order_Greatest_a_decl,type,
order_Greatest_a: ( a > $o ) > a ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(member_multiset_a_decl,type,
member_multiset_a: multiset_a > set_multiset_a > $o ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(l_decl,type,
l: tree_a ).
thf(r_decl,type,
r: tree_a ).
thf(v_decl,type,
v: a ).
thf(129,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/sandbox/benchmark/theBenchmark.p',fact_5_Tree_Oinject) ).
thf(645,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)],[129]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',fact_62_multi__member__split) ).
thf(365,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)],[56]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',fact_67_add__eq__conv__ex) ).
thf(333,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)],[49]) ).
thf(84,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_antisym__conv) ).
thf(468,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_78_multiset__induct2) ).
thf(481,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)],[89]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',fact_77_multiset__induct) ).
thf(170,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)],[13]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',fact_22_siftDown_Osimps_I4_J) ).
thf(582,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)],[115]) ).
thf(22,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( ord_less_eq_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_eq__refl) ).
thf(217,plain,
! [A: a,B: a] :
( ( A = B )
=> ( ord_less_eq_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,axiom,
! [A: multiset_a,B: a] :
( A
!= ( add_mset_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_multi__self__add__other__not__self) ).
thf(247,plain,
! [A: multiset_a,B: a] :
( A
!= ( add_mset_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(62,axiom,
! [A: a,B: multiset_a] :
( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_diff__single__trivial) ).
thf(384,plain,
! [A: a,B: multiset_a] :
( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',fact_111_multi__member__this) ).
thf(550,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)],[103]) ).
thf(90,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( ord_less_eq_a @ D @ B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( ord_less_eq_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_GreatestI2__order) ).
thf(500,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( ord_less_eq_a @ D @ B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( ord_less_eq_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(45,axiom,
! [A: a,B: a > a,C: a,D: a] :
( ( ord_less_eq_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_order__subst1) ).
thf(320,plain,
! [A: a,B: a > a,C: a,D: a] :
( ( ord_less_eq_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(76,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ C @ A )
=> ( ord_less_eq_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_dual__order_Otrans) ).
thf(436,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ C @ A )
=> ( ord_less_eq_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(15,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_empty__neutral_I2_J) ).
thf(184,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(122,axiom,
is_heap_a @ e_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_is__heap_Osimps_I1_J) ).
thf(619,plain,
is_heap_a @ e_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(100,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_order_Otrans) ).
thf(542,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_87_subset__mset_Oadd__eq__0__iff__both__eq__0) ).
thf(325,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)],[46]) ).
thf(8,axiom,
! [A: multiset_a] :
( ( ( minus_1649712171iset_a @ A @ zero_zero_multiset_a )
= A )
& ( ( minus_1649712171iset_a @ zero_zero_multiset_a @ A )
= zero_zero_multiset_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_diff__empty) ).
thf(152,plain,
! [A: multiset_a] :
( ( ( minus_1649712171iset_a @ A @ zero_zero_multiset_a )
= A )
& ( ( minus_1649712171iset_a @ zero_zero_multiset_a @ A )
= zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,axiom,
! [A: a,B: a,C: multiset_a] :
( ( A != B )
=> ( ( add_mset_a @ B @ ( minus_1649712171iset_a @ C @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= ( minus_1649712171iset_a @ ( add_mset_a @ B @ C ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_diff__union__swap) ).
thf(316,plain,
! [A: a,B: a,C: multiset_a] :
( ( A != B )
=> ( ( add_mset_a @ B @ ( minus_1649712171iset_a @ C @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= ( minus_1649712171iset_a @ ( add_mset_a @ B @ C ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_100_union__iff) ).
thf(261,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)],[32]) ).
thf(60,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ B )
= C )
=> ( B
= ( minus_1649712171iset_a @ C @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_union__single__eq__diff) ).
thf(376,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ B )
= C )
=> ( B
= ( minus_1649712171iset_a @ C @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(52,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_siftDown__in__tree) ).
thf(348,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(112,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_right_Osimps) ).
thf(574,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)],[112]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',fact_4_siftDown__heap__is__heap) ).
thf(634,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)],[126]) ).
thf(23,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__right__mono) ).
