%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP068^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:17 AM UTC 2026
% Result : Theorem 7.73s 2.35s
% Output : Refutation 7.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 27 unt; 0 typ; 6 def)
% Number of atoms : 255 ( 83 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 783 ( 59 ~; 50 |; 12 &; 647 @)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 120 ( 117 usr; 21 con; 0-3 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
multiset_a: $tType ).
thf(type_def_7,type,
tree_a: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(type_def_9,type,
set_a: $tType ).
thf(type_def_10,type,
multiset_multiset_a: $tType ).
thf(type_def_11,type,
set_Product_prod_a_a: $tType ).
thf(type_def_12,type,
set_Pr158363655iset_a: $tType ).
thf(type_def_13,type,
set_multiset_a: $tType ).
thf(type_def_14,type,
produc1127127335iset_a: $tType ).
thf(type_def_15,type,
product_prod_a_a: $tType ).
thf(func_def_0,type,
set_Pr158363655iset_a: $tType ).
thf(func_def_1,type,
produc1127127335iset_a: $tType ).
thf(func_def_2,type,
set_Product_prod_a_a: $tType ).
thf(func_def_3,type,
multiset_multiset_a: $tType ).
thf(func_def_4,type,
set_multiset_a: $tType ).
thf(func_def_5,type,
product_prod_a_a: $tType ).
thf(func_def_6,type,
multiset_a: $tType ).
thf(func_def_7,type,
tree_a: $tType ).
thf(func_def_8,type,
set_a: $tType ).
thf(func_def_9,type,
a: $tType ).
thf(func_def_10,type,
plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
thf(func_def_11,type,
zero_zero_multiset_a: multiset_a ).
thf(func_def_12,type,
nO_MAT1617603563iset_a: multiset_a > multiset_a > $o ).
thf(func_def_13,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(func_def_14,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(func_def_15,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(func_def_16,type,
e_a: tree_a ).
thf(func_def_17,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(func_def_18,type,
rel_Tree_a_a: ( a > a > $o ) > tree_a > tree_a > $o ).
thf(func_def_19,type,
in_tree_a: a > tree_a > $o ).
thf(func_def_20,type,
is_heap_a: tree_a > $o ).
thf(func_def_21,type,
multiset_a2: tree_a > multiset_a ).
thf(func_def_22,type,
val_a: tree_a > a ).
thf(func_def_23,type,
lattic146396397_Max_a: set_a > a ).
thf(func_def_24,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(func_def_25,type,
comm_m315775925iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
thf(func_def_26,type,
fold_m382157835iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
thf(func_def_27,type,
fold_m364285649iset_a: ( a > multiset_a > multiset_a ) > multiset_a > multiset_a > multiset_a ).
thf(func_def_28,type,
image_929116801iset_a: ( a > multiset_a ) > multiset_a > multiset_multiset_a ).
thf(func_def_29,type,
image_mset_a_a: ( a > a ) > multiset_a > multiset_a ).
thf(func_def_30,type,
mult1_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
thf(func_def_31,type,
mult_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
thf(func_def_32,type,
set_mset_multiset_a: multiset_multiset_a > set_multiset_a ).
thf(func_def_33,type,
set_mset_a: multiset_a > set_a ).
thf(func_def_34,type,
subseteq_mset_a: multiset_a > multiset_a > $o ).
thf(func_def_35,type,
ord_less_eq_o_o_a: ( $o > $o > a ) > ( $o > $o > a ) > $o ).
thf(func_def_36,type,
ord_less_eq_o_a: ( $o > a ) > ( $o > a ) > $o ).
thf(func_def_37,type,
ord_le1530450702ee_a_o: ( tree_a > tree_a > $o ) > ( tree_a > tree_a > $o ) > $o ).
thf(func_def_38,type,
ord_less_eq_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(func_def_39,type,
ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
thf(func_def_40,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_41,type,
ord_less_eq_a: a > a > $o ).
thf(func_def_42,type,
order_Greatest_o_a: ( ( $o > a ) > $o ) > $o > a ).
thf(func_def_43,type,
order_Greatest_a: ( a > $o ) > a ).
thf(func_def_44,type,
produc2037245207iset_a: multiset_a > multiset_a > produc1127127335iset_a ).
thf(func_def_45,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(func_def_46,type,
irrefl_a: set_Product_prod_a_a > $o ).
thf(func_def_47,type,
trans_a: set_Product_prod_a_a > $o ).
thf(func_def_48,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_49,type,
member_multiset_a: multiset_a > set_multiset_a > $o ).
thf(func_def_50,type,
member340150864iset_a: produc1127127335iset_a > set_Pr158363655iset_a > $o ).
thf(func_def_51,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_52,type,
member_a: a > set_a > $o ).
thf(func_def_53,type,
l: tree_a ).
thf(func_def_54,type,
l1: tree_a ).
thf(func_def_55,type,
la: tree_a ).
thf(func_def_56,type,
r: tree_a ).
thf(func_def_57,type,
r1: tree_a ).
thf(func_def_58,type,
ra: tree_a ).
thf(func_def_59,type,
t: tree_a ).
thf(func_def_60,type,
v: a ).
thf(func_def_61,type,
v1: a ).
thf(func_def_62,type,
v2: a ).
thf(func_def_63,type,
va: a ).
thf(func_def_75,type,
sP0: a > a > a > $o ).
thf(func_def_76,type,
sP1: a > a > a > $o ).
thf(func_def_77,type,
sP2: a > a > a > $o ).
thf(func_def_78,type,
sK3: ( a > a > $o ) > a ).
thf(func_def_79,type,
sK4: ( a > a > $o ) > a ).
thf(func_def_80,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_81,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_82,type,
sK7: tree_a > tree_a ).
thf(func_def_83,type,
sK8: tree_a > tree_a ).
thf(func_def_84,type,
sK9: tree_a > a ).
thf(func_def_85,type,
sK10: tree_a > a ).
thf(func_def_86,type,
sK11: tree_a > a ).
thf(func_def_87,type,
sK12: tree_a > a ).
thf(func_def_88,type,
sK13: tree_a > tree_a ).
thf(func_def_89,type,
sK14: tree_a > tree_a ).
thf(func_def_90,type,
sK15: tree_a > tree_a ).
thf(func_def_91,type,
sK16: tree_a > tree_a ).
thf(func_def_92,type,
sK17: tree_a > a ).
thf(func_def_93,type,
sK18: tree_a > a ).
thf(func_def_94,type,
sK19: tree_a > tree_a ).
thf(func_def_95,type,
sK20: tree_a > a ).
thf(func_def_96,type,
sK21: tree_a > tree_a ).
thf(func_def_97,type,
sK22: tree_a > tree_a ).
thf(func_def_98,type,
sK23: tree_a > a ).
thf(func_def_99,type,
sK24: tree_a > a ).
thf(func_def_100,type,
sK25: tree_a > tree_a ).
thf(func_def_101,type,
sK26: ( tree_a > $o ) > a ).
thf(func_def_102,type,
sK27: ( tree_a > $o ) > tree_a ).
thf(func_def_103,type,
sK28: ( tree_a > $o ) > tree_a ).
thf(func_def_104,type,
sK29: tree_a > a > tree_a ).
thf(func_def_105,type,
sK30: tree_a > a > tree_a ).
thf(func_def_106,type,
sK31: tree_a > a > a ).
thf(func_def_107,type,
sK32: ( a > a ) > a ).
thf(func_def_108,type,
sK33: ( a > a ) > a ).
thf(func_def_109,type,
sK34: ( a > a ) > a ).
thf(func_def_110,type,
sK35: ( a > a ) > a ).
thf(func_def_111,type,
sK36: ( a > a ) > a ).
thf(func_def_112,type,
sK37: ( a > a ) > a ).
thf(func_def_113,type,
sK38: tree_a > a ).
thf(func_def_114,type,
sK39: tree_a > tree_a ).
thf(func_def_115,type,
sK40: tree_a > a ).
thf(func_def_116,type,
sK41: tree_a > tree_a ).
thf(func_def_117,type,
sK42: tree_a > tree_a ).
thf(func_def_118,type,
sK43: tree_a > a ).
thf(func_def_119,type,
sK44: tree_a > tree_a ).
thf(func_def_120,type,
sK45: tree_a > tree_a ).
thf(func_def_121,type,
sK46: tree_a > a ).
thf(func_def_122,type,
sK47: tree_a > a ).
thf(func_def_123,type,
sK48: tree_a > tree_a ).
thf(func_def_124,type,
sK49: tree_a > a ).
thf(func_def_125,type,
sK50: tree_a > tree_a ).
thf(func_def_126,type,
sK51: tree_a > a ).
thf(func_def_127,type,
sK52: tree_a > tree_a ).
thf(func_def_128,type,
sK53: tree_a > a ).
thf(func_def_129,type,
sK54: ( a > a ) > a ).
thf(func_def_130,type,
sK55: ( a > a ) > a ).
thf(func_def_133,type,
ph57:
!>[X0: $tType] : X0 ).
thf(f1538,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f704,f719,f736,f741,f1031,f1496,f1531]) ).
thf(f1531,plain,
( ~ spl56_48
| ~ spl56_1
| spl56_8
| ~ spl56_9 ),
inference(avatar_split_clause,[status(thm)],[f1530,f738,f733,f701,f1488]) ).
thf(f1488,definition,
( spl56_48
<=> ( $true
= ( is_heap_a @ ( t_a @ va @ la @ ra ) ) ) ),
introduced(definition,[new_symbols(naming,[spl56_48])],[avatar_definition]) ).
thf(f701,definition,
( spl56_1
<=> ( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
= ( t_a @ va @ la @ ra ) ) ),
introduced(definition,[new_symbols(naming,[spl56_1])],[avatar_definition]) ).
thf(f733,definition,
( spl56_8
<=> ( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl56_8])],[avatar_definition]) ).
thf(f738,definition,
( spl56_9
<=> ( ( ord_less_eq_a @ v1 @ v2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl56_9])],[avatar_definition]) ).
thf(f1530,plain,
( ( $true
!= ( is_heap_a @ ( t_a @ va @ la @ ra ) ) )
| ~ spl56_1
| spl56_8
| ~ spl56_9 ),
inference(forward_demodulation,[status(thm)],[f1529,f703]) ).
thf(f703,plain,
( ( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
= ( t_a @ va @ la @ ra ) )
| ~ spl56_1 ),
inference(avatar_component_clause,[status(thm)],[f701]) ).
thf(f1529,plain,
( ( $true
!= ( is_heap_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
| spl56_8
| ~ spl56_9 ),
inference(subsumption_resolution,[status(thm)],[f1528,f740]) ).
thf(f740,plain,
( ( ( ord_less_eq_a @ v1 @ v2 )
= $true )
| ~ spl56_9 ),
inference(avatar_component_clause,[status(thm)],[f738]) ).
thf(f1528,plain,
( ( $true
!= ( is_heap_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
| ( ( ord_less_eq_a @ v1 @ v2 )
!= $true )
| spl56_8 ),
inference(superposition,[status(thm)],[f735,f1523]) ).
thf(f1523,plain,
! [X2: tree_a,X3: a,X0: tree_a,X1: a] :
( ( ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) )
= ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) )
| ( ( ord_less_eq_a @ X3 @ X1 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f601,f607]) ).
thf(f607,plain,
! [X2: tree_a,X0: tree_a,X1: a] :
( ( val_a @ ( t_a @ X1 @ X2 @ X0 ) )
= X1 ),
inference(cnf_transformation,[status(thm)],[f488]) ).
thf(f488,plain,
! [X0: tree_a,X1: a,X2: tree_a] :
( ( val_a @ ( t_a @ X1 @ X2 @ X0 ) )
= X1 ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,axiom,
! [X33: tree_a,X0: a,X32: tree_a] :
( ( val_a @ ( t_a @ X0 @ X32 @ X33 ) )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_22_val_Osimps) ).
