%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP068^1 : 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 : n012.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 08:06:38 AM UTC 2026
% Result : Theorem 10.77s 3.27s
% Output : Refutation 11.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 141
% Syntax : Number of formulae : 284 ( 140 unt; 0 typ; 0 def)
% Number of atoms : 822 ( 338 equ; 10 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 3622 ( 120 ~; 22 |; 96 &;2996 @)
% ( 0 <=>; 388 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 15 con; 0-3 aty)
% Number of variables : 968 ( 30 ^; 902 !; 36 ?; 968 :)
% 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(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(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(rel_Tree_a_a_decl,type,
rel_Tree_a_a: ( a > a > $o ) > tree_a > tree_a > $o ).
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(image_929116801iset_a_decl,type,
image_929116801iset_a: ( a > multiset_a ) > multiset_a > multiset_multiset_a ).
thf(image_mset_a_a_decl,type,
image_mset_a_a: ( a > a ) > multiset_a > multiset_a ).
thf(mult1_a_decl,type,
mult1_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
thf(mult_a_decl,type,
mult_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
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(subseteq_mset_a_decl,type,
subseteq_mset_a: multiset_a > multiset_a > $o ).
thf(ord_le1530450702ee_a_o_decl,type,
ord_le1530450702ee_a_o: ( tree_a > tree_a > $o ) > ( tree_a > tree_a > $o ) > $o ).
thf(ord_less_eq_a_a_o_decl,type,
ord_less_eq_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(ord_le1199012836iset_a_decl,type,
ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_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(produc2037245207iset_a_decl,type,
produc2037245207iset_a: multiset_a > multiset_a > produc1127127335iset_a ).
thf(product_Pair_a_a_decl,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(irrefl_a_decl,type,
irrefl_a: set_Product_prod_a_a > $o ).
thf(trans_a_decl,type,
trans_a: set_Product_prod_a_a > $o ).
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(member340150864iset_a_decl,type,
member340150864iset_a: produc1127127335iset_a > set_Pr158363655iset_a > $o ).
thf(member449909584od_a_a_decl,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(l_decl,type,
l: tree_a ).
thf(l1_decl,type,
l1: tree_a ).
thf(la_decl,type,
la: tree_a ).
thf(r_decl,type,
r: tree_a ).
thf(r1_decl,type,
r1: tree_a ).
thf(ra_decl,type,
ra: tree_a ).
thf(t_decl,type,
t: tree_a ).
thf(v_decl,type,
v: a ).
thf(v1_decl,type,
v1: a ).
thf(v2_decl,type,
v2: a ).
thf(va_decl,type,
va: a ).
thf(95,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_verit__sum__simplify) ).
thf(577,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
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_15_Tree_Odistinct_I1_J) ).
thf(645,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(48,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_112_multi__member__split) ).
thf(347,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)],[48]) ).
thf(44,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_129_multi__nonempty__split) ).
thf(333,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)],[44]) ).
thf(9,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_139_add__mono__thms__linordered__semiring_I2_J) ).
thf(170,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)],[9]) ).
thf(137,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(762,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)],[137]) ).
thf(29,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_144_union__iff) ).
thf(247,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)],[29]) ).
thf(65,axiom,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a,D: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ B ) )
=> ? [F: a] :
( ( member_a @ F @ ( set_mset_a @ A ) )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ C ) ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ ( plus_plus_multiset_a @ D @ B ) @ ( plus_plus_multiset_a @ D @ A ) ) @ ( mult_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_one__step__implies__mult) ).
thf(440,plain,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a,D: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ B ) )
=> ? [F: a] :
( ( member_a @ F @ ( set_mset_a @ A ) )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ C ) ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ ( plus_plus_multiset_a @ D @ B ) @ ( plus_plus_multiset_a @ D @ A ) ) @ ( mult_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(34,axiom,
( plus_plus_multiset_a
= ( fold_m364285649iset_a @ add_mset_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_union__fold__mset__add__mset) ).
thf(269,plain,
( plus_plus_multiset_a
= ( fold_m364285649iset_a @ add_mset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(98,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_siftDown__in__tree) ).
thf(597,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(126,axiom,
is_heap_a @ l,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
thf(730,plain,
is_heap_a @ l,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(36,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_125_multiset__induct) ).
thf(276,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)],[36]) ).
thf(54,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a > $o] :
( ( subseteq_mset_a @ A @ B )
=> ( ( C @ zero_zero_multiset_a )
=> ( ! [D: a,E: multiset_a] :
( ( member_a @ D @ ( set_mset_a @ B ) )
=> ( ( C @ E )
=> ( C @ ( add_mset_a @ D @ E ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_multi__subset__induct) ).