thf(221,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(81,axiom,
! [A: a,B: a,C: a > a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_ord__le__eq__subst) ).
thf(453,plain,
! [A: a,B: a,C: a > a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(43,axiom,
! [A: a,B: multiset_a] :
( zero_zero_multiset_a
!= ( add_mset_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_empty__not__add__mset) ).
thf(312,plain,
! [A: a,B: multiset_a] :
( zero_zero_multiset_a
!= ( add_mset_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_63_insert__noteq__member) ).
thf(380,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)],[61]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_110_multi__member__skip) ).
thf(439,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)],[77]) ).
thf(97,axiom,
! [A: a,B: a] :
( ~ ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_le__cases) ).
thf(534,plain,
! [A: a,B: a] :
( ~ ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',fact_72_add__mset__eq__singleton__iff) ).
thf(302,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)],[40]) ).
thf(9,axiom,
! [A: multiset_a,B: multiset_a] :
( ( minus_1649712171iset_a @ ( plus_plus_multiset_a @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_diff__union__cancelR) ).
thf(160,plain,
! [A: multiset_a,B: multiset_a] :
( ( minus_1649712171iset_a @ ( plus_plus_multiset_a @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',fact_90_union__mset__add__mset__right) ).
thf(192,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)],[18]) ).
thf(3,axiom,
! [A: multiset_a,B: multiset_a] :
( ( minus_1649712171iset_a @ ( plus_plus_multiset_a @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_diff__union__cancelL) ).
thf(137,plain,
! [A: multiset_a,B: multiset_a] :
( ( minus_1649712171iset_a @ ( plus_plus_multiset_a @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',fact_26_siftDown__Node) ).
thf(625,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)],[125]) ).
thf(93,axiom,
! [A: a,B: multiset_a] :
( ( minus_1649712171iset_a @ ( add_mset_a @ A @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_add__mset__remove__trivial) ).
thf(522,plain,
! [A: a,B: multiset_a] :
( ( minus_1649712171iset_a @ ( add_mset_a @ A @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(24,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_dual__order_Oantisym) ).
thf(224,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,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 ) )
| ( ( B
= ( add_mset_a @ C @ ( minus_1649712171iset_a @ D @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) )
& ( D
= ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ C @ zero_zero_multiset_a ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_add__eq__conv__diff) ).
thf(229,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 ) )
| ( ( B
= ( add_mset_a @ C @ ( minus_1649712171iset_a @ D @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) )
& ( D
= ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ C @ zero_zero_multiset_a ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_11_in__tree_Osimps_I2_J) ).
thf(566,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)],[109]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_88_union__eq__empty) ).
thf(519,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)],[92]) ).
thf(120,axiom,
is_heap_a @ ( heapIm970322378pify_a @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_T_Ohyps_I2_J) ).
thf(615,plain,
is_heap_a @ ( heapIm970322378pify_a @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',fact_25_siftDown_Osimps_I5_J) ).
thf(593,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)],[117]) ).
thf(87,axiom,
( plus_plus_multiset_a
= ( fold_m364285649iset_a @ add_mset_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_union__fold__mset__add__mset) ).
thf(476,plain,
( plus_plus_multiset_a
= ( fold_m364285649iset_a @ add_mset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',fact_27_is__heap_Osimps_I6_J) ).
thf(642,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)],[128]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_31_is__heap_Osimps_I4_J) ).
thf(590,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)],[116]) ).
thf(102,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( plus_plus_multiset_a @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_insert__DiffM2) ).
thf(547,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( plus_plus_multiset_a @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(47,axiom,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_multiset_Osimps_I1_J) ).
thf(328,plain,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',fact_108_union__is__single) ).
thf(471,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)],[85]) ).
thf(65,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_eq__iff) ).
thf(393,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(110,axiom,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_is__heap_Osimps_I2_J) ).
thf(569,plain,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',fact_101_union__assoc) ).
thf(371,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)],[58]) ).
thf(67,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_order__class_Oorder_Oantisym) ).
thf(398,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(106,axiom,
( ( heapIm970322378pify_a @ e_a )
= e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_heapify_Osimps_I1_J) ).
thf(558,plain,
( ( heapIm970322378pify_a @ e_a )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',fact_29_is__heap__max) ).