thf(f601,plain,
! [X2: tree_a,X3: a,X0: tree_a,X1: a] :
( ( ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) )
= ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f527]) ).
thf(f527,plain,
! [X0: tree_a,X1: a,X2: tree_a,X3: a] :
( ( ( ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) )
= ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ X1 )
!= $true ) )
& ( ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) ) )
= ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f484]) ).
thf(f484,plain,
! [X0: tree_a,X1: a,X2: tree_a,X3: a] :
( ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ X1 )
= $true )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) )
= ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) )
& ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ X1 )
!= $true )
=> ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) ) )
= ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f312]) ).
thf(f312,plain,
! [X0: tree_a,X1: a,X2: tree_a,X3: a] :
( ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ X1 )
= $true )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) )
= ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) )
& ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ X1 )
!= $true )
=> ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) ) )
= ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f311]) ).
thf(f311,plain,
! [X0: tree_a,X1: a,X2: tree_a,X3: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ X1 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) )
= ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ X1 )
=> ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) ) )
= ( heapIm1091024090Down_a @ ( t_a @ X1 @ e_a @ ( t_a @ X3 @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,axiom,
! [X39: tree_a,X0: a,X40: tree_a,X38: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X38 @ X39 @ X40 ) ) @ X0 )
=> ( ( t_a @ X0 @ e_a @ ( t_a @ X38 @ X39 @ X40 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X0 @ e_a @ ( t_a @ X38 @ X39 @ X40 ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X38 @ X39 @ X40 ) ) @ X0 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X0 @ e_a @ ( t_a @ X38 @ X39 @ X40 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X38 @ X39 @ X40 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ X0 @ ( heapIm1140443833left_a @ ( t_a @ X38 @ X39 @ X40 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X38 @ X39 @ X40 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_30_siftDown_Osimps_I4_J) ).
thf(f735,plain,
( ( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
!= $true )
| spl56_8 ),
inference(avatar_component_clause,[status(thm)],[f733]) ).
thf(f1496,plain,
( spl56_48
| ~ spl56_1
| ~ spl56_4
| ~ spl56_9
| ~ spl56_18 ),
inference(avatar_split_clause,[status(thm)],[f1495,f1028,f738,f716,f701,f1488]) ).
thf(f716,definition,
( spl56_4
<=> ( ( is_heap_a @ ra )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl56_4])],[avatar_definition]) ).
thf(f1028,definition,
( spl56_18
<=> ( ra
= ( t_a @ v1 @ l1 @ r1 ) ) ),
introduced(definition,[new_symbols(naming,[spl56_18])],[avatar_definition]) ).
thf(f1495,plain,
( ( $true
= ( is_heap_a @ ( t_a @ va @ la @ ra ) ) )
| ~ spl56_1
| ~ spl56_4
| ~ spl56_9
| ~ spl56_18 ),
inference(subsumption_resolution,[status(thm)],[f1494,f718]) ).
thf(f718,plain,
( ( ( is_heap_a @ ra )
= $true )
| ~ spl56_4 ),
inference(avatar_component_clause,[status(thm)],[f716]) ).
thf(f1494,plain,
( ( $true
= ( is_heap_a @ ( t_a @ va @ la @ ra ) ) )
| ( ( is_heap_a @ ra )
!= $true )
| ~ spl56_1
| ~ spl56_9
| ~ spl56_18 ),
inference(forward_demodulation,[status(thm)],[f1493,f1030]) ).
thf(f1030,plain,
( ( ra
= ( t_a @ v1 @ l1 @ r1 ) )
| ~ spl56_18 ),
inference(avatar_component_clause,[status(thm)],[f1028]) ).
thf(f1493,plain,
( ( $true
= ( is_heap_a @ ( t_a @ va @ la @ ra ) ) )
| ( $true
!= ( is_heap_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
| ~ spl56_1
| ~ spl56_9 ),
inference(subsumption_resolution,[status(thm)],[f1481,f740]) ).
thf(f1481,plain,
( ( $true
= ( is_heap_a @ ( t_a @ va @ la @ ra ) ) )
| ( ( ord_less_eq_a @ v1 @ v2 )
!= $true )
| ( $true
!= ( is_heap_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
| ~ spl56_1 ),
inference(superposition,[status(thm)],[f1477,f703]) ).
thf(f1477,plain,
! [X2: tree_a,X3: a,X0: tree_a,X1: a] :
( ( ( is_heap_a @ ( t_a @ X3 @ e_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
= $true )
| ( $true
!= ( is_heap_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
| ( ( ord_less_eq_a @ X1 @ X3 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f651,f607]) ).
thf(f651,plain,
! [X2: tree_a,X3: a,X0: tree_a,X1: a] :
( ( $true
!= ( is_heap_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
| ( ( is_heap_a @ ( t_a @ X3 @ e_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
= $true )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X1 @ X2 @ X0 ) ) @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f574]) ).
thf(f574,plain,
! [X0: tree_a,X1: a,X2: tree_a,X3: a] :
( ( ( ( is_heap_a @ ( t_a @ X3 @ e_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
= $true )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X1 @ X2 @ X0 ) ) @ X3 ) )
| ( $true
!= ( is_heap_a @ ( t_a @ X1 @ X2 @ X0 ) ) ) )
& ( ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X1 @ X2 @ X0 ) ) @ X3 ) )
& ( $true
= ( is_heap_a @ ( t_a @ X1 @ X2 @ X0 ) ) ) )
| ( ( is_heap_a @ ( t_a @ X3 @ e_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f573]) ).
thf(f573,plain,
! [X0: tree_a,X1: a,X2: tree_a,X3: a] :
( ( ( ( is_heap_a @ ( t_a @ X3 @ e_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
= $true )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X1 @ X2 @ X0 ) ) @ X3 ) )
| ( $true
!= ( is_heap_a @ ( t_a @ X1 @ X2 @ X0 ) ) ) )
& ( ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X1 @ X2 @ X0 ) ) @ X3 ) )
& ( $true
= ( is_heap_a @ ( t_a @ X1 @ X2 @ X0 ) ) ) )
| ( ( is_heap_a @ ( t_a @ X3 @ e_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f342]) ).
thf(f342,plain,
! [X0: tree_a,X1: a,X2: tree_a,X3: a] :
( ( ( is_heap_a @ ( t_a @ X3 @ e_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
= $true )
<=> ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X1 @ X2 @ X0 ) ) @ X3 ) )
& ( $true
= ( is_heap_a @ ( t_a @ X1 @ X2 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f341]) ).
thf(f341,plain,
! [X0: tree_a,X1: a,X2: tree_a,X3: a] :
( ( ( is_heap_a @ ( t_a @ X3 @ e_a @ ( t_a @ X1 @ X2 @ X0 ) ) )
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X1 @ X2 @ X0 ) ) @ X3 ) )
& ( is_heap_a @ ( t_a @ X1 @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,axiom,
! [X40: tree_a,X38: a,X39: tree_a,X0: a] :
( ( ( is_heap_a @ ( t_a @ X0 @ e_a @ ( t_a @ X38 @ X39 @ X40 ) ) )
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X38 @ X39 @ X40 ) ) @ X0 ) )
& ( is_heap_a @ ( t_a @ X38 @ X39 @ X40 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_32_is__heap_Osimps_I3_J) ).
thf(f1031,plain,
( spl56_18
| ~ spl56_1 ),
inference(avatar_split_clause,[status(thm)],[f1026,f701,f1028]) ).
thf(f1026,plain,
( ( ra
= ( t_a @ v1 @ l1 @ r1 ) )
| ~ spl56_1 ),
inference(forward_demodulation,[status(thm)],[f1011,f622]) ).
thf(f622,plain,
! [X2: tree_a,X0: a,X1: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X0 @ X2 @ X1 ) )
= X1 ),
inference(cnf_transformation,[status(thm)],[f487]) ).
thf(f487,plain,
! [X0: a,X1: tree_a,X2: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X0 @ X2 @ X1 ) )
= X1 ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,axiom,
! [X0: a,X11: tree_a,X10: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X0 @ X10 @ X11 ) )
= X11 ),
file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_34_right_Osimps) ).
thf(f1011,plain,
( ( ( t_a @ v1 @ l1 @ r1 )
= ( heapIm1257206334ight_a @ ( t_a @ va @ la @ ra ) ) )
| ~ spl56_1 ),
inference(superposition,[status(thm)],[f622,f703]) ).
thf(f741,plain,
spl56_9,
inference(avatar_split_clause,[status(thm)],[f680,f738]) ).
thf(f680,plain,
( ( ord_less_eq_a @ v1 @ v2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f276]) ).
thf(f276,plain,
( ( ord_less_eq_a @ v1 @ v2 )
= $true ),
inference(fool_elimination,[status(thm)],[f275]) ).
thf(f275,plain,
ord_less_eq_a @ v1 @ v2,
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
ord_less_eq_a @ v1 @ v2,
file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_4_True) ).
thf(f736,plain,
~ spl56_8,
inference(avatar_split_clause,[status(thm)],[f638,f733]) ).
thf(f638,plain,
( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f473]) ).
thf(f473,plain,
( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f256]) ).
thf(f256,plain,
( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f255]) ).
thf(f255,plain,
~ ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
inference(rectify,[status(thm)],[f177]) ).
thf(f177,negated_conjecture,
~ ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f176]) ).
thf(f176,conjecture,
is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',conj_0) ).
thf(f719,plain,
spl56_4,
inference(avatar_split_clause,[status(thm)],[f602,f716]) ).
thf(f602,plain,
( ( is_heap_a @ ra )
= $true ),
inference(cnf_transformation,[status(thm)],[f348]) ).
thf(f348,plain,
( ( is_heap_a @ ra )
= $true ),
inference(fool_elimination,[status(thm)],[f347]) ).
thf(f347,plain,
is_heap_a @ ra,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
is_heap_a @ ra,
file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_0__C4_Oprems_C_I2_J) ).
thf(f704,plain,
spl56_1,
inference(avatar_split_clause,[status(thm)],[f593,f701]) ).