thf(385,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a > $o] :
( ( subseteq_mset_a @ A @ B )
=> ( ( C @ zero_zero_multiset_a )
=> ( ! [D: a,E: multiset_a] :
( ( member_a @ D @ ( set_mset_a @ B ) )
=> ( ( C @ E )
=> ( C @ ( add_mset_a @ D @ E ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(113,axiom,
is_heap_a @ e_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_is__heap_Osimps_I1_J) ).
thf(698,plain,
is_heap_a @ e_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(109,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(670,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)],[109]) ).
thf(10,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_80_antisym__conv) ).
thf(174,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)],[10]) ).
thf(40,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_167_in__mset__fold__plus__iff) ).
thf(301,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)],[40]) ).
thf(42,axiom,
! [A: multiset_a,B: a,C: multiset_a,D: multiset_a,E: multiset_a,F: set_Product_prod_a_a] :
( ( A
= ( add_mset_a @ B @ C ) )
=> ( ( D
= ( plus_plus_multiset_a @ C @ E ) )
=> ( ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ G @ B ) @ F ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ D @ A ) @ ( mult1_a @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_mult1I) ).
thf(320,plain,
! [A: multiset_a,B: a,C: multiset_a,D: multiset_a,E: multiset_a,F: set_Product_prod_a_a] :
( ( A
= ( add_mset_a @ B @ C ) )
=> ( ( D
= ( plus_plus_multiset_a @ C @ E ) )
=> ( ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ G @ B ) @ F ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ D @ A ) @ ( mult1_a @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(106,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_I5_J) ).
thf(651,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)],[106]) ).
thf(124,axiom,
( t
= ( t_a @ v @ l @ r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_assms_I3_J) ).
thf(724,plain,
( t
= ( t_a @ v @ l @ r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(14,axiom,
! [A: a,B: multiset_a] :
( zero_zero_multiset_a
!= ( add_mset_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_empty__not__add__mset) ).
thf(184,plain,
! [A: a,B: multiset_a] :
( zero_zero_multiset_a
!= ( add_mset_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(135,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_108_heap__top__geq) ).
thf(751,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)],[135]) ).
thf(83,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_124_multiset__cases) ).
thf(542,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)],[83]) ).
thf(5,axiom,
! [A: set_Product_prod_a_a,B: a,C: multiset_a,D: multiset_a] :
( ( trans_a @ A )
=> ( ( irrefl_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( add_mset_a @ B @ C ) @ ( add_mset_a @ B @ D ) ) @ ( mult_a @ A ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ ( mult_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_mult__cancel__add__mset) ).
thf(157,plain,
! [A: set_Product_prod_a_a,B: a,C: multiset_a,D: multiset_a] :
( ( trans_a @ A )
=> ( ( irrefl_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( add_mset_a @ B @ C ) @ ( add_mset_a @ B @ D ) ) @ ( mult_a @ A ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ ( mult_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(61,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_115_union__single__eq__member) ).
thf(421,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)],[61]) ).
thf(140,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_20_left_Osimps) ).
thf(770,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)],[140]) ).
thf(25,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_53_ord__eq__le__subst) ).
thf(228,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)],[25]) ).
thf(66,axiom,
! [A: a,B: multiset_a] :
( ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B )
= ( member_a @ A @ ( set_mset_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_single__subset__iff) ).
thf(448,plain,
! [A: a,B: multiset_a] :
( ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B )
= ( member_a @ A @ ( set_mset_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(32,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_148_single__is__union) ).
thf(261,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)],[32]) ).
thf(21,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_121_single__eq__add__mset) ).
thf(216,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)],[21]) ).
thf(7,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( ord_less_eq_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_eq__refl) ).
thf(164,plain,
! [A: a,B: a] :
( ( A = B )
=> ( ord_less_eq_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,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_123_single__eq__single) ).
thf(179,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)],[12]) ).
thf(19,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_122_add__mset__eq__single) ).
thf(211,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)],[19]) ).
thf(76,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Collect__mem__eq) ).
thf(485,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(80,axiom,
! [A: a > a,B: multiset_a,C: a,D: multiset_a] :
( ( ( image_mset_a_a @ A @ B )
= ( add_mset_a @ C @ D ) )
=> ? [E: multiset_a,F: a] :
( ( B
= ( add_mset_a @ F @ E ) )
& ( ( A @ F )
= C )
& ( ( image_mset_a_a @ A @ E )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_msed__map__invR) ).
thf(514,plain,
! [A: a > a,B: multiset_a,C: a,D: multiset_a] :
( ( ( image_mset_a_a @ A @ B )
= ( add_mset_a @ C @ D ) )
=> ? [E: multiset_a,F: a] :
( ( B
= ( add_mset_a @ F @ E ) )
& ( ( A @ F )
= C )
& ( ( image_mset_a_a @ A @ E )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(74,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_subset__iff) ).
thf(480,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(138,axiom,
is_heap_a @ r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I2_J) ).
thf(766,plain,
is_heap_a @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(23,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_in__mono) ).
thf(221,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(63,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_57_ord__le__eq__subst) ).