thf(662,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)],[131]) ).
thf(11,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( ord_le1199012836iset_a @ A @ B )
& ( ord_le1199012836iset_a @ C @ D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__mono__thms__linordered__semiring_I1_J) ).
thf(166,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( ord_le1199012836iset_a @ A @ B )
& ( ord_le1199012836iset_a @ C @ D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(33,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_insert__DiffM) ).
thf(264,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( minus_1649712171iset_a @ ( minus_1649712171iset_a @ A @ B ) @ C )
= ( minus_1649712171iset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_diff__diff__add__mset) ).
thf(149,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( minus_1649712171iset_a @ ( minus_1649712171iset_a @ A @ B ) @ C )
= ( minus_1649712171iset_a @ A @ ( plus_plus_multiset_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_28_is__heap_Osimps_I5_J) ).
thf(577,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)],[113]) ).
thf(101,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ B @ A )
& ( ord_less_eq_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_dual__order_Oeq__iff) ).
thf(545,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ B @ A )
& ( ord_less_eq_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(79,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ord__le__eq__trans) ).
thf(445,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_10_siftDown_Ocases) ).
thf(611,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)],[119]) ).
thf(14,axiom,
! [A: multiset_multiset_a] :
( ( ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= zero_zero_multiset_a )
= ( ! [B: multiset_a] :
( ( member_multiset_a @ B @ ( set_mset_multiset_a @ A ) )
=> ( B = zero_zero_multiset_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_subset__mset_Osum__mset__0__iff) ).
thf(181,plain,
! [A: multiset_multiset_a] :
( ( ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= zero_zero_multiset_a )
= ( ! [B: multiset_a] :
( ( member_multiset_a @ B @ ( set_mset_multiset_a @ A ) )
=> ( B = zero_zero_multiset_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',fact_65_heap__top__max) ).
thf(672,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)],[133]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',fact_86_subset__mset_Ozero__eq__add__iff__both__eq__0) ).
thf(187,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)],[16]) ).
thf(69,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( ord_less_eq_a @ C @ B ) )
=> ( ( order_Greatest_a @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Greatest__equality) ).
thf(406,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( ord_less_eq_a @ C @ B ) )
=> ( ( order_Greatest_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_105_union__right__cancel) ).
thf(419,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)],[71]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',fact_3_heapify_Osimps_I2_J) ).
thf(616,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)],[121]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',fact_107_add__mset__add__single) ).
thf(271,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)],[35]) ).
thf(63,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( minus_1649712171iset_a @ B @ C ) ) )
=> ( member_a @ A @ ( set_mset_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_in__diffD) ).
thf(387,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( minus_1649712171iset_a @ B @ C ) ) )
=> ( member_a @ A @ ( set_mset_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(4,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( minus_1649712171iset_a @ ( add_mset_a @ A @ B ) @ ( add_mset_a @ A @ C ) )
= ( minus_1649712171iset_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_add__mset__diff__bothsides) ).
thf(140,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( minus_1649712171iset_a @ ( add_mset_a @ A @ B ) @ ( add_mset_a @ A @ C ) )
= ( minus_1649712171iset_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',fact_16_is__heap_Ocases) ).
thf(621,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)],[124]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',fact_75_single__eq__single) ).
thf(251,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)],[29]) ).
thf(20,axiom,
! [A: a] : ( ord_less_eq_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_order__refl) ).
thf(198,plain,
! [A: a] : ( ord_less_eq_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(48,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add__mset__add__mset__same__iff) ).
thf(330,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)],[48]) ).
thf(82,axiom,
! [A: a] : ( member_a @ A @ ( set_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_multi__member__last) ).
thf(462,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)],[82]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',fact_74_add__mset__eq__single) ).
thf(345,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)],[51]) ).
thf(104,axiom,
! [A: a,B: tree_a,C: tree_a] :
( e_a
!= ( t_a @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Tree_Odistinct_I1_J) ).
thf(552,plain,
! [A: a,B: tree_a,C: tree_a] :
( e_a
!= ( t_a @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(108,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( val_a @ ( t_a @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_val_Osimps) ).
thf(563,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)],[108]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',fact_104_union__left__cancel) ).
thf(299,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)],[39]) ).