thf(f593,plain,
( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
= ( t_a @ va @ la @ ra ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
= ( t_a @ va @ la @ ra ) ),
file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_5__C4_Oprems_C_I3_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP068^1 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:25:39 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP068^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer HeapImperative problem prob_383__5342344_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : HeapImperative/prob_383__5342344_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 240 ( 77 unt; 64 typ; 0 def)
% 0.30/0.46 % Number of atoms : 543 ( 193 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 12 ( 3 avg)
% 0.30/0.46 % Number of connectives : 2155 ( 59 ~; 11 |; 53 &;1759 @)
% 0.30/0.46 % ( 0 <=>; 273 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 22 ( 8 avg)
% 0.30/0.46 % Number of types : 11 ( 10 usr)
% 0.30/0.46 % Number of type conns : 278 ( 278 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 57 ( 54 usr; 15 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 630 ( 43 ^; 569 !; 18 ?; 630 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:28.993
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (10)
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_Itf__a_J_Mt__Multiset__Omultiset_Itf__a_J_J_J,type,
% 0.30/0.46 set_Pr158363655iset_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Multiset__Omultiset_Itf__a_J_Mt__Multiset__Omultiset_Itf__a_J_J,type,
% 0.30/0.46 produc1127127335iset_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.30/0.46 set_Product_prod_a_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Multiset__Omultiset_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.30/0.46 multiset_multiset_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.30/0.46 set_multiset_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.30/0.46 product_prod_a_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 multiset_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Heap__OTree_Itf__a_J,type,
% 0.30/0.46 tree_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 set_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (54)
% 0.30/0.46 thf(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 zero_zero_multiset_a: multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_HOL_ONO__MATCH_001t__Multiset__Omultiset_Itf__a_J_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 nO_MAT1617603563iset_a: multiset_a > multiset_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oleft_001tf__a,type,
% 0.30/0.46 heapIm1140443833left_a: tree_a > tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oright_001tf__a,type,
% 0.30/0.46 heapIm1257206334ight_a: tree_a > tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_OsiftDown_001tf__a,type,
% 0.30/0.46 heapIm1091024090Down_a: tree_a > tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OTree_OE_001tf__a,type,
% 0.30/0.46 e_a: tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OTree_OT_001tf__a,type,
% 0.30/0.46 t_a: a > tree_a > tree_a > tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_OTree_Orel__Tree_001tf__a_001tf__a,type,
% 0.30/0.46 rel_Tree_a_a: ( a > a > $o ) > tree_a > tree_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_Oin__tree_001tf__a,type,
% 0.30/0.46 in_tree_a: a > tree_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_Ois__heap_001tf__a,type,
% 0.30/0.46 is_heap_a: tree_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_Omultiset_001tf__a,type,
% 0.30/0.46 multiset_a2: tree_a > multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Heap_Oval_001tf__a,type,
% 0.30/0.46 val_a: tree_a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001tf__a,type,
% 0.30/0.46 lattic146396397_Max_a: set_a > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Oadd__mset_001tf__a,type,
% 0.30/0.46 add_mset_a: a > multiset_a > multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Ocomm__monoid__add_Osum__mset_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 comm_m315775925iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Ofold__mset_001t__Multiset__Omultiset_Itf__a_J_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 fold_m382157835iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Ofold__mset_001tf__a_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 fold_m364285649iset_a: ( a > multiset_a > multiset_a ) > multiset_a > multiset_a > multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Oimage__mset_001tf__a_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 image_929116801iset_a: ( a > multiset_a ) > multiset_a > multiset_multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Oimage__mset_001tf__a_001tf__a,type,
% 0.30/0.46 image_mset_a_a: ( a > a ) > multiset_a > multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Omult1_001tf__a,type,
% 0.30/0.46 mult1_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Omult_001tf__a,type,
% 0.30/0.46 mult_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Oset__mset_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 set_mset_multiset_a: multiset_multiset_a > set_multiset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Oset__mset_001tf__a,type,
% 0.30/0.46 set_mset_a: multiset_a > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Multiset_Osubseteq__mset_001tf__a,type,
% 0.30/0.46 subseteq_mset_a: multiset_a > multiset_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mtf__a_J_J,type,
% 0.30/0.46 ord_less_eq_o_o_a: ( $o > $o > a ) > ( $o > $o > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mtf__a_J,type,
% 0.30/0.46 ord_less_eq_o_a: ( $o > a ) > ( $o > a ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Heap__OTree_Itf__a_J_M_062_It__Heap__OTree_Itf__a_J_M_Eo_J_J,type,
% 0.30/0.46 ord_le1530450702ee_a_o: ( tree_a > tree_a > $o ) > ( tree_a > tree_a > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 0.30/0.46 ord_less_eq_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__a,type,
% 0.30/0.46 ord_less_eq_a: a > a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mtf__a_J,type,
% 0.30/0.46 order_Greatest_o_a: ( ( $o > a ) > $o ) > $o > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oorder__class_OGreatest_001tf__a,type,
% 0.30/0.46 order_Greatest_a: ( a > $o ) > a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Multiset__Omultiset_Itf__a_J_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 produc2037245207iset_a: multiset_a > multiset_a > produc1127127335iset_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001tf__a_001tf__a,type,
% 0.30/0.46 product_Pair_a_a: a > a > product_prod_a_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_Oirrefl_001tf__a,type,
% 0.30/0.46 irrefl_a: set_Product_prod_a_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_Otrans_001tf__a,type,
% 0.30/0.46 trans_a: set_Product_prod_a_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.30/0.46 collect_a: ( a > $o ) > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.30/0.46 member_multiset_a: multiset_a > set_multiset_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Multiset__Omultiset_Itf__a_J_Mt__Multiset__Omultiset_Itf__a_J_J,type,
% 0.30/0.46 member340150864iset_a: produc1127127335iset_a > set_Pr158363655iset_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.30/0.46 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001tf__a,type,
% 0.30/0.46 member_a: a > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_l,type,
% 0.30/0.46 l: tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_l1____,type,
% 0.30/0.46 l1: tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_la____,type,
% 0.30/0.46 la: tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_r,type,
% 0.30/0.46 r: tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_r1____,type,
% 0.30/0.46 r1: tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_ra____,type,
% 0.30/0.46 ra: tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_t,type,
% 0.30/0.46 t: tree_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_v,type,
% 0.30/0.46 v: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_v1____,type,
% 0.30/0.46 v1: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_v2____,type,
% 0.30/0.46 v2: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_va____,type,
% 0.30/0.46 va: a ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (175)
% 0.30/0.46 thf(fact_0__C4_Oprems_C_I2_J,axiom,
% 0.30/0.46 is_heap_a @ ra ).
% 0.30/0.46
% 0.30/0.46 % "4.prems"(2)
% 0.30/0.46 thf(fact_1__C4_Oprems_C_I1_J,axiom,
% 0.30/0.46 is_heap_a @ la ).
% 0.30/0.46
% 0.30/0.46 % "4.prems"(1)
% 0.30/0.46 thf(fact_2_assms_I2_J,axiom,
% 0.30/0.46 is_heap_a @ r ).
% 0.30/0.46
% 0.30/0.46 % assms(2)
% 0.30/0.46 thf(fact_3_assms_I1_J,axiom,
% 0.30/0.46 is_heap_a @ l ).
% 0.30/0.46
% 0.30/0.46 % assms(1)
% 0.30/0.46 thf(fact_4_True,axiom,
% 0.30/0.46 ord_less_eq_a @ v1 @ v2 ).
% 0.30/0.46
% 0.30/0.46 % True
% 0.30/0.46 thf(fact_5__C4_Oprems_C_I3_J,axiom,
% 0.30/0.46 ( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
% 0.30/0.46 = ( t_a @ va @ la @ ra ) ) ).
% 0.30/0.46
% 0.30/0.46 % "4.prems"(3)
% 0.30/0.46 thf(fact_6_siftDown_Osimps_I2_J,axiom,
% 0.30/0.46 ! [V: a] :
% 0.30/0.46 ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ e_a ) )
% 0.30/0.46 = ( t_a @ V @ e_a @ e_a ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(2)
% 0.30/0.46 thf(fact_7_siftDown_Osimps_I1_J,axiom,
% 0.30/0.46 ( ( heapIm1091024090Down_a @ e_a )
% 0.30/0.46 = e_a ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(1)
% 0.30/0.46 thf(fact_8_siftDown_Ocases,axiom,
% 0.30/0.46 ! [X: tree_a] :
% 0.30/0.46 ( ( X != e_a )
% 0.30/0.46 => ( ! [V2: a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t_a @ V2 @ e_a @ e_a ) )
% 0.30/0.46 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.30/0.46 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t_a @ V2 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.30/0.46 => ~ ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.cases
% 0.30/0.46 thf(fact_9_assms_I3_J,axiom,
% 0.30/0.46 ( t
% 0.30/0.46 = ( t_a @ v @ l @ r ) ) ).
% 0.30/0.46
% 0.30/0.46 % assms(3)
% 0.30/0.46 thf(fact_10_is__heap_Osimps_I2_J,axiom,
% 0.30/0.46 ! [V: a] : ( is_heap_a @ ( t_a @ V @ e_a @ e_a ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(2)
% 0.30/0.46 thf(fact_11_siftDown__Node,axiom,
% 0.30/0.46 ! [T: tree_a,V: a,L: tree_a,R: tree_a] :
% 0.30/0.46 ( ( T
% 0.30/0.46 = ( t_a @ V @ L @ R ) )
% 0.30/0.46 => ? [L2: tree_a,V3: a,R2: tree_a] :
% 0.30/0.46 ( ( ( heapIm1091024090Down_a @ T )
% 0.30/0.46 = ( t_a @ V3 @ L2 @ R2 ) )
% 0.30/0.46 & ( ord_less_eq_a @ V @ V3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown_Node
% 0.30/0.46 thf(fact_12__C4_Ohyps_C,axiom,
% 0.30/0.46 ! [L: tree_a,R: tree_a,V: a] :
% 0.30/0.46 ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v2 )
% 0.30/0.46 => ( ( is_heap_a @ L )
% 0.30/0.46 => ( ( is_heap_a @ R )
% 0.30/0.46 => ( ( ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
% 0.30/0.46 = ( t_a @ V @ L @ R ) )
% 0.30/0.46 => ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % "4.hyps"
% 0.30/0.46 thf(fact_13_Tree_Oinject,axiom,
% 0.30/0.46 ! [X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.30/0.46 ( ( ( t_a @ X21 @ X22 @ X23 )
% 0.30/0.46 = ( t_a @ Y21 @ Y22 @ Y23 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X22 = Y22 )
% 0.30/0.46 & ( X23 = Y23 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.inject
% 0.30/0.46 thf(fact_14_is__heap_Osimps_I1_J,axiom,
% 0.30/0.46 is_heap_a @ e_a ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(1)
% 0.30/0.46 thf(fact_15_Tree_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X21: a,X22: tree_a,X23: tree_a] :
% 0.30/0.46 ( e_a
% 0.30/0.46 != ( t_a @ X21 @ X22 @ X23 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.distinct(1)
% 0.30/0.46 thf(fact_16_Tree_Oinduct,axiom,
% 0.30/0.46 ! [P: tree_a > $o,Tree: tree_a] :
% 0.30/0.46 ( ( P @ e_a )
% 0.30/0.46 => ( ! [X1: a,X2: tree_a,X3: tree_a] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( ( P @ X3 )
% 0.30/0.46 => ( P @ ( t_a @ X1 @ X2 @ X3 ) ) ) )
% 0.30/0.46 => ( P @ Tree ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.induct
% 0.30/0.46 thf(fact_17_Tree_Oexhaust,axiom,
% 0.30/0.46 ! [Y: tree_a] :
% 0.30/0.46 ( ( Y != e_a )
% 0.30/0.46 => ~ ! [X212: a,X222: tree_a,X232: tree_a] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( t_a @ X212 @ X222 @ X232 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.exhaust
% 0.30/0.46 thf(fact_18_is__heap_Ocases,axiom,
% 0.30/0.46 ! [X: tree_a] :
% 0.30/0.46 ( ( X != e_a )
% 0.30/0.46 => ( ! [V2: a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t_a @ V2 @ e_a @ e_a ) )
% 0.30/0.46 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t_a @ V2 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.30/0.46 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.30/0.46 => ~ ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.cases
% 0.30/0.46 thf(fact_19_siftDown__in__tree__set,axiom,
% 0.30/0.46 ( in_tree_a
% 0.30/0.46 = ( ^ [V4: a,T2: tree_a] : ( in_tree_a @ V4 @ ( heapIm1091024090Down_a @ T2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown_in_tree_set
% 0.30/0.46 thf(fact_20_left_Osimps,axiom,
% 0.30/0.46 ! [V: a,L: tree_a,R: tree_a] :
% 0.30/0.46 ( ( heapIm1140443833left_a @ ( t_a @ V @ L @ R ) )
% 0.30/0.46 = L ) ).
% 0.30/0.46
% 0.30/0.46 % left.simps
% 0.30/0.46 thf(fact_21_is__heap__max,axiom,
% 0.30/0.46 ! [V: a,T: tree_a] :
% 0.30/0.46 ( ( in_tree_a @ V @ T )
% 0.30/0.46 => ( ( is_heap_a @ T )
% 0.30/0.46 => ( ord_less_eq_a @ V @ ( val_a @ T ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap_max
% 0.30/0.46 thf(fact_22_val_Osimps,axiom,
% 0.30/0.46 ! [V: a,Uu: tree_a,Uv: tree_a] :
% 0.30/0.46 ( ( val_a @ ( t_a @ V @ Uu @ Uv ) )
% 0.30/0.46 = V ) ).