thf(428,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)],[63]) ).
thf(17,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_subset__eq) ).
thf(206,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(84,axiom,
! [A: a,B: multiset_a,C: a] :
( ( subseteq_mset_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_136_add__mset__subseteq__single__iff) ).
thf(546,plain,
! [A: a,B: multiset_a,C: a] :
( ( subseteq_mset_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)],[84]) ).
thf(53,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_126_multiset__induct2) ).
thf(366,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)],[53]) ).
thf(120,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_6_siftDown_Osimps_I2_J) ).
thf(714,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)],[120]) ).
thf(89,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_113_add__mset__commute) ).
thf(561,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)],[89]) ).
thf(57,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_63_dual__order_Oeq__iff) ).
thf(407,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)],[57]) ).
thf(31,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_93_Greatest__equality) ).
thf(252,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)],[31]) ).
thf(43,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_subsetI) ).
thf(329,plain,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(119,axiom,
! [A: tree_a,B: tree_a,C: a] :
( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v2 )
=> ( ( is_heap_a @ A )
=> ( ( is_heap_a @ B )
=> ( ( ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
= ( t_a @ C @ A @ B ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__C4_Ohyps_C) ).
thf(710,plain,
! [A: tree_a,B: tree_a,C: a] :
( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v2 )
=> ( ( is_heap_a @ A )
=> ( ( is_heap_a @ B )
=> ( ( ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
= ( t_a @ C @ A @ B ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(24,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_138_add__mono__thms__linordered__semiring_I3_J) ).
thf(224,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)],[24]) ).
thf(97,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_I6_J) ).
thf(583,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)],[97]) ).
thf(81,axiom,
! [A: a > a,B: a] :
( ( image_mset_a_a @ A @ ( add_mset_a @ B @ zero_zero_multiset_a ) )
= ( add_mset_a @ ( A @ B ) @ zero_zero_multiset_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_image__mset__single) ).
thf(522,plain,
! [A: a > a,B: a] :
( ( image_mset_a_a @ A @ ( add_mset_a @ B @ zero_zero_multiset_a ) )
= ( add_mset_a @ ( A @ B ) @ zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(131,axiom,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_in__tree_Osimps_I1_J) ).
thf(742,plain,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(100,axiom,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_multiset_Osimps_I1_J) ).
thf(615,plain,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(56,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_128_multiset__nonemptyE) ).
thf(403,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)],[56]) ).
thf(15,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_81_le__cases3) ).
thf(188,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)],[15]) ).
thf(50,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_70_order__trans) ).
thf(356,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)],[50]) ).
thf(77,axiom,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( mult1_a @ C ) )
=> ~ ! [D: a,E: multiset_a] :
( ( B
= ( add_mset_a @ D @ E ) )
=> ! [F: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ E @ F ) )
=> ~ ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ F ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ G @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_mult1E) ).
thf(488,plain,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( mult1_a @ C ) )
=> ~ ! [D: a,E: multiset_a] :
( ( B
= ( add_mset_a @ D @ E ) )
=> ! [F: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ E @ F ) )
=> ~ ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ F ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ G @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(136,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_11_siftDown__Node) ).
thf(753,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)],[136]) ).
thf(103,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_117_heap__top__max) ).
thf(642,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)],[103]) ).
thf(107,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_30_siftDown_Osimps_I4_J) ).
thf(654,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)],[107]) ).
thf(69,axiom,
! [A: multiset_a,B: a,C: multiset_a,D: set_Product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ ( add_mset_a @ B @ C ) ) @ ( mult1_a @ D ) )
=> ( ? [E: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ E @ C ) @ ( mult1_a @ D ) )
& ( A
= ( add_mset_a @ B @ E ) ) )
| ? [E: multiset_a] :
( ! [F: a] :
( ( member_a @ F @ ( set_mset_a @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ F @ B ) @ D ) )
& ( A
= ( plus_plus_multiset_a @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_less__add) ).
thf(457,plain,
! [A: multiset_a,B: a,C: multiset_a,D: set_Product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ ( add_mset_a @ B @ C ) ) @ ( mult1_a @ D ) )
=> ( ? [E: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ E @ C ) @ ( mult1_a @ D ) )
& ( A
= ( add_mset_a @ B @ E ) ) )
| ? [E: multiset_a] :
( ! [F: a] :
( ( member_a @ F @ ( set_mset_a @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ F @ B ) @ D ) )
& ( A
= ( plus_plus_multiset_a @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(92,axiom,
! [A: a] : ( ord_less_eq_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_order__refl) ).
thf(569,plain,
! [A: a] : ( ord_less_eq_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(28,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_mem__Collect__eq) ).
thf(244,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(88,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_89_antisym) ).
thf(558,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)],[88]) ).
thf(141,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_I5_J) ).
thf(773,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)],[141]) ).
thf(108,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_29_siftDown_Osimps_I3_J) ).