thf(34,axiom,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( add_mset_a @ C @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= ( add_mset_a @ C @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_diff__union__swap2) ).
thf(267,plain,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( add_mset_a @ C @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= ( add_mset_a @ C @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(74,axiom,
! [A: a] : ( ord_less_eq_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dual__order_Orefl) ).
thf(431,plain,
! [A: a] : ( ord_less_eq_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',fact_18_Tree_Oinduct) ).
thf(675,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)],[134]) ).
thf(73,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_ord__eq__le__trans) ).
thf(426,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(59,axiom,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_siftDown_Osimps_I1_J) ).
thf(374,plain,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',fact_24_siftDown_Osimps_I6_J) ).
thf(648,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)],[130]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',fact_89_empty__eq__union) ).
thf(516,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)],[91]) ).
thf(54,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_empty__neutral_I1_J) ).
thf(355,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ zero_zero_multiset_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(94,axiom,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_in__tree_Osimps_I1_J) ).
thf(525,plain,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(114,axiom,
( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
=> ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
=> ( ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062) ).
thf(580,plain,
( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
=> ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',fact_85_multiset_Osimps_I2_J) ).
thf(690,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)],[135]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',fact_70_multiset__induct__min) ).
thf(282,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)],[38]) ).
thf(50,axiom,
! [A: a,B: a > a,C: a,D: a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_ord__eq__le__subst) ).
thf(336,plain,
! [A: a,B: a > a,C: a,D: a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',fact_32_is__heap_Osimps_I3_J) ).
thf(571,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)],[111]) ).
thf(5,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( minus_1649712171iset_a @ A @ ( plus_plus_multiset_a @ B @ C ) )
= ( minus_1649712171iset_a @ ( minus_1649712171iset_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Multiset_Odiff__add) ).
thf(143,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( minus_1649712171iset_a @ A @ ( plus_plus_multiset_a @ B @ C ) )
= ( minus_1649712171iset_a @ ( minus_1649712171iset_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',fact_109_single__is__union) ).
thf(450,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)],[80]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_36_heap__top__geq) ).
thf(556,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)],[105]) ).
thf(99,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ( ord_le1199012836iset_a @ C @ D )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_add__mono) ).
thf(539,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ( ord_le1199012836iset_a @ C @ D )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(57,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add__left__mono) ).
thf(368,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(31,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_mem__Collect__eq) ).
thf(258,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(53,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( A = B )
& ( ord_le1199012836iset_a @ C @ D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__mono__thms__linordered__semiring_I2_J) ).
thf(351,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( A = B )
& ( ord_le1199012836iset_a @ C @ D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',fact_73_single__eq__add__mset) ).
thf(390,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)],[64]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',fact_106_multi__union__self__other__eq) ).
thf(401,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)],[68]) ).
thf(75,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Collect__mem__eq) ).
thf(433,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',fact_91_union__mset__add__mset__left) ).
thf(478,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)],[88]) ).
thf(98,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_antisym) ).
thf(536,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(123,axiom,
is_heap_a @ ( heapIm970322378pify_a @ l ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_T_Ohyps_I1_J) ).
thf(620,plain,
is_heap_a @ ( heapIm970322378pify_a @ l ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(12,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_order__class_Oorder_Oeq__iff) ).
thf(168,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: multiset_a] :
( ( minus_1649712171iset_a @ A @ A )
= zero_zero_multiset_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Multiset_Odiff__cancel) ).
thf(146,plain,
! [A: multiset_a] :
( ( minus_1649712171iset_a @ A @ A )
= zero_zero_multiset_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
( is_empty_a
= ( ^ [A: multiset_a] : ( A = zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Multiset_Ois__empty__def) ).
thf(190,plain,
( is_empty_a
= ( ^ [A: multiset_a] : ( A = zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(72,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( ord_le1199012836iset_a @ A @ B )
& ( C = D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__mono__thms__linordered__semiring_I3_J) ).
thf(422,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( ord_le1199012836iset_a @ A @ B )
& ( C = D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(36,axiom,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ~ ! [B: a] :
~ ( member_a @ B @ ( set_mset_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_multiset__nonemptyE) ).
thf(273,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)],[36]) ).