% 0.30/0.46
% 0.30/0.46 % val.simps
% 0.30/0.46 thf(fact_23_in__tree_Osimps_I2_J,axiom,
% 0.30/0.46 ! [V: a,V5: a,L: tree_a,R: tree_a] :
% 0.30/0.46 ( ( in_tree_a @ V @ ( t_a @ V5 @ L @ R ) )
% 0.30/0.46 = ( ( V = V5 )
% 0.30/0.46 | ( in_tree_a @ V @ L )
% 0.30/0.46 | ( in_tree_a @ V @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_tree.simps(2)
% 0.30/0.46 thf(fact_24_siftDown_Osimps_I5_J,axiom,
% 0.30/0.46 ! [Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 0.30/0.46 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(5)
% 0.30/0.46 thf(fact_25_siftDown_Osimps_I6_J,axiom,
% 0.30/0.46 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a,V: a] :
% 0.30/0.46 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(6)
% 0.30/0.46 thf(fact_26_in__tree_Osimps_I1_J,axiom,
% 0.30/0.46 ! [V: a] :
% 0.30/0.46 ~ ( in_tree_a @ V @ e_a ) ).
% 0.30/0.46
% 0.30/0.46 % in_tree.simps(1)
% 0.30/0.46 thf(fact_27_is__heap_Osimps_I5_J,axiom,
% 0.30/0.46 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 0.30/0.46 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.30/0.46 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) )
% 0.30/0.46 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(5)
% 0.30/0.46 thf(fact_28_is__heap_Osimps_I6_J,axiom,
% 0.30/0.46 ! [V: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.30/0.46 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.30/0.46 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.30/0.46 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(6)
% 0.30/0.46 thf(fact_29_siftDown_Osimps_I3_J,axiom,
% 0.30/0.46 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 0.30/0.46 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.30/0.46 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.30/0.46 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ e_a ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(3)
% 0.30/0.46 thf(fact_30_siftDown_Osimps_I4_J,axiom,
% 0.30/0.46 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 0.30/0.46 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.30/0.46 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown.simps(4)
% 0.30/0.46 thf(fact_31_siftDown__in__tree,axiom,
% 0.30/0.46 ! [T: tree_a] :
% 0.30/0.46 ( ( T != e_a )
% 0.30/0.46 => ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ T ) ) @ T ) ) ).
% 0.30/0.46
% 0.30/0.46 % siftDown_in_tree
% 0.30/0.46 thf(fact_32_is__heap_Osimps_I3_J,axiom,
% 0.30/0.46 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.30/0.46 ( ( is_heap_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.30/0.46 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(3)
% 0.30/0.46 thf(fact_33_is__heap_Osimps_I4_J,axiom,
% 0.30/0.46 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.30/0.46 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.30/0.46 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.30/0.46 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_heap.simps(4)
% 0.30/0.46 thf(fact_34_right_Osimps,axiom,
% 0.30/0.46 ! [V: a,L: tree_a,R: tree_a] :
% 0.30/0.46 ( ( heapIm1257206334ight_a @ ( t_a @ V @ L @ R ) )
% 0.30/0.46 = R ) ).
% 0.30/0.46
% 0.30/0.46 % right.simps
% 0.30/0.46 thf(fact_35_order__refl,axiom,
% 0.30/0.46 ! [X: $o > a] : ( ord_less_eq_o_a @ X @ X ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_36_order__refl,axiom,
% 0.30/0.46 ! [X: a] : ( ord_less_eq_a @ X @ X ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_37_le__funD,axiom,
% 0.30/0.46 ! [F: $o > a,G: $o > a,X: $o] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ F @ G )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funD
% 0.30/0.46 thf(fact_38_le__funE,axiom,
% 0.30/0.46 ! [F: $o > a,G: $o > a,X: $o] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ F @ G )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funE
% 0.30/0.46 thf(fact_39_le__funI,axiom,
% 0.30/0.46 ! [F: $o > a,G: $o > a] :
% 0.30/0.46 ( ! [X4: $o] : ( ord_less_eq_a @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.30/0.46 => ( ord_less_eq_o_a @ F @ G ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funI
% 0.30/0.46 thf(fact_40_le__fun__def,axiom,
% 0.30/0.46 ( ord_less_eq_o_a
% 0.30/0.46 = ( ^ [F2: $o > a,G2: $o > a] :
% 0.30/0.46 ! [X5: $o] : ( ord_less_eq_a @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_fun_def
% 0.30/0.46 thf(fact_41_order__subst1,axiom,
% 0.30/0.46 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.30/0.46 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_42_order__subst1,axiom,
% 0.30/0.46 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 0.30/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.30/0.46 => ( ! [X4: a,Y2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_43_order__subst1,axiom,
% 0.30/0.46 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.30/0.46 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_44_order__subst1,axiom,
% 0.30/0.46 ! [A: a,F: a > a,B: a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 0.30/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.30/0.46 => ( ! [X4: a,Y2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_45_order__subst2,axiom,
% 0.30/0.46 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 0.30/0.46 => ( ! [X4: a,Y2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_46_order__subst2,axiom,
% 0.30/0.46 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 0.30/0.46 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_47_order__subst2,axiom,
% 0.30/0.46 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 0.30/0.46 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_48_order__subst2,axiom,
% 0.30/0.46 ! [A: a,B: a,F: a > a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 0.30/0.46 => ( ! [X4: a,Y2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_49_verit__la__disequality,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 | ~ ( ord_less_eq_a @ A @ B )
% 0.30/0.46 | ~ ( ord_less_eq_a @ B @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % verit_la_disequality
% 0.30/0.46 thf(fact_50_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( F @ B ) )
% 0.30/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.30/0.46 => ( ! [X4: a,Y2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_51_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( F @ B ) )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.30/0.46 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_52_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( F @ B ) )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.30/0.46 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_53_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: a,F: a > a,B: a,C: a] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( F @ B ) )
% 0.30/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.30/0.46 => ( ! [X4: a,Y2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_54_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.30/0.46 => ( ( ( F @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X4: a,Y2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_55_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.30/0.46 => ( ( ( F @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_56_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.30/0.46 => ( ( ( F @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X4: $o > a,Y2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_57_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: a,B: a,F: a > a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.30/0.46 => ( ( ( F @ B )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X4: a,Y2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X4 @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_58_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: a,P: a > $o] :
% 0.30/0.46 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.30/0.46 = ( P @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_59_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( collect_a
% 0.30/0.46 @ ^ [X5: a] : ( member_a @ X5 @ A2 ) )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_60_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [B: $o > a,A: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ B @ A )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ A @ B )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_61_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ B @ A )
% 0.30/0.46 => ( ( ord_less_eq_a @ A @ B )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_62_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A3: $o > a,B2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ B2 @ A3 )
% 0.30/0.46 & ( ord_less_eq_o_a @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_63_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A3: a,B2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ B2 @ A3 )
% 0.30/0.46 & ( ord_less_eq_a @ A3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_64_dual__order_Otrans,axiom,
% 0.30/0.46 ! [B: $o > a,A: $o > a,C: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ B @ A )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ C @ B )
% 0.30/0.46 => ( ord_less_eq_o_a @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_65_dual__order_Otrans,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ B @ A )
% 0.30/0.46 => ( ( ord_less_eq_a @ C @ B )
% 0.30/0.46 => ( ord_less_eq_a @ C @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_66_linorder__wlog,axiom,
% 0.30/0.46 ! [P: a > a > $o,A: a,B: a] :
% 0.30/0.46 ( ! [A4: a,B3: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A4 @ B3 )
% 0.30/0.46 => ( P @ A4 @ B3 ) )
% 0.30/0.46 => ( ! [A4: a,B3: a] :
% 0.30/0.46 ( ( P @ B3 @ A4 )
% 0.30/0.46 => ( P @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_wlog
% 0.30/0.46 thf(fact_67_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A: $o > a] : ( ord_less_eq_o_a @ A @ A ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_68_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A: a] : ( ord_less_eq_a @ A @ A ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_69_order__trans,axiom,
% 0.30/0.46 ! [X: $o > a,Y: $o > a,Z2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ Y @ Z2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_70_order__trans,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq_a @ Y @ Z2 )