thf(662,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)],[108]) ).
thf(47,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_169_add__mset__replicate__mset__safe) ).
thf(343,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)],[47]) ).
thf(26,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_116_insert__noteq__member) ).
thf(237,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)],[26]) ).
thf(39,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_141_add__mono) ).
thf(298,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)],[39]) ).
thf(59,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_66_linorder__wlog) ).
thf(412,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)],[59]) ).
thf(134,axiom,
is_heap_a @ ra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__C4_Oprems_C_I2_J) ).
thf(750,plain,
is_heap_a @ ra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(62,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_135_union__mset__add__mset__right) ).
thf(425,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)],[62]) ).
thf(33,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_76_ord__eq__le__trans) ).
thf(264,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)],[33]) ).
thf(94,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_111_mset__add) ).
thf(573,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)],[94]) ).
thf(128,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_34_right_Osimps) ).
thf(733,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)],[128]) ).
thf(6,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_149_union__is__single) ).
thf(161,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)],[6]) ).
thf(132,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_18_is__heap_Ocases) ).
thf(745,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)],[132]) ).
thf(142,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_I6_J) ).
thf(787,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)],[142]) ).
thf(3,axiom,
! [A: multiset_a,B: multiset_a] :
( ( subseteq_mset_a @ A @ B )
=> ( ord_less_eq_set_a @ ( set_mset_a @ A ) @ ( set_mset_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_set__mset__mono) ).
thf(144,plain,
! [A: multiset_a,B: multiset_a] :
( ( subseteq_mset_a @ A @ B )
=> ( ord_less_eq_set_a @ ( set_mset_a @ A ) @ ( set_mset_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(70,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_142_add__left__mono) ).
thf(466,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)],[70]) ).
thf(49,axiom,
! [A: a > a > $o,B: tree_a] :
( ! [C: a] : ( A @ C @ C )
=> ( rel_Tree_a_a @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Tree_Orel__refl) ).
thf(350,plain,
! [A: a > a > $o,B: tree_a] :
( ! [C: a] : ( A @ C @ C )
=> ( rel_Tree_a_a @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(22,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_130_multi__member__last) ).
thf(219,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)],[22]) ).
thf(60,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_91_eq__iff) ).
thf(419,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)],[60]) ).
thf(129,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_132_multiset_Osimps_I2_J) ).
thf(736,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)],[129]) ).
thf(105,axiom,
( in_tree_a
= ( ^ [A: a,B: tree_a] : ( in_tree_a @ A @ ( heapIm1091024090Down_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_siftDown__in__tree__set) ).
thf(649,plain,
( in_tree_a
= ( ^ [A: a,B: tree_a] : ( in_tree_a @ A @ ( heapIm1091024090Down_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(67,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_114_add__eq__conv__ex) ).
thf(451,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)],[67]) ).
thf(91,axiom,
( ( rel_Tree_a_a @ ( (=) @ a ) )
= ( (=) @ tree_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_Tree_Orel__eq) ).
thf(567,plain,
( ( rel_Tree_a_a @ ( (=) @ a ) )
= ( (=) @ tree_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(35,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_48_order__subst2) ).
thf(271,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)],[35]) ).
thf(18,axiom,
! [A: multiset_a,B: multiset_a,C: a] :
( ( subseteq_mset_a @ A @ B )
=> ( ( member_a @ C @ ( set_mset_a @ A ) )
=> ( member_a @ C @ ( set_mset_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_mset__subset__eqD) ).
thf(208,plain,
! [A: multiset_a,B: multiset_a,C: a] :
( ( subseteq_mset_a @ A @ B )
=> ( ( member_a @ C @ ( set_mset_a @ A ) )
=> ( member_a @ C @ ( set_mset_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(73,axiom,
! [A: a > a,B: a,C: multiset_a] :
( ( image_mset_a_a @ A @ ( add_mset_a @ B @ C ) )
= ( add_mset_a @ ( A @ B ) @ ( image_mset_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_image__mset__add__mset) ).
thf(477,plain,
! [A: a > a,B: a,C: multiset_a] :
( ( image_mset_a_a @ A @ ( add_mset_a @ B @ C ) )
= ( add_mset_a @ ( A @ B ) @ ( image_mset_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(86,axiom,
! [A: multiset_a,B: a > multiset_a,C: a > multiset_a] :
( ! [D: a] :
( ( member_a @ D @ ( set_mset_a @ A ) )
=> ( subseteq_mset_a @ ( B @ D ) @ ( C @ D ) ) )
=> ( subseteq_mset_a @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ B @ A ) ) @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_subset__mset_Osum__mset__mono) ).
thf(552,plain,
! [A: multiset_a,B: a > multiset_a,C: a > multiset_a] :
( ! [D: a] :
( ( member_a @ D @ ( set_mset_a @ A ) )
=> ( subseteq_mset_a @ ( B @ D ) @ ( C @ D ) ) )
=> ( subseteq_mset_a @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ B @ A ) ) @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(125,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_8_siftDown_Ocases) ).