thf(41,axiom,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ~ ! [B: a,C: multiset_a] :
( A
!= ( add_mset_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_multiset__cases) ).
thf(305,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)],[41]) ).
thf(1,conjecture,
is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(136,plain,
~ ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(55,axiom,
! [A: a > a > $o,B: a,C: a] :
( ! [D: a,E: a] :
( ( ord_less_eq_a @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: a,E: a] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_linorder__wlog) ).
thf(358,plain,
! [A: a > a > $o,B: a,C: a] :
( ! [D: a,E: a] :
( ( ord_less_eq_a @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: a,E: a] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',fact_66_add__mset__commute) ).
thf(195,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)],[19]) ).
thf(86,axiom,
( in_tree_a
= ( ^ [A: a,B: tree_a] : ( in_tree_a @ A @ ( heapIm1091024090Down_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_siftDown__in__tree__set) ).
thf(474,plain,
( in_tree_a
= ( ^ [A: a,B: tree_a] : ( in_tree_a @ A @ ( heapIm1091024090Down_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',fact_23_siftDown_Osimps_I3_J) ).
thf(664,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)],[132]) ).
thf(96,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
| ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_linear) ).
thf(532,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
| ( ord_less_eq_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_124_add__mset__replicate__mset__safe) ).
thf(415,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)],[70]) ).
thf(66,axiom,
! [A: a,B: multiset_a,C: multiset_multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( fold_m382157835iset_a @ plus_plus_multiset_a @ B @ C ) ) )
= ( ( member_a @ A @ ( set_mset_a @ B ) )
| ? [D: multiset_a] :
( ( member_multiset_a @ D @ ( set_mset_multiset_a @ C ) )
& ( member_a @ A @ ( set_mset_a @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_in__mset__fold__plus__iff) ).
thf(395,plain,
! [A: a,B: multiset_a,C: multiset_multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( fold_m382157835iset_a @ plus_plus_multiset_a @ B @ C ) ) )
= ( ( member_a @ A @ ( set_mset_a @ B ) )
| ? [D: multiset_a] :
( ( member_multiset_a @ D @ ( set_mset_multiset_a @ C ) )
& ( member_a @ A @ ( set_mset_a @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',fact_61_mset__add) ).
thf(464,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)],[83]) ).
thf(95,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( add_mset_a @ A @ C ) @ B )
= ( add_mset_a @ A @ ( minus_1649712171iset_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_diff__add__mset__swap) ).
thf(528,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( add_mset_a @ A @ C ) @ B )
= ( add_mset_a @ A @ ( minus_1649712171iset_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(37,axiom,
! [A: a,B: a,C: a > a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ ( C @ B ) @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_order__subst2) ).
thf(277,plain,
! [A: a,B: a,C: a > a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ ( C @ B ) @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(78,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_order__trans) ).
thf(442,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(118,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ~ ! [B: a,C: tree_a,D: tree_a] :
( A
!= ( t_a @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Tree_Oexhaust) ).
thf(607,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)],[118]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',fact_102_union__lcomm) ).
thf(163,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)],[10]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',fact_71_multiset__induct__max) ).
thf(200,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)],[21]) ).
thf(42,axiom,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ? [B: multiset_a,C: a] :
( A
= ( add_mset_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_multi__nonempty__split) ).
thf(309,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)],[42]) ).
thf(107,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_left_Osimps) ).
thf(560,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)],[107]) ).
thf(127,axiom,
! [A: a] :
( ( heapIm1091024090Down_a @ ( t_a @ A @ e_a @ e_a ) )
= ( t_a @ A @ e_a @ e_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_siftDown_Osimps_I2_J) ).
thf(639,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)],[127]) ).
thf(27,axiom,
! [A: a,B: a,C: a] :
( ( ( ord_less_eq_a @ A @ B )
=> ~ ( ord_less_eq_a @ B @ C ) )
=> ( ( ( ord_less_eq_a @ B @ A )
=> ~ ( ord_less_eq_a @ A @ C ) )
=> ( ( ( ord_less_eq_a @ A @ C )
=> ~ ( ord_less_eq_a @ C @ B ) )
=> ( ( ( ord_less_eq_a @ C @ B )
=> ~ ( ord_less_eq_a @ B @ A ) )
=> ( ( ( ord_less_eq_a @ B @ C )
=> ~ ( ord_less_eq_a @ C @ A ) )
=> ~ ( ( ord_less_eq_a @ C @ A )
=> ~ ( ord_less_eq_a @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_le__cases3) ).