% 0.30/0.46 => ( ord_less_eq_a @ X @ Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_71_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: $o > a,B: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_72_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_eq_a @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_73_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.30/0.46 => ( ( B = C )
% 0.30/0.46 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_74_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.30/0.46 => ( ( B = C )
% 0.30/0.46 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_75_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.30/0.46 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_76_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.30/0.46 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_77_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A3: $o > a,B2: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A3 @ B2 )
% 0.30/0.46 & ( ord_less_eq_o_a @ B2 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_78_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A3: a,B2: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A3 @ B2 )
% 0.30/0.46 & ( ord_less_eq_a @ B2 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_79_antisym__conv,axiom,
% 0.30/0.46 ! [Y: $o > a,X: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ Y @ X )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_80_antisym__conv,axiom,
% 0.30/0.46 ! [Y: a,X: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ Y @ X )
% 0.30/0.46 => ( ( ord_less_eq_a @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_81_le__cases3,axiom,
% 0.30/0.46 ! [X: a,Y: a,Z2: a] :
% 0.30/0.46 ( ( ( ord_less_eq_a @ X @ Y )
% 0.30/0.46 => ~ ( ord_less_eq_a @ Y @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq_a @ Y @ X )
% 0.30/0.46 => ~ ( ord_less_eq_a @ X @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq_a @ X @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq_a @ Z2 @ Y ) )
% 0.30/0.46 => ( ( ( ord_less_eq_a @ Z2 @ Y )
% 0.30/0.46 => ~ ( ord_less_eq_a @ Y @ X ) )
% 0.30/0.46 => ( ( ( ord_less_eq_a @ Y @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq_a @ Z2 @ X ) )
% 0.30/0.46 => ~ ( ( ord_less_eq_a @ Z2 @ X )
% 0.30/0.46 => ~ ( ord_less_eq_a @ X @ Y ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases3
% 0.30/0.46 thf(fact_82_order_Otrans,axiom,
% 0.30/0.46 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.30/0.46 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_83_order_Otrans,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.30/0.46 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_84_le__cases,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ~ ( ord_less_eq_a @ X @ Y )
% 0.30/0.46 => ( ord_less_eq_a @ Y @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases
% 0.30/0.46 thf(fact_85_eq__refl,axiom,
% 0.30/0.46 ! [X: $o > a,Y: $o > a] :
% 0.30/0.46 ( ( X = Y )
% 0.30/0.46 => ( ord_less_eq_o_a @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_86_eq__refl,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( X = Y )
% 0.30/0.46 => ( ord_less_eq_a @ X @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_87_linear,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X @ Y )
% 0.30/0.46 | ( ord_less_eq_a @ Y @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % linear
% 0.30/0.46 thf(fact_88_antisym,axiom,
% 0.30/0.46 ! [X: $o > a,Y: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq_o_a @ Y @ X )
% 0.30/0.46 => ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_89_antisym,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq_a @ Y @ X )
% 0.30/0.46 => ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_90_eq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [X5: $o > a,Y4: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.30/0.46 & ( ord_less_eq_o_a @ Y4 @ X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_91_eq__iff,axiom,
% 0.30/0.46 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [X5: a,Y4: a] :
% 0.30/0.46 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.30/0.46 & ( ord_less_eq_a @ Y4 @ X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_92_Greatest__equality,axiom,
% 0.30/0.46 ! [P: ( $o > a ) > $o,X: $o > a] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: $o > a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ Y2 @ X ) )
% 0.30/0.46 => ( ( order_Greatest_o_a @ P )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Greatest_equality
% 0.30/0.46 thf(fact_93_Greatest__equality,axiom,
% 0.30/0.46 ! [P: a > $o,X: a] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ Y2 @ X ) )
% 0.30/0.46 => ( ( order_Greatest_a @ P )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Greatest_equality
% 0.30/0.46 thf(fact_94_GreatestI2__order,axiom,
% 0.30/0.46 ! [P: ( $o > a ) > $o,X: $o > a,Q: ( $o > a ) > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: $o > a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq_o_a @ Y2 @ X ) )
% 0.30/0.46 => ( ! [X4: $o > a] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 => ( ! [Y5: $o > a] :
% 0.30/0.46 ( ( P @ Y5 )
% 0.30/0.46 => ( ord_less_eq_o_a @ Y5 @ X4 ) )
% 0.30/0.46 => ( Q @ X4 ) ) )
% 0.30/0.46 => ( Q @ ( order_Greatest_o_a @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % GreatestI2_order
% 0.30/0.46 thf(fact_95_GreatestI2__order,axiom,
% 0.30/0.46 ! [P: a > $o,X: a,Q: a > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y2: a] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq_a @ Y2 @ X ) )
% 0.30/0.46 => ( ! [X4: a] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 => ( ! [Y5: a] :
% 0.30/0.46 ( ( P @ Y5 )
% 0.30/0.46 => ( ord_less_eq_a @ Y5 @ X4 ) )
% 0.30/0.46 => ( Q @ X4 ) ) )
% 0.30/0.46 => ( Q @ ( order_Greatest_a @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % GreatestI2_order
% 0.30/0.46 thf(fact_96_le__rel__bool__arg__iff,axiom,
% 0.30/0.46 ( ord_less_eq_o_o_a
% 0.30/0.46 = ( ^ [X6: $o > $o > a,Y6: $o > $o > a] :
% 0.30/0.46 ( ( ord_less_eq_o_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 0.30/0.46 & ( ord_less_eq_o_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_rel_bool_arg_iff
% 0.30/0.46 thf(fact_97_le__rel__bool__arg__iff,axiom,
% 0.30/0.46 ( ord_less_eq_o_a
% 0.30/0.46 = ( ^ [X6: $o > a,Y6: $o > a] :
% 0.30/0.46 ( ( ord_less_eq_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 0.30/0.46 & ( ord_less_eq_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_rel_bool_arg_iff
% 0.30/0.46 thf(fact_98_Tree_Orel__induct,axiom,
% 0.30/0.46 ! [R3: a > a > $o,X: tree_a,Y: tree_a,Q: tree_a > tree_a > $o] :
% 0.30/0.46 ( ( rel_Tree_a_a @ R3 @ X @ Y )
% 0.30/0.46 => ( ( Q @ e_a @ e_a )
% 0.30/0.46 => ( ! [A21: a,A22: tree_a,A23: tree_a,B21: a,B22: tree_a,B23: tree_a] :
% 0.30/0.46 ( ( R3 @ A21 @ B21 )
% 0.30/0.46 => ( ( Q @ A22 @ B22 )
% 0.30/0.46 => ( ( Q @ A23 @ B23 )
% 0.30/0.46 => ( Q @ ( t_a @ A21 @ A22 @ A23 ) @ ( t_a @ B21 @ B22 @ B23 ) ) ) ) )
% 0.30/0.46 => ( Q @ X @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_induct
% 0.30/0.46 thf(fact_99_Tree_Orel__mono,axiom,
% 0.30/0.46 ! [R3: a > a > $o,Ra: a > a > $o] :
% 0.30/0.46 ( ( ord_less_eq_a_a_o @ R3 @ Ra )
% 0.30/0.46 => ( ord_le1530450702ee_a_o @ ( rel_Tree_a_a @ R3 ) @ ( rel_Tree_a_a @ Ra ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_mono
% 0.30/0.46 thf(fact_100_Tree_Orel__eq,axiom,
% 0.30/0.46 ( ( rel_Tree_a_a
% 0.30/0.46 @ ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [Y3: tree_a,Z: tree_a] : ( Y3 = Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_eq
% 0.30/0.46 thf(fact_101_Tree_Orel__refl,axiom,
% 0.30/0.46 ! [Ra: a > a > $o,X: tree_a] :
% 0.30/0.46 ( ! [X4: a] : ( Ra @ X4 @ X4 )
% 0.30/0.46 => ( rel_Tree_a_a @ Ra @ X @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_refl
% 0.30/0.46 thf(fact_102_Tree_Orel__inject_I2_J,axiom,
% 0.30/0.46 ! [R3: a > a > $o,X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.30/0.46 ( ( rel_Tree_a_a @ R3 @ ( t_a @ X21 @ X22 @ X23 ) @ ( t_a @ Y21 @ Y22 @ Y23 ) )
% 0.30/0.46 = ( ( R3 @ X21 @ Y21 )
% 0.30/0.46 & ( rel_Tree_a_a @ R3 @ X22 @ Y22 )
% 0.30/0.46 & ( rel_Tree_a_a @ R3 @ X23 @ Y23 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_inject(2)
% 0.30/0.46 thf(fact_103_Tree_Orel__intros_I2_J,axiom,
% 0.30/0.46 ! [R3: a > a > $o,X21: a,Y21: a,X22: tree_a,Y22: tree_a,X23: tree_a,Y23: tree_a] :
% 0.30/0.46 ( ( R3 @ X21 @ Y21 )
% 0.30/0.46 => ( ( rel_Tree_a_a @ R3 @ X22 @ Y22 )
% 0.30/0.46 => ( ( rel_Tree_a_a @ R3 @ X23 @ Y23 )
% 0.30/0.46 => ( rel_Tree_a_a @ R3 @ ( t_a @ X21 @ X22 @ X23 ) @ ( t_a @ Y21 @ Y22 @ Y23 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_intros(2)
% 0.30/0.46 thf(fact_104_Tree_Octr__transfer_I1_J,axiom,
% 0.30/0.46 ! [R3: a > a > $o] : ( rel_Tree_a_a @ R3 @ e_a @ e_a ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.ctr_transfer(1)
% 0.30/0.46 thf(fact_105_Tree_Orel__distinct_I2_J,axiom,
% 0.30/0.46 ! [R3: a > a > $o,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.30/0.46 ~ ( rel_Tree_a_a @ R3 @ ( t_a @ Y21 @ Y22 @ Y23 ) @ e_a ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_distinct(2)
% 0.30/0.46 thf(fact_106_Tree_Orel__distinct_I1_J,axiom,
% 0.30/0.46 ! [R3: a > a > $o,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.30/0.46 ~ ( rel_Tree_a_a @ R3 @ e_a @ ( t_a @ Y21 @ Y22 @ Y23 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_distinct(1)
% 0.30/0.46 thf(fact_107_Tree_Orel__cases,axiom,
% 0.30/0.46 ! [R3: a > a > $o,A: tree_a,B: tree_a] :
% 0.30/0.46 ( ( rel_Tree_a_a @ R3 @ A @ B )
% 0.30/0.46 => ( ( ( A = e_a )
% 0.30/0.46 => ( B != e_a ) )
% 0.30/0.46 => ~ ! [X1: a,X2: tree_a,X3: tree_a] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( t_a @ X1 @ X2 @ X3 ) )
% 0.30/0.46 => ! [Y1: a,Y24: tree_a,Y32: tree_a] :
% 0.30/0.46 ( ( B
% 0.30/0.46 = ( t_a @ Y1 @ Y24 @ Y32 ) )
% 0.30/0.46 => ( ( R3 @ X1 @ Y1 )
% 0.30/0.46 => ( ( rel_Tree_a_a @ R3 @ X2 @ Y24 )
% 0.30/0.46 => ~ ( rel_Tree_a_a @ R3 @ X3 @ Y32 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Tree.rel_cases
% 0.30/0.46 thf(fact_108_heap__top__geq,axiom,
% 0.30/0.46 ! [A: a,T: tree_a] :
% 0.30/0.46 ( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ T ) ) )
% 0.30/0.46 => ( ( is_heap_a @ T )
% 0.30/0.46 => ( ord_less_eq_a @ A @ ( val_a @ T ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % heap_top_geq
% 0.30/0.46 thf(fact_109_add__mset__add__mset__same__iff,axiom,
% 0.30/0.46 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.30/0.46 ( ( ( add_mset_a @ A @ A2 )
% 0.30/0.46 = ( add_mset_a @ A @ B4 ) )
% 0.30/0.46 = ( A2 = B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mset_add_mset_same_iff