thf(726,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)],[125]) ).
thf(115,axiom,
! [A: a > a > $o,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( rel_Tree_a_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) )
= ( ( A @ B @ E )
& ( rel_Tree_a_a @ A @ C @ F )
& ( rel_Tree_a_a @ A @ D @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Tree_Orel__inject_I2_J) ).
thf(700,plain,
! [A: a > a > $o,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( rel_Tree_a_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) )
= ( ( A @ B @ E )
& ( rel_Tree_a_a @ A @ C @ F )
& ( rel_Tree_a_a @ A @ D @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(112,axiom,
! [A: a > a > $o,B: a,C: tree_a,D: tree_a] :
~ ( rel_Tree_a_a @ A @ e_a @ ( t_a @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_Tree_Orel__distinct_I1_J) ).
thf(695,plain,
! [A: a > a > $o,B: a,C: tree_a,D: tree_a] :
~ ( rel_Tree_a_a @ A @ e_a @ ( t_a @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(27,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_61_dual__order_Oantisym) ).
thf(241,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)],[27]) ).
thf(123,axiom,
! [A: a > a > $o] : ( rel_Tree_a_a @ A @ e_a @ e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_Tree_Octr__transfer_I1_J) ).
thf(722,plain,
! [A: a > a > $o] : ( rel_Tree_a_a @ A @ e_a @ e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(133,axiom,
ord_less_eq_a @ v1 @ v2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_True) ).
thf(749,plain,
ord_less_eq_a @ v1 @ v2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(101,axiom,
! [A: a > a > $o,B: tree_a,C: tree_a] :
( ( rel_Tree_a_a @ A @ B @ C )
=> ( ( ( B = e_a )
=> ( C != e_a ) )
=> ~ ! [D: a,E: tree_a,F: tree_a] :
( ( B
= ( t_a @ D @ E @ F ) )
=> ! [G: a,H: tree_a,I: tree_a] :
( ( C
= ( t_a @ G @ H @ I ) )
=> ( ( A @ D @ G )
=> ( ( rel_Tree_a_a @ A @ E @ H )
=> ~ ( rel_Tree_a_a @ A @ F @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Tree_Orel__cases) ).
thf(617,plain,
! [A: a > a > $o,B: tree_a,C: tree_a] :
( ( rel_Tree_a_a @ A @ B @ C )
=> ( ( ( B = e_a )
=> ( C != e_a ) )
=> ~ ! [D: a,E: tree_a,F: tree_a] :
( ( B
= ( t_a @ D @ E @ F ) )
=> ! [G: a,H: tree_a,I: tree_a] :
( ( C
= ( t_a @ G @ H @ I ) )
=> ( ( A @ D @ G )
=> ( ( rel_Tree_a_a @ A @ E @ H )
=> ~ ( rel_Tree_a_a @ A @ F @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(82,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_118_multiset__induct__max) ).
thf(525,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)],[82]) ).
thf(96,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_72_order__class_Oorder_Oantisym) ).
thf(580,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)],[96]) ).
thf(38,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_143_add__right__mono) ).
thf(295,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)],[38]) ).
thf(117,axiom,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_siftDown_Osimps_I1_J) ).
thf(705,plain,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(118,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_33_is__heap_Osimps_I4_J) ).
thf(707,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)],[118]) ).
thf(130,axiom,
! [A: a > a > $o,B: a,C: a,D: tree_a,E: tree_a,F: tree_a,G: tree_a] :
( ( A @ B @ C )
=> ( ( rel_Tree_a_a @ A @ D @ E )
=> ( ( rel_Tree_a_a @ A @ F @ G )
=> ( rel_Tree_a_a @ A @ ( t_a @ B @ D @ F ) @ ( t_a @ C @ E @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Tree_Orel__intros_I2_J) ).
thf(739,plain,
! [A: a > a > $o,B: a,C: a,D: tree_a,E: tree_a,F: tree_a,G: tree_a] :
( ( A @ B @ C )
=> ( ( rel_Tree_a_a @ A @ D @ E )
=> ( ( rel_Tree_a_a @ A @ F @ G )
=> ( rel_Tree_a_a @ A @ ( t_a @ B @ D @ F ) @ ( t_a @ C @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(58,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_153_multi__member__skip) ).
thf(409,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)],[58]) ).
thf(110,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_13_Tree_Oinject) ).
thf(673,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)],[110]) ).
thf(121,axiom,
! [A: a > a > $o,B: a,C: tree_a,D: tree_a] :
~ ( rel_Tree_a_a @ A @ ( t_a @ B @ C @ D ) @ e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_Tree_Orel__distinct_I2_J) ).
thf(717,plain,
! [A: a > a > $o,B: a,C: tree_a,D: tree_a] :
~ ( rel_Tree_a_a @ A @ ( t_a @ B @ C @ D ) @ e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(46,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_74_ord__le__eq__trans) ).