thf(232,plain,
! [A: a,B: a,C: a] :
( ( ( ord_less_eq_a @ A @ B )
=> ~ ( ord_less_eq_a @ B @ C ) )
=> ( ( ( ord_less_eq_a @ B @ A )
=> ~ ( ord_less_eq_a @ A @ C ) )
=> ( ( ( ord_less_eq_a @ A @ C )
=> ~ ( ord_less_eq_a @ C @ B ) )
=> ( ( ( ord_less_eq_a @ C @ B )
=> ~ ( ord_less_eq_a @ B @ A ) )
=> ( ( ( ord_less_eq_a @ B @ C )
=> ~ ( ord_less_eq_a @ C @ A ) )
=> ~ ( ( ord_less_eq_a @ C @ A )
=> ~ ( ord_less_eq_a @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',fact_64_union__single__eq__member) ).
thf(254,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)],[30]) ).
thf(25,axiom,
( plus_plus_multiset_a
= ( ^ [A: multiset_a,B: multiset_a] : ( plus_plus_multiset_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_union__commute) ).
thf(227,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)],[25]) ).
thf(699,plain,
$false,
inference(e,[status(thm)],[645,365,333,468,481,170,582,217,247,384,550,500,320,436,184,619,542,325,152,316,261,376,348,574,634,221,453,312,380,439,534,302,160,192,137,625,522,224,229,566,519,615,593,476,642,590,547,328,471,393,569,371,398,558,662,166,264,149,577,545,445,611,181,672,187,406,419,616,271,387,140,621,251,198,330,462,345,552,563,299,267,431,675,426,374,648,516,355,525,580,690,282,336,571,143,450,556,539,368,258,351,390,401,433,478,536,620,168,146,190,422,273,305,136,358,195,474,664,532,415,395,464,528,277,442,607,163,200,309,560,639,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP069^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:48:41 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.02/1.15 % [INFO] Parsing done (368ms).
% 2.02/1.17 % [INFO] Running in sequential loop mode.
% 2.88/1.56 % [INFO] eprover registered as external prover.
% 2.88/1.57 % [INFO] Scanning for conjecture ...
% 3.27/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 142 axioms. Running axiom selection ...
% 3.46/1.83 % [INFO] Axiom selection finished. Selected 133 axioms (removed 9 axioms).
% 4.04/2.08 % [INFO] Problem is higher-order (TPTP THF).
% 4.04/2.10 % [INFO] Type checking passed.
% 4.04/2.11 % [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 ...
% 10.77/3.99 % External prover 'e' found a proof!
% 10.77/3.99 % [INFO] Killing All external provers ...
% 10.77/4.00 % Time passed: 3655ms (effective reasoning time: 2821ms)
% 10.77/4.00 % 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)>
% 10.77/4.00 % Axioms used in derivation (133): fact_74_add__mset__eq__single, fact_139_diff__union__cancelL, fact_66_add__mset__commute, fact_119_subset__mset_Osum__mset__0__iff, fact_69_GreatestI2__order, fact_78_multiset__induct2, fact_122_in__mset__fold__plus__iff, fact_81_multiset__nonemptyE, fact_101_union__assoc, fact_140_Multiset_Odiff__add, fact_61_mset__add, fact_6_left_Osimps, fact_60_multi__self__add__other__not__self, fact_100_union__iff, fact_75_single__eq__single, fact_33_mem__Collect__eq, fact_97_add__mono__thms__linordered__semiring_I3_J, fact_39_ord__eq__le__subst, fact_84_Multiset_Ois__empty__def, fact_58_dual__order_Oantisym, fact_23_siftDown_Osimps_I3_J, fact_7_right_Osimps, fact_129_diff__union__swap2, fact_133_Multiset_Odiff__cancel, fact_98_empty__neutral_I2_J, fact_132_add__mset__diff__bothsides, fact_124_add__mset__replicate__mset__safe, fact_0_T_Ohyps_I2_J, fact_18_Tree_Oinduct, fact_9_