% 0.30/0.46 thf(fact_110_multi__self__add__other__not__self,axiom,
% 0.30/0.46 ! [M: multiset_a,X: a] :
% 0.30/0.46 ( M
% 0.30/0.46 != ( add_mset_a @ X @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % multi_self_add_other_not_self
% 0.30/0.46 thf(fact_111_mset__add,axiom,
% 0.30/0.46 ! [A: a,A2: multiset_a] :
% 0.30/0.46 ( ( member_a @ A @ ( set_mset_a @ A2 ) )
% 0.30/0.46 => ~ ! [B5: multiset_a] :
% 0.30/0.46 ( A2
% 0.30/0.46 != ( add_mset_a @ A @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mset_add
% 0.30/0.46 thf(fact_112_multi__member__split,axiom,
% 0.30/0.46 ! [X: a,M: multiset_a] :
% 0.30/0.46 ( ( member_a @ X @ ( set_mset_a @ M ) )
% 0.30/0.46 => ? [A5: multiset_a] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( add_mset_a @ X @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multi_member_split
% 0.30/0.46 thf(fact_113_add__mset__commute,axiom,
% 0.30/0.46 ! [X: a,Y: a,M: multiset_a] :
% 0.30/0.46 ( ( add_mset_a @ X @ ( add_mset_a @ Y @ M ) )
% 0.30/0.46 = ( add_mset_a @ Y @ ( add_mset_a @ X @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mset_commute
% 0.30/0.46 thf(fact_114_add__eq__conv__ex,axiom,
% 0.30/0.46 ! [A: a,M: multiset_a,B: a,N: multiset_a] :
% 0.30/0.46 ( ( ( add_mset_a @ A @ M )
% 0.30/0.46 = ( add_mset_a @ B @ N ) )
% 0.30/0.46 = ( ( ( M = N )
% 0.30/0.46 & ( A = B ) )
% 0.30/0.46 | ? [K: multiset_a] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( add_mset_a @ B @ K ) )
% 0.30/0.46 & ( N
% 0.30/0.46 = ( add_mset_a @ A @ K ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_eq_conv_ex
% 0.30/0.46 thf(fact_115_union__single__eq__member,axiom,
% 0.30/0.46 ! [X: a,M: multiset_a,N: multiset_a] :
% 0.30/0.46 ( ( ( add_mset_a @ X @ M )
% 0.30/0.46 = N )
% 0.30/0.46 => ( member_a @ X @ ( set_mset_a @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % union_single_eq_member
% 0.30/0.46 thf(fact_116_insert__noteq__member,axiom,
% 0.30/0.46 ! [B: a,B4: multiset_a,C: a,C2: multiset_a] :
% 0.30/0.46 ( ( ( add_mset_a @ B @ B4 )
% 0.30/0.46 = ( add_mset_a @ C @ C2 ) )
% 0.30/0.46 => ( ( B != C )
% 0.30/0.46 => ( member_a @ C @ ( set_mset_a @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_noteq_member
% 0.30/0.46 thf(fact_117_heap__top__max,axiom,
% 0.30/0.46 ! [T: tree_a] :
% 0.30/0.46 ( ( T != e_a )
% 0.30/0.46 => ( ( is_heap_a @ T )
% 0.30/0.46 => ( ( val_a @ T )
% 0.30/0.46 = ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ T ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % heap_top_max
% 0.30/0.46 thf(fact_118_multiset__induct__max,axiom,
% 0.30/0.46 ! [P: multiset_a > $o,M: multiset_a] :
% 0.30/0.46 ( ( P @ zero_zero_multiset_a )
% 0.30/0.46 => ( ! [X4: a,M2: multiset_a] :
% 0.30/0.46 ( ( P @ M2 )
% 0.30/0.46 => ( ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 0.30/0.46 => ( ord_less_eq_a @ Xa @ X4 ) )
% 0.30/0.46 => ( P @ ( add_mset_a @ X4 @ M2 ) ) ) )
% 0.30/0.46 => ( P @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multiset_induct_max
% 0.30/0.46 thf(fact_119_multiset__induct__min,axiom,
% 0.30/0.46 ! [P: multiset_a > $o,M: multiset_a] :
% 0.30/0.46 ( ( P @ zero_zero_multiset_a )
% 0.30/0.46 => ( ! [X4: a,M2: multiset_a] :
% 0.30/0.46 ( ( P @ M2 )
% 0.30/0.46 => ( ! [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 0.30/0.46 => ( ord_less_eq_a @ X4 @ Xa ) )
% 0.30/0.46 => ( P @ ( add_mset_a @ X4 @ M2 ) ) ) )
% 0.30/0.46 => ( P @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multiset_induct_min
% 0.30/0.46 thf(fact_120_add__mset__eq__singleton__iff,axiom,
% 0.30/0.46 ! [X: a,M: multiset_a,Y: a] :
% 0.30/0.46 ( ( ( add_mset_a @ X @ M )
% 0.30/0.46 = ( add_mset_a @ Y @ zero_zero_multiset_a ) )
% 0.30/0.46 = ( ( M = zero_zero_multiset_a )
% 0.30/0.46 & ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mset_eq_singleton_iff
% 0.30/0.46 thf(fact_121_single__eq__add__mset,axiom,
% 0.30/0.46 ! [A: a,B: a,M: multiset_a] :
% 0.30/0.46 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.30/0.46 = ( add_mset_a @ B @ M ) )
% 0.30/0.46 = ( ( B = A )
% 0.30/0.46 & ( M = zero_zero_multiset_a ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % single_eq_add_mset
% 0.30/0.46 thf(fact_122_add__mset__eq__single,axiom,
% 0.30/0.46 ! [B: a,M: multiset_a,A: a] :
% 0.30/0.46 ( ( ( add_mset_a @ B @ M )
% 0.30/0.46 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 0.30/0.46 = ( ( B = A )
% 0.30/0.46 & ( M = zero_zero_multiset_a ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mset_eq_single
% 0.30/0.46 thf(fact_123_single__eq__single,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.30/0.46 = ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 0.30/0.46 = ( A = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % single_eq_single
% 0.30/0.46 thf(fact_124_multiset__cases,axiom,
% 0.30/0.46 ! [M: multiset_a] :
% 0.30/0.46 ( ( M != zero_zero_multiset_a )
% 0.30/0.46 => ~ ! [X4: a,N2: multiset_a] :
% 0.30/0.46 ( M
% 0.30/0.46 != ( add_mset_a @ X4 @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multiset_cases
% 0.30/0.46 thf(fact_125_multiset__induct,axiom,
% 0.30/0.46 ! [P: multiset_a > $o,M: multiset_a] :
% 0.30/0.46 ( ( P @ zero_zero_multiset_a )
% 0.30/0.46 => ( ! [X4: a,M2: multiset_a] :
% 0.30/0.46 ( ( P @ M2 )
% 0.30/0.46 => ( P @ ( add_mset_a @ X4 @ M2 ) ) )
% 0.30/0.46 => ( P @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multiset_induct
% 0.30/0.46 thf(fact_126_multiset__induct2,axiom,
% 0.30/0.46 ! [P: multiset_a > multiset_a > $o,M: multiset_a,N: multiset_a] :
% 0.30/0.46 ( ( P @ zero_zero_multiset_a @ zero_zero_multiset_a )
% 0.30/0.46 => ( ! [A4: a,M2: multiset_a,N2: multiset_a] :
% 0.30/0.46 ( ( P @ M2 @ N2 )
% 0.30/0.46 => ( P @ ( add_mset_a @ A4 @ M2 ) @ N2 ) )
% 0.30/0.46 => ( ! [A4: a,M2: multiset_a,N2: multiset_a] :
% 0.30/0.46 ( ( P @ M2 @ N2 )
% 0.30/0.46 => ( P @ M2 @ ( add_mset_a @ A4 @ N2 ) ) )
% 0.30/0.46 => ( P @ M @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multiset_induct2
% 0.30/0.46 thf(fact_127_empty__not__add__mset,axiom,
% 0.30/0.46 ! [A: a,A2: multiset_a] :
% 0.30/0.46 ( zero_zero_multiset_a
% 0.30/0.46 != ( add_mset_a @ A @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_not_add_mset
% 0.30/0.46 thf(fact_128_multiset__nonemptyE,axiom,
% 0.30/0.46 ! [A2: multiset_a] :
% 0.30/0.46 ( ( A2 != zero_zero_multiset_a )
% 0.30/0.46 => ~ ! [X4: a] :
% 0.30/0.46 ~ ( member_a @ X4 @ ( set_mset_a @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multiset_nonemptyE
% 0.30/0.46 thf(fact_129_multi__nonempty__split,axiom,
% 0.30/0.46 ! [M: multiset_a] :
% 0.30/0.46 ( ( M != zero_zero_multiset_a )
% 0.30/0.46 => ? [A5: multiset_a,A4: a] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( add_mset_a @ A4 @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multi_nonempty_split
% 0.30/0.46 thf(fact_130_multi__member__last,axiom,
% 0.30/0.46 ! [X: a] : ( member_a @ X @ ( set_mset_a @ ( add_mset_a @ X @ zero_zero_multiset_a ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multi_member_last
% 0.30/0.46 thf(fact_131_multiset_Osimps_I1_J,axiom,
% 0.30/0.46 ( ( multiset_a2 @ e_a )
% 0.30/0.46 = zero_zero_multiset_a ) ).
% 0.30/0.46
% 0.30/0.46 % multiset.simps(1)
% 0.30/0.46 thf(fact_132_multiset_Osimps_I2_J,axiom,
% 0.30/0.46 ! [V: a,L: tree_a,R: tree_a] :
% 0.30/0.46 ( ( multiset_a2 @ ( t_a @ V @ L @ R ) )
% 0.30/0.46 = ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ L ) @ ( add_mset_a @ V @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multiset.simps(2)
% 0.30/0.46 thf(fact_133_single__subset__iff,axiom,
% 0.30/0.46 ! [A: a,M: multiset_a] :
% 0.30/0.46 ( ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ M )
% 0.30/0.46 = ( member_a @ A @ ( set_mset_a @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % single_subset_iff
% 0.30/0.46 thf(fact_134_union__mset__add__mset__left,axiom,
% 0.30/0.46 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.30/0.46 ( ( plus_plus_multiset_a @ ( add_mset_a @ A @ A2 ) @ B4 )
% 0.30/0.46 = ( add_mset_a @ A @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % union_mset_add_mset_left
% 0.30/0.46 thf(fact_135_union__mset__add__mset__right,axiom,
% 0.30/0.46 ! [A2: multiset_a,A: a,B4: multiset_a] :
% 0.30/0.46 ( ( plus_plus_multiset_a @ A2 @ ( add_mset_a @ A @ B4 ) )
% 0.30/0.46 = ( add_mset_a @ A @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % union_mset_add_mset_right
% 0.30/0.46 thf(fact_136_add__mset__subseteq__single__iff,axiom,
% 0.30/0.46 ! [A: a,M: multiset_a,B: a] :
% 0.30/0.46 ( ( subseteq_mset_a @ ( add_mset_a @ A @ M ) @ ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 0.30/0.46 = ( ( M = zero_zero_multiset_a )
% 0.30/0.46 & ( A = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mset_subseteq_single_iff
% 0.30/0.46 thf(fact_137_verit__sum__simplify,axiom,
% 0.30/0.46 ! [A: multiset_a] :
% 0.30/0.46 ( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % verit_sum_simplify
% 0.30/0.46 thf(fact_138_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.46 ! [I: multiset_a,J: multiset_a,K2: multiset_a,L: multiset_a] :
% 0.30/0.46 ( ( ( ord_le1199012836iset_a @ I @ J )
% 0.30/0.46 & ( K2 = L ) )
% 0.30/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K2 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_semiring(3)
% 0.30/0.46 thf(fact_139_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.46 ! [I: multiset_a,J: multiset_a,K2: multiset_a,L: multiset_a] :
% 0.30/0.46 ( ( ( I = J )
% 0.30/0.46 & ( ord_le1199012836iset_a @ K2 @ L ) )
% 0.30/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K2 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_semiring(2)
% 0.30/0.46 thf(fact_140_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.46 ! [I: multiset_a,J: multiset_a,K2: multiset_a,L: multiset_a] :
% 0.30/0.46 ( ( ( ord_le1199012836iset_a @ I @ J )
% 0.30/0.46 & ( ord_le1199012836iset_a @ K2 @ L ) )
% 0.30/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K2 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_semiring(1)
% 0.30/0.46 thf(fact_141_add__mono,axiom,
% 0.30/0.46 ! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
% 0.30/0.46 ( ( ord_le1199012836iset_a @ A @ B )
% 0.30/0.46 => ( ( ord_le1199012836iset_a @ C @ D )
% 0.30/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono
% 0.30/0.46 thf(fact_142_add__left__mono,axiom,
% 0.30/0.46 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.30/0.46 ( ( ord_le1199012836iset_a @ A @ B )
% 0.30/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_left_mono
% 0.30/0.46 thf(fact_143_add__right__mono,axiom,