thf(338,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)],[46]) ).
thf(51,axiom,
! [A: multiset_a,B: a] :
( A
!= ( add_mset_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_multi__self__add__other__not__self) ).
thf(359,plain,
! [A: multiset_a,B: a] :
( A
!= ( add_mset_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(11,axiom,
! [A: a] : ( ord_less_eq_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_dual__order_Orefl) ).
thf(177,plain,
! [A: a] : ( ord_less_eq_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: a > a > $o,B: a > a > $o] :
( ( ord_less_eq_a_a_o @ A @ B )
=> ( ord_le1530450702ee_a_o @ ( rel_Tree_a_a @ A ) @ ( rel_Tree_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Tree_Orel__mono) ).
thf(182,plain,
! [A: a > a > $o,B: a > a > $o] :
( ( ord_less_eq_a_a_o @ A @ B )
=> ( ord_le1530450702ee_a_o @ ( rel_Tree_a_a @ A ) @ ( rel_Tree_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,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_87_linear) ).
thf(336,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)],[45]) ).
thf(116,axiom,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_is__heap_Osimps_I2_J) ).
thf(703,plain,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(99,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_16_Tree_Oinduct) ).
thf(600,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)],[99]) ).
thf(93,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_150_add__mset__add__single) ).
thf(571,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)],[93]) ).
thf(1,conjecture,
is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(143,plain,
~ ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(79,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_119_multiset__induct__min) ).
thf(497,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)],[79]) ).
thf(30,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_84_le__cases) ).
thf(250,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)],[30]) ).
thf(78,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_mset__subset__eq__single) ).
thf(495,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(52,axiom,
! [A: a,B: a] :
( ( A = B )
| ~ ( ord_less_eq_a @ A @ B )
| ~ ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_verit__la__disequality) ).
thf(363,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)],[52]) ).
thf(87,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_78_order__class_Oorder_Oeq__iff) ).
thf(556,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)],[87]) ).
thf(75,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_134_union__mset__add__mset__left) ).
thf(482,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)],[75]) ).
thf(16,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_83_order_Otrans) ).
thf(203,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)],[16]) ).
thf(114,axiom,
is_heap_a @ la,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C4_Oprems_C_I1_J) ).
thf(699,plain,
is_heap_a @ la,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(41,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_95_GreatestI2__order) ).
thf(304,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)],[41]) ).
thf(127,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_21_is__heap__max) ).
thf(731,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)],[127]) ).
thf(85,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_109_add__mset__add__mset__same__iff) ).
thf(549,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)],[85]) ).
thf(20,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_140_add__mono__thms__linordered__semiring_I1_J) ).
thf(214,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)],[20]) ).
thf(37,axiom,
! [A: a > a,B: a,C: multiset_a,D: multiset_a] :
( ( ( image_mset_a_a @ A @ ( add_mset_a @ B @ C ) )
= D )
=> ? [E: multiset_a] :
( ( D
= ( add_mset_a @ ( A @ B ) @ E ) )
& ( ( image_mset_a_a @ A @ C )
= E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_msed__map__invL) ).
thf(287,plain,
! [A: a > a,B: a,C: multiset_a,D: multiset_a] :
( ( ( image_mset_a_a @ A @ ( add_mset_a @ B @ C ) )
= D )
=> ? [E: multiset_a] :
( ( D
= ( add_mset_a @ ( A @ B ) @ E ) )
& ( ( image_mset_a_a @ A @ C )
= E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(8,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_154_multi__member__this) ).
thf(168,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)],[8]) ).
thf(4,axiom,
! [A: set_Product_prod_a_a,B: multiset_a,C: multiset_a] :
( ( trans_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ ( mult_a @ A ) )
=> ? [D: multiset_a,E: multiset_a] :
( ( C
= ( plus_plus_multiset_a @ D @ E ) )
& ? [F: multiset_a] :
( ( B
= ( plus_plus_multiset_a @ D @ F ) )
& ( E != zero_zero_multiset_a )
& ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ F ) )
=> ? [H: a] :
( ( member_a @ H @ ( set_mset_a @ E ) )
& ( member449909584od_a_a @ ( product_Pair_a_a @ G @ H ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_mult__implies__one__step) ).
thf(146,plain,
! [A: set_Product_prod_a_a,B: multiset_a,C: multiset_a] :
( ( trans_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ ( mult_a @ A ) )
=> ? [D: multiset_a,E: multiset_a] :
( ( C
= ( plus_plus_multiset_a @ D @ E ) )
& ? [F: multiset_a] :
( ( B
= ( plus_plus_multiset_a @ D @ F ) )
& ( E != zero_zero_multiset_a )
& ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ F ) )
=> ? [H: a] :
( ( member_a @ H @ ( set_mset_a @ E ) )
& ( member449909584od_a_a @ ( product_Pair_a_a @ G @ H ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(90,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_65_dual__order_Otrans) ).