heapify_Osimps_I1_J, fact_80_multi__nonempty__split, fact_71_multiset__induct__max, fact_138_diff__union__cancelR, fact_87_subset__mset_Oadd__eq__0__iff__both__eq__0, fact_31_is__heap_Osimps_I4_J, fact_13_in__tree_Osimps_I1_J, fact_102_union__lcomm, fact_12_siftDown_Osimps_I2_J, fact_25_siftDown_Osimps_I5_J, fact_43_linear, fact_137_diff__union__swap, fact_141_diff__single__trivial, fact_111_multi__member__this, fact_40_ord__le__eq__subst, fact_90_union__mset__add__mset__right, fact_86_subset__mset_Ozero__eq__add__iff__both__eq__0, fact_107_add__mset__add__single, fact_76_multiset__cases, fact_125_insert__DiffM2, fact_93_add__left__mono, fact_21_siftDown__in__tree, fact_72_add__mset__eq__singleton__iff, fact_77_multiset__induct, fact_14_siftDown_Osimps_I1_J, fact_34_Collect__mem__eq, fact_57_dual__order_Oeq__iff, fact_46_order_Otrans, fact_92_add__right__mono, fact_5_Tree_Oinject, fact_131_in__diffD, fact_4_siftDown__heap__is__heap, fact_127_add__mset__remove__trivial, fact_36_heap__top__geq, fact_134_diff__empty, fact_91_union__mset__add__mset__left, fact_1_T_Ohyps_I1_J, fact_103_union__commute, fact_123_union__fold__mset__add__mset, fact_20_is__heap_Osimps_I1_J, fact_135_union__single__eq__diff, fact_106_multi__union__self__other__eq, fact_128_diff__add__mset__swap, fact_48_antisym__conv, fact_28_is__heap_Osimps_I5_J, fact_108_union__is__single, fact_96_add__mono__thms__linordered__semiring_I2_J, fact_109_single__is__union, fact_10_siftDown_Ocases, fact_67_add__eq__conv__ex, fact_15_siftDown__in__tree__set, fact_42_antisym, fact_79_empty__not__add__mset, fact_29_is__heap__max, fact_30_val_Osimps, fact_52_order__class_Oorder_Oantisym, fact_49_order__class_Oorder_Oeq__iff, fact_99_empty__neutral_I1_J, fact_83_multiset_Osimps_I1_J, fact_95_add__mono__thms__linordered__semiring_I1_J, fact_126_diff__diff__add__mset, fact_32_is__heap_Osimps_I3_J, fact_11_in__tree_Osimps_I2_J, fact_85_multiset_Osimps_I2_J, fact_53_order__trans, fact_22_siftDown_Osimps_I4_J, fact_55_linorder__wlog, fact_130_insert__DiffM, fact_27_is__heap_Osimps_I6_J, fact_8_is__heap_Osimps_I2_J, fact_94_add__mono, fact_70_multiset__induct__min, fact_82_multi__member__last, fact_26_siftDown__Node, fact_24_siftDown_Osimps_I6_J, fact_35_order__refl, fact_50_ord__eq__le__trans, fact_68_Greatest__equality, fact_44_eq__refl, fact_3_heapify_Osimps_I2_J, fact_65_heap__top__max, fact_64_union__single__eq__member, fact_63_insert__noteq__member, fact_19_Tree_Odistinct_I1_J, fact_59_add__mset__add__mset__same__iff, fact_41_eq__iff, fact_54_dual__order_Orefl, fact_73_single__eq__add__mset, fact_105_union__right__cancel, fact_17_Tree_Oexhaust, fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062, fact_104_union__left__cancel, fact_37_order__subst1, fact_136_add__eq__conv__diff, fact_56_dual__order_Otrans, fact_89_empty__eq__union, fact_16_is__heap_Ocases, fact_47_le__cases3, fact_51_ord__le__eq__trans, fact_62_multi__member__split, fact_88_union__eq__empty, fact_38_order__subst2, fact_45_le__cases, fact_110_multi__member__skip
% 10.77/4.00 % No. of inferences in proof: 270
% 10.77/4.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3655 ms resp. 2821 ms w/o parsing
% 11.85/4.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.85/4.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------