% 0.30/0.46 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.30/0.46 ( ( ord_le1199012836iset_a @ A @ B )
% 0.30/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_right_mono
% 0.30/0.46 thf(fact_144_union__iff,axiom,
% 0.30/0.46 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.30/0.46 ( ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ A2 @ B4 ) ) )
% 0.30/0.46 = ( ( member_a @ A @ ( set_mset_a @ A2 ) )
% 0.30/0.46 | ( member_a @ A @ ( set_mset_a @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % union_iff
% 0.30/0.46 thf(fact_145_mset__subset__eqD,axiom,
% 0.30/0.46 ! [A2: multiset_a,B4: multiset_a,X: a] :
% 0.30/0.46 ( ( subseteq_mset_a @ A2 @ B4 )
% 0.30/0.46 => ( ( member_a @ X @ ( set_mset_a @ A2 ) )
% 0.30/0.46 => ( member_a @ X @ ( set_mset_a @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mset_subset_eqD
% 0.30/0.46 thf(fact_146_mset__subset__eq__add__mset__cancel,axiom,
% 0.30/0.46 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 0.30/0.46 ( ( subseteq_mset_a @ ( add_mset_a @ A @ A2 ) @ ( add_mset_a @ A @ B4 ) )
% 0.30/0.46 = ( subseteq_mset_a @ A2 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mset_subset_eq_add_mset_cancel
% 0.30/0.46 thf(fact_147_set__mset__mono,axiom,
% 0.30/0.46 ! [A2: multiset_a,B4: multiset_a] :
% 0.30/0.46 ( ( subseteq_mset_a @ A2 @ B4 )
% 0.30/0.46 => ( ord_less_eq_set_a @ ( set_mset_a @ A2 ) @ ( set_mset_a @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_mset_mono
% 0.30/0.46 thf(fact_148_single__is__union,axiom,
% 0.30/0.46 ! [A: a,M: multiset_a,N: multiset_a] :
% 0.30/0.46 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.30/0.46 = ( plus_plus_multiset_a @ M @ N ) )
% 0.30/0.46 = ( ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.30/0.46 = M )
% 0.30/0.46 & ( N = zero_zero_multiset_a ) )
% 0.30/0.46 | ( ( M = zero_zero_multiset_a )
% 0.30/0.46 & ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 0.30/0.46 = N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % single_is_union
% 0.30/0.46 thf(fact_149_union__is__single,axiom,
% 0.30/0.46 ! [M: multiset_a,N: multiset_a,A: a] :
% 0.30/0.46 ( ( ( plus_plus_multiset_a @ M @ N )
% 0.30/0.46 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 0.30/0.46 = ( ( ( M
% 0.30/0.46 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 0.30/0.46 & ( N = zero_zero_multiset_a ) )
% 0.30/0.46 | ( ( M = zero_zero_multiset_a )
% 0.30/0.46 & ( N
% 0.30/0.46 = ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % union_is_single
% 0.30/0.46 thf(fact_150_add__mset__add__single,axiom,
% 0.30/0.46 ( add_mset_a
% 0.30/0.46 = ( ^ [A3: a,A6: multiset_a] : ( plus_plus_multiset_a @ A6 @ ( add_mset_a @ A3 @ zero_zero_multiset_a ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mset_add_single
% 0.30/0.46 thf(fact_151_multi__subset__induct,axiom,
% 0.30/0.46 ! [F3: multiset_a,A2: multiset_a,P: multiset_a > $o] :
% 0.30/0.46 ( ( subseteq_mset_a @ F3 @ A2 )
% 0.30/0.46 => ( ( P @ zero_zero_multiset_a )
% 0.30/0.46 => ( ! [A4: a,F4: multiset_a] :
% 0.30/0.46 ( ( member_a @ A4 @ ( set_mset_a @ A2 ) )
% 0.30/0.46 => ( ( P @ F4 )
% 0.30/0.46 => ( P @ ( add_mset_a @ A4 @ F4 ) ) ) )
% 0.30/0.46 => ( P @ F3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multi_subset_induct
% 0.30/0.46 thf(fact_152_mset__subset__eq__single,axiom,
% 0.30/0.46 ! [A: a,B4: multiset_a] :
% 0.30/0.46 ( ( member_a @ A @ ( set_mset_a @ B4 ) )
% 0.30/0.46 => ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mset_subset_eq_single
% 0.30/0.46 thf(fact_153_multi__member__skip,axiom,
% 0.30/0.46 ! [X: a,XS: multiset_a,Y: a] :
% 0.30/0.46 ( ( member_a @ X @ ( set_mset_a @ XS ) )
% 0.30/0.46 => ( member_a @ X @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ Y @ zero_zero_multiset_a ) @ XS ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multi_member_skip
% 0.30/0.46 thf(fact_154_multi__member__this,axiom,
% 0.30/0.46 ! [X: a,XS: multiset_a] : ( member_a @ X @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ X @ zero_zero_multiset_a ) @ XS ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % multi_member_this
% 0.30/0.46 thf(fact_155_mult1E,axiom,
% 0.30/0.46 ! [N: multiset_a,M: multiset_a,R: set_Product_prod_a_a] :
% 0.30/0.46 ( ( member340150864iset_a @ ( produc2037245207iset_a @ N @ M ) @ ( mult1_a @ R ) )
% 0.30/0.46 => ~ ! [A4: a,M0: multiset_a] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( add_mset_a @ A4 @ M0 ) )
% 0.30/0.46 => ! [K3: multiset_a] :
% 0.30/0.46 ( ( N
% 0.30/0.46 = ( plus_plus_multiset_a @ M0 @ K3 ) )
% 0.30/0.46 => ~ ! [B6: a] :
% 0.30/0.46 ( ( member_a @ B6 @ ( set_mset_a @ K3 ) )
% 0.30/0.46 => ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A4 ) @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult1E
% 0.30/0.46 thf(fact_156_mult1I,axiom,
% 0.30/0.46 ! [M: multiset_a,A: a,M02: multiset_a,N: multiset_a,K4: multiset_a,R: set_Product_prod_a_a] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( add_mset_a @ A @ M02 ) )
% 0.30/0.46 => ( ( N
% 0.30/0.46 = ( plus_plus_multiset_a @ M02 @ K4 ) )
% 0.30/0.46 => ( ! [B3: a] :
% 0.30/0.46 ( ( member_a @ B3 @ ( set_mset_a @ K4 ) )
% 0.30/0.46 => ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A ) @ R ) )
% 0.30/0.46 => ( member340150864iset_a @ ( produc2037245207iset_a @ N @ M ) @ ( mult1_a @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult1I
% 0.30/0.46 thf(fact_157_less__add,axiom,
% 0.30/0.46 ! [N: multiset_a,A: a,M02: multiset_a,R: set_Product_prod_a_a] :
% 0.30/0.46 ( ( member340150864iset_a @ ( produc2037245207iset_a @ N @ ( add_mset_a @ A @ M02 ) ) @ ( mult1_a @ R ) )
% 0.30/0.46 => ( ? [M2: multiset_a] :
% 0.30/0.46 ( ( member340150864iset_a @ ( produc2037245207iset_a @ M2 @ M02 ) @ ( mult1_a @ R ) )
% 0.30/0.46 & ( N
% 0.30/0.46 = ( add_mset_a @ A @ M2 ) ) )
% 0.30/0.46 | ? [K3: multiset_a] :
% 0.30/0.46 ( ! [B6: a] :
% 0.30/0.46 ( ( member_a @ B6 @ ( set_mset_a @ K3 ) )
% 0.30/0.46 => ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A ) @ R ) )
% 0.30/0.46 & ( N
% 0.30/0.46 = ( plus_plus_multiset_a @ M02 @ K3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_add
% 0.30/0.46 thf(fact_158_subsetI,axiom,
% 0.30/0.46 ! [A2: set_a,B4: set_a] :
% 0.30/0.46 ( ! [X4: a] :
% 0.30/0.46 ( ( member_a @ X4 @ A2 )
% 0.30/0.46 => ( member_a @ X4 @ B4 ) )
% 0.30/0.46 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_159_in__mono,axiom,
% 0.30/0.46 ! [A2: set_a,B4: set_a,X: a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.46 => ( ( member_a @ X @ A2 )
% 0.30/0.46 => ( member_a @ X @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mono
% 0.30/0.46 thf(fact_160_subsetD,axiom,
% 0.30/0.46 ! [A2: set_a,B4: set_a,C: a] :
% 0.30/0.46 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.30/0.46 => ( ( member_a @ C @ A2 )
% 0.30/0.46 => ( member_a @ C @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetD
% 0.30/0.46 thf(fact_161_subset__eq,axiom,
% 0.30/0.46 ( ord_less_eq_set_a
% 0.30/0.46 = ( ^ [A6: set_a,B7: set_a] :
% 0.30/0.46 ! [X5: a] :
% 0.30/0.46 ( ( member_a @ X5 @ A6 )
% 0.30/0.46 => ( member_a @ X5 @ B7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_eq
% 0.30/0.46 thf(fact_162_subset__iff,axiom,
% 0.30/0.46 ( ord_less_eq_set_a
% 0.30/0.46 = ( ^ [A6: set_a,B7: set_a] :
% 0.30/0.46 ! [T2: a] :
% 0.30/0.46 ( ( member_a @ T2 @ A6 )
% 0.30/0.46 => ( member_a @ T2 @ B7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_iff
% 0.30/0.46 thf(fact_163_one__step__implies__mult,axiom,
% 0.30/0.46 ! [J2: multiset_a,K4: multiset_a,R: set_Product_prod_a_a,I2: multiset_a] :
% 0.30/0.46 ( ( J2 != zero_zero_multiset_a )
% 0.30/0.46 => ( ! [X4: a] :
% 0.30/0.46 ( ( member_a @ X4 @ ( set_mset_a @ K4 ) )
% 0.30/0.46 => ? [Xa: a] :
% 0.30/0.46 ( ( member_a @ Xa @ ( set_mset_a @ J2 ) )
% 0.30/0.46 & ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Xa ) @ R ) ) )
% 0.30/0.46 => ( member340150864iset_a @ ( produc2037245207iset_a @ ( plus_plus_multiset_a @ I2 @ K4 ) @ ( plus_plus_multiset_a @ I2 @ J2 ) ) @ ( mult_a @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % one_step_implies_mult
% 0.30/0.46 thf(fact_164_mult__implies__one__step,axiom,
% 0.30/0.46 ! [R: set_Product_prod_a_a,M: multiset_a,N: multiset_a] :
% 0.30/0.46 ( ( trans_a @ R )
% 0.30/0.46 => ( ( member340150864iset_a @ ( produc2037245207iset_a @ M @ N ) @ ( mult_a @ R ) )
% 0.30/0.46 => ? [I3: multiset_a,J3: multiset_a] :
% 0.30/0.46 ( ( N
% 0.30/0.46 = ( plus_plus_multiset_a @ I3 @ J3 ) )
% 0.30/0.46 & ? [K3: multiset_a] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( plus_plus_multiset_a @ I3 @ K3 ) )
% 0.30/0.46 & ( J3 != zero_zero_multiset_a )
% 0.30/0.46 & ! [X7: a] :
% 0.30/0.46 ( ( member_a @ X7 @ ( set_mset_a @ K3 ) )
% 0.30/0.46 => ? [Xa2: a] :
% 0.30/0.46 ( ( member_a @ Xa2 @ ( set_mset_a @ J3 ) )
% 0.30/0.46 & ( member449909584od_a_a @ ( product_Pair_a_a @ X7 @ Xa2 ) @ R ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_implies_one_step
% 0.30/0.46 thf(fact_165_subset__mset_Osum__mset__0__iff,axiom,
% 0.30/0.46 ! [M: multiset_multiset_a] :
% 0.30/0.46 ( ( ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ M )
% 0.30/0.46 = zero_zero_multiset_a )
% 0.30/0.46 = ( ! [X5: multiset_a] :
% 0.30/0.46 ( ( member_multiset_a @ X5 @ ( set_mset_multiset_a @ M ) )
% 0.30/0.46 => ( X5 = zero_zero_multiset_a ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_mset.sum_mset_0_iff
% 0.30/0.46 thf(fact_166_mult__cancel__add__mset,axiom,
% 0.30/0.46 ! [S: set_Product_prod_a_a,Uu: a,X8: multiset_a,Y7: multiset_a] :
% 0.30/0.46 ( ( trans_a @ S )
% 0.30/0.46 => ( ( irrefl_a @ S )
% 0.30/0.46 => ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( add_mset_a @ Uu @ X8 ) @ ( add_mset_a @ Uu @ Y7 ) ) @ ( mult_a @ S ) )
% 0.30/0.46 = ( member340150864iset_a @ ( produc2037245207iset_a @ X8 @ Y7 ) @ ( mult_a @ S ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel_add_mset
% 0.30/0.46 thf(fact_167_in__mset__fold__plus__iff,axiom,
% 0.30/0.46 ! [X: a,M: multiset_a,NN: multiset_multiset_a] :
% 0.30/0.46 ( ( member_a @ X @ ( set_mset_a @ ( fold_m382157835iset_a @ plus_plus_multiset_a @ M @ NN ) ) )
% 0.30/0.46 = ( ( member_a @ X @ ( set_mset_a @ M ) )
% 0.30/0.46 | ? [N3: multiset_a] :
% 0.30/0.46 ( ( member_multiset_a @ N3 @ ( set_mset_multiset_a @ NN ) )
% 0.30/0.46 & ( member_a @ X @ ( set_mset_a @ N3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mset_fold_plus_iff
% 0.30/0.46 thf(fact_168_union__fold__mset__add__mset,axiom,
% 0.30/0.46 ( plus_plus_multiset_a
% 0.30/0.46 = ( fold_m364285649iset_a @ add_mset_a ) ) ).