thf(564,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)],[90]) ).
thf(64,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( subseteq_mset_a @ ( add_mset_a @ A @ B ) @ ( add_mset_a @ A @ C ) )
= ( subseteq_mset_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_mset__subset__eq__add__mset__cancel) ).
thf(437,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( subseteq_mset_a @ ( add_mset_a @ A @ B ) @ ( add_mset_a @ A @ C ) )
= ( subseteq_mset_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(55,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_120_add__mset__eq__singleton__iff) ).
thf(400,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)],[55]) ).
thf(122,axiom,
( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
= ( t_a @ va @ la @ ra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__C4_Oprems_C_I3_J) ).
thf(720,plain,
( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
= ( t_a @ va @ la @ ra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(72,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_subsetD) ).
thf(474,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(139,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_22_val_Osimps) ).
thf(767,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)],[139]) ).
thf(71,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_44_order__subst1) ).
thf(469,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)],[71]) ).
thf(102,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_23_in__tree_Osimps_I2_J) ).
thf(639,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)],[102]) ).
thf(111,axiom,
! [A: a > a > $o,B: tree_a,C: tree_a,D: tree_a > tree_a > $o] :
( ( rel_Tree_a_a @ A @ B @ C )
=> ( ( D @ e_a @ e_a )
=> ( ! [E: a,F: tree_a,G: tree_a,H: a,I: tree_a,J: tree_a] :
( ( A @ E @ H )
=> ( ( D @ F @ I )
=> ( ( D @ G @ J )
=> ( D @ ( t_a @ E @ F @ G ) @ ( t_a @ H @ I @ J ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Tree_Orel__induct) ).
thf(676,plain,
! [A: a > a > $o,B: tree_a,C: tree_a,D: tree_a > tree_a > $o] :
( ( rel_Tree_a_a @ A @ B @ C )
=> ( ( D @ e_a @ e_a )
=> ( ! [E: a,F: tree_a,G: tree_a,H: a,I: tree_a,J: tree_a] :
( ( A @ E @ H )
=> ( ( D @ F @ I )
=> ( ( D @ G @ J )
=> ( D @ ( t_a @ E @ F @ G ) @ ( t_a @ H @ I @ J ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(68,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_165_subset__mset_Osum__mset__0__iff) ).
thf(454,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)],[68]) ).
thf(809,plain,
$false,
inference(e,[status(thm)],[577,645,347,333,170,762,247,440,269,597,730,276,385,698,670,174,301,320,651,724,184,751,542,157,421,770,228,448,261,216,164,179,211,485,514,480,766,221,428,206,546,366,714,561,407,252,329,710,224,583,522,742,615,403,188,356,488,753,642,654,457,569,244,558,773,662,343,237,298,412,750,425,264,573,733,161,745,787,144,466,350,219,419,736,649,451,567,271,208,477,552,726,700,695,241,722,749,617,525,580,295,705,707,739,409,673,717,338,359,177,182,336,703,600,571,143,497,250,495,363,556,482,203,699,304,731,549,214,287,168,146,564,437,400,720,474,767,469,639,676,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP068^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % 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
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 19:46:33 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 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
% 0.40/0.38 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.59 % [INFO] Parsing done (205ms).
% 0.91/0.60 % [INFO] Running in sequential loop mode.
% 1.76/0.89 % [INFO] eprover registered as external prover.
% 1.76/0.90 % [INFO] Scanning for conjecture ...
% 2.04/0.98 % [INFO] Found a conjecture (or negated_conjecture) and 175 axioms. Running axiom selection ...
% 2.31/1.09 % [INFO] Axiom selection finished. Selected 140 axioms (removed 35 axioms).
% 2.84/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 2.84/1.26 % [INFO] Type checking passed.
% 2.84/1.27 % [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 ...
% 10.77/3.26 % External prover 'e' found a proof!
% 10.77/3.26 % [INFO] Killing All external provers ...
% 10.77/3.27 % Time passed: 3082ms (effective reasoning time: 2664ms)
% 10.77/3.27 % 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)>
% 10.77/3.27 % Axioms used in derivation (140): fact_106_Tree_Orel__distinct_I1_J, fact_132_multiset_Osimps_I2_J, fact_29_siftDown_Osimps_I3_J, fact_31_siftDown__in__tree, fact_111_mset__add, fact_143_add__right__mono, fact_89_antisym, fact_116_insert__noteq__member, fact_165_subset__mset_Osum__mset__0__iff, fact_80_antisym__conv, fact_133_single__subset__iff, fact_12__C4_Ohyps_C, fact_44_order__subst1, fact_128_multiset__nonemptyE, fact_171_image__mset__add__mset, fact_10_is__heap_Osimps_I2_J, fact_28_is__heap_Osimps_I6_J, fact_109_add__mset__add__mset__same__iff, fact_14_is__heap_Osimps_I1_J, fact_153_multi__member__skip, fact_78_order__class_Oorder_Oeq__iff, fact_36_order__refl, fact_0__C4_Oprems_C_I2_J, fact_70_order__trans, fact_98_Tree_Orel__induct, fact_160_subsetD, fact_99_Tree_Orel__mono, fact_1__C4_Oprems_C_I1_J, fact_166_mult__cancel__add__mset, fact_86_eq__refl, fact_103_Tree_Orel__intros_I2_J, fact_81_le__cases3, fact_84_le__cases, fact_21_is__heap__max, fact_172_msed__map__invR, fact_152_mset__subset__eq__single, fact_19_siftDown__in__tree__set, fact_101_Tree_Orel__refl, fact_48_order__subst2, fact_138_add__mono__thms__linordered__semiring_I3_J, fact_134_union__mset__add__mset__left, fact_163_one__step__implies__mult, fact_118_multiset__induct__max, fact_4_True, fact_5__C4_Oprems_C_I3_J, fact_15_Tree_Odistinct_I1_J, fact_127_empty__not__add__mset, fact_130_multi__member__last, fact_141_add__mono, fact_57_ord__le__eq__subst, fact_173_msed__map__invL, fact_87_linear, fact_8_siftDown_Ocases, fact_7_siftDown_Osimps_I1_J, fact_147_set__mset__mono, fact_22_val_Osimps, fact_11_siftDown__Node, fact_161_subset__eq, fact_102_Tree_Orel__inject_I2_J, fact_154_multi__member__this, fact_105_Tree_Orel__distinct_I2_J, fact_159_in__mono, fact_150_add__mset__add__single, fact_120_add__mset__eq__singleton__iff, fact_126_multiset__induct2, fact_61_dual__order_Oantisym, fact_142_add__left__mono, fact_129_multi__nonempty__split, fact_131_multiset_Osimps_I1_J, fact_27_is__heap_Osimps_I5_J, fact_108_heap__top__geq, fact_135_union__mset__add__mset__right, fact_76_ord__eq__le__trans, fact_148_single__is__union, fact_33_is__heap_Osimps_I4_J, fact_107_Tree_Orel__cases, fact_63_dual__order_Oeq__iff, fact_49_verit__la__disequality, fact_112_multi__member__split, fact_65_dual__order_Otrans, fact_95_GreatestI2__order, fact_25_siftDown_Osimps_I6_J, fact_24_siftDown_Osimps_I5_J, fact_151_multi__subset__induct, fact_91_eq__iff, fact_104_Tree_Octr__transfer_I1_J, fact_2_assms_I2_J, fact_149_union__is__single, fact_26_in__tree_Osimps_I1_J, fact_124_multiset__cases, fact_32_is__heap_Osimps_I3_J, fact_164_mult__implies__one__step, fact_9_assms_I3_J, fact_121_single__eq__add__mset, fact_20_left_Osimps, fact_110_multi__self__add__other__not__self, fact_59_Collect__mem__eq, fact_174_image__mset__single, fact_145_mset__subset__eqD, fact_13_Tree_Oinject, fact_157_less__add, fact_68_dual__order_Orefl, fact_3_assms_I1_J, fact_100_Tree_Orel__eq, fact_23_in__tree_Osimps_I2_J, fact_114_add__eq__conv__ex, fact_140_add__mono__thms__linordered__semiring_I1_J, fact_170_subset__mset_Osum__mset__mono, fact_30_siftDown_Osimps_I4_J, fact_155_mult1E, fact_119_multiset__induct__min, fact_169_add__mset__replicate__mset__safe, fact_16_Tree_Oinduct, fact_53_ord__eq__le__subst, fact_72_order__class_Oorder_Oantisym, fact_139_add__mono__thms__linordered__semiring_I2_J, fact_6_siftDown_Osimps_I2_J, fact_17_Tree_Oexhaust, fact_167_in__mset__fold__plus__iff, fact_156_mult1I, fact_66_linorder__wlog, fact_83_order_Otrans, fact_74_ord__le__eq__trans, fact_158_subsetI, fact_117_heap__top__max, fact_115_union__single__eq__member, fact_125_multiset__induct, fact_146_mset__subset__eq__add__mset__cancel, fact_123_single__eq__single, fact_136_add__mset__subseteq__single__iff, fact_93_Greatest__equality, fact_113_add__mset__commute, fact_122_add__mset__eq__single, fact_144_union__iff, fact_168_union__fold__mset__add__mset, fact_162_subset__iff, fact_18_is__heap_Ocases, fact_34_right_Osimps, fact_137_verit__sum__simplify, fact_58_mem__Collect__eq
% 10.77/3.27 % No. of inferences in proof: 284
% 10.77/3.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3082 ms resp. 2664 ms w/o parsing
% 11.82/3.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.82/3.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------