% 0.30/0.46
% 0.30/0.46 % union_fold_mset_add_mset
% 0.30/0.46 thf(fact_169_add__mset__replicate__mset__safe,axiom,
% 0.30/0.46 ! [M: multiset_a,A: a] :
% 0.30/0.46 ( ( nO_MAT1617603563iset_a @ zero_zero_multiset_a @ M )
% 0.30/0.46 => ( ( add_mset_a @ A @ M )
% 0.30/0.46 = ( plus_plus_multiset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mset_replicate_mset_safe
% 0.30/0.46 thf(fact_170_subset__mset_Osum__mset__mono,axiom,
% 0.30/0.46 ! [K4: multiset_a,F: a > multiset_a,G: a > multiset_a] :
% 0.30/0.46 ( ! [I4: a] :
% 0.30/0.46 ( ( member_a @ I4 @ ( set_mset_a @ K4 ) )
% 0.30/0.46 => ( subseteq_mset_a @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.30/0.46 => ( subseteq_mset_a @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ F @ K4 ) ) @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ G @ K4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_mset.sum_mset_mono
% 0.30/0.46 thf(fact_171_image__mset__add__mset,axiom,
% 0.30/0.46 ! [F: a > a,A: a,M: multiset_a] :
% 0.30/0.46 ( ( image_mset_a_a @ F @ ( add_mset_a @ A @ M ) )
% 0.30/0.46 = ( add_mset_a @ ( F @ A ) @ ( image_mset_a_a @ F @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % image_mset_add_mset
% 0.30/0.46 thf(fact_172_msed__map__invR,axiom,
% 0.30/0.46 ! [F: a > a,M: multiset_a,B: a,N: multiset_a] :
% 0.30/0.46 ( ( ( image_mset_a_a @ F @ M )
% 0.30/0.46 = ( add_mset_a @ B @ N ) )
% 0.30/0.46 => ? [M1: multiset_a,A4: a] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( add_mset_a @ A4 @ M1 ) )
% 0.30/0.46 & ( ( F @ A4 )
% 0.30/0.46 = B )
% 0.30/0.46 & ( ( image_mset_a_a @ F @ M1 )
% 0.30/0.46 = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % msed_map_invR
% 0.30/0.46 thf(fact_173_msed__map__invL,axiom,
% 0.30/0.46 ! [F: a > a,A: a,M: multiset_a,N: multiset_a] :
% 0.30/0.46 ( ( ( image_mset_a_a @ F @ ( add_mset_a @ A @ M ) )
% 0.30/0.46 = N )
% 0.30/0.46 => ? [N1: multiset_a] :
% 0.30/0.46 ( ( N
% 0.30/0.46 = ( add_mset_a @ ( F @ A ) @ N1 ) )
% 0.30/0.46 & ( ( image_mset_a_a @ F @ M )
% 0.30/0.46 = N1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % msed_map_invL
% 0.30/0.46 thf(fact_174_image__mset__single,axiom,
% 0.30/0.46 ! [F: a > a,X: a] :
% 0.30/0.46 ( ( image_mset_a_a @ F @ ( add_mset_a @ X @ zero_zero_multiset_a ) )
% 0.30/0.46 = ( add_mset_a @ ( F @ X ) @ zero_zero_multiset_a ) ) ).
% 0.30/0.46
% 0.30/0.46 % image_mset_single
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.39/1.48 ---- Embedded in THF ---
% 2.39/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.39/1.48 %%% Generated on Tue Feb 24 08:25:40 EST 2026
% 2.39/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.39/1.48 %%% Logic specification used:
% 2.39/1.48 %%% thf(spec, logic, $$dhol).
% 2.39/1.48
% 2.39/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2DTF30403.p
% See solution above
% 2.39/1.48 ------------------------
% 2.63/1.51 ---- Cleaned THF ---
% 2.63/1.52 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_Itf__a_J_Mt__Multiset__Omultiset_Itf__a_J_J_J,type,
% 2.63/1.52 set_Pr158363655iset_a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(ty_n_t__Product____Type__Oprod_It__Multiset__Omultiset_Itf__a_J_Mt__Multiset__Omultiset_Itf__a_J_J,type,
% 2.63/1.52 produc1127127335iset_a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 2.63/1.52 set_Product_prod_a_a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(ty_n_t__Multiset__Omultiset_It__Multiset__Omultiset_Itf__a_J_J,type,
% 2.63/1.52 multiset_multiset_a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(ty_n_t__Set__Oset_It__Multiset__Omultiset_Itf__a_J_J,type,
% 2.63/1.52 set_multiset_a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 2.63/1.52 product_prod_a_a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 multiset_a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(ty_n_t__Heap__OTree_Itf__a_J,type,
% 2.63/1.52 tree_a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.63/1.52 set_a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(ty_n_tf__a,type,
% 2.63/1.52 a: $tType ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 zero_zero_multiset_a: multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_HOL_ONO__MATCH_001t__Multiset__Omultiset_Itf__a_J_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 nO_MAT1617603563iset_a: multiset_a > multiset_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oleft_001tf__a,type,
% 2.63/1.52 heapIm1140443833left_a: tree_a > tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oright_001tf__a,type,
% 2.63/1.52 heapIm1257206334ight_a: tree_a > tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_OsiftDown_001tf__a,type,
% 2.63/1.52 heapIm1091024090Down_a: tree_a > tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Heap_OTree_OE_001tf__a,type,
% 2.63/1.52 e_a: tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Heap_OTree_OT_001tf__a,type,
% 2.63/1.52 t_a: a > tree_a > tree_a > tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Heap_OTree_Orel__Tree_001tf__a_001tf__a,type,
% 2.63/1.52 rel_Tree_a_a: ( a > a > $o ) > tree_a > tree_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Heap_Oin__tree_001tf__a,type,
% 2.63/1.52 in_tree_a: a > tree_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Heap_Ois__heap_001tf__a,type,
% 2.63/1.52 is_heap_a: tree_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Heap_Omultiset_001tf__a,type,
% 2.63/1.52 multiset_a2: tree_a > multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Heap_Oval_001tf__a,type,
% 2.63/1.52 val_a: tree_a > a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001tf__a,type,
% 2.63/1.52 lattic146396397_Max_a: set_a > a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Oadd__mset_001tf__a,type,
% 2.63/1.52 add_mset_a: a > multiset_a > multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Ocomm__monoid__add_Osum__mset_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 comm_m315775925iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Ofold__mset_001t__Multiset__Omultiset_Itf__a_J_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 fold_m382157835iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Ofold__mset_001tf__a_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 fold_m364285649iset_a: ( a > multiset_a > multiset_a ) > multiset_a > multiset_a > multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Oimage__mset_001tf__a_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 image_929116801iset_a: ( a > multiset_a ) > multiset_a > multiset_multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Oimage__mset_001tf__a_001tf__a,type,
% 2.63/1.52 image_mset_a_a: ( a > a ) > multiset_a > multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Omult1_001tf__a,type,
% 2.63/1.52 mult1_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Omult_001tf__a,type,
% 2.63/1.52 mult_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Oset__mset_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 set_mset_multiset_a: multiset_multiset_a > set_multiset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Oset__mset_001tf__a,type,
% 2.63/1.52 set_mset_a: multiset_a > set_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Multiset_Osubseteq__mset_001tf__a,type,
% 2.63/1.52 subseteq_mset_a: multiset_a > multiset_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mtf__a_J_J,type,
% 2.63/1.52 ord_less_eq_o_o_a: ( $o > $o > a ) > ( $o > $o > a ) > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mtf__a_J,type,
% 2.63/1.52 ord_less_eq_o_a: ( $o > a ) > ( $o > a ) > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Heap__OTree_Itf__a_J_M_062_It__Heap__OTree_Itf__a_J_M_Eo_J_J,type,
% 2.63/1.52 ord_le1530450702ee_a_o: ( tree_a > tree_a > $o ) > ( tree_a > tree_a > $o ) > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 2.63/1.52 ord_less_eq_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 2.63/1.52 ord_less_eq_set_a: set_a > set_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__a,type,
% 2.63/1.52 ord_less_eq_a: a > a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mtf__a_J,type,
% 2.63/1.52 order_Greatest_o_a: ( ( $o > a ) > $o ) > $o > a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Orderings_Oorder__class_OGreatest_001tf__a,type,
% 2.63/1.52 order_Greatest_a: ( a > $o ) > a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Product__Type_OPair_001t__Multiset__Omultiset_Itf__a_J_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 produc2037245207iset_a: multiset_a > multiset_a > produc1127127335iset_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Product__Type_OPair_001tf__a_001tf__a,type,
% 2.63/1.52 product_Pair_a_a: a > a > product_prod_a_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Relation_Oirrefl_001tf__a,type,
% 2.63/1.52 irrefl_a: set_Product_prod_a_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Relation_Otrans_001tf__a,type,
% 2.63/1.52 trans_a: set_Product_prod_a_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.63/1.52 collect_a: ( a > $o ) > set_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_member_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.63/1.52 member_multiset_a: multiset_a > set_multiset_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_member_001t__Product____Type__Oprod_It__Multiset__Omultiset_Itf__a_J_Mt__Multiset__Omultiset_Itf__a_J_J,type,
% 2.63/1.52 member340150864iset_a: produc1127127335iset_a > set_Pr158363655iset_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 2.63/1.52 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_c_member_001tf__a,type,
% 2.63/1.52 member_a: a > set_a > $o ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_l,type,
% 2.63/1.52 l: tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_l1____,type,
% 2.63/1.52 l1: tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_la____,type,
% 2.63/1.52 la: tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_r,type,
% 2.63/1.52 r: tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_r1____,type,
% 2.63/1.52 r1: tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_ra____,type,
% 2.63/1.52 ra: tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_t,type,
% 2.63/1.52 t: tree_a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_v,type,
% 2.63/1.52 v: a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_v1____,type,
% 2.63/1.52 v1: a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_v2____,type,
% 2.63/1.52 v2: a ).
% 2.63/1.52
% 2.63/1.52 thf(sy_v_va____,type,
% 2.63/1.52 va: a ).
% 2.63/1.52
% 2.63/1.52 thf(fact_0__C4_Oprems_C_I2_J,axiom,
% 2.63/1.52 is_heap_a @ ra ).
% 2.63/1.52
% 2.63/1.52 thf(fact_1__C4_Oprems_C_I1_J,axiom,
% 2.63/1.52 is_heap_a @ la ).
% 2.63/1.52
% 2.63/1.52 thf(fact_2_assms_I2_J,axiom,
% 2.63/1.52 is_heap_a @ r ).
% 2.63/1.52
% 2.63/1.52 thf(fact_3_assms_I1_J,axiom,
% 2.63/1.52 is_heap_a @ l ).
% 2.63/1.52
% 2.63/1.52 thf(fact_4_True,axiom,
% 2.63/1.52 ord_less_eq_a @ v1 @ v2 ).
% 2.63/1.52
% 2.63/1.52 thf(fact_5__C4_Oprems_C_I3_J,axiom,
% 2.63/1.52 ( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
% 2.63/1.52 = ( t_a @ va @ la @ ra ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_6_siftDown_Osimps_I2_J,axiom,
% 2.63/1.52 ! [V: a] :
% 2.63/1.52 ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ e_a ) )
% 2.63/1.52 = ( t_a @ V @ e_a @ e_a ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_7_siftDown_Osimps_I1_J,axiom,
% 2.63/1.52 ( ( heapIm1091024090Down_a @ e_a )
% 2.63/1.52 = e_a ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_8_siftDown_Ocases,axiom,
% 2.63/1.52 ! [X: tree_a] :
% 2.63/1.52 ( ( X != e_a )
% 2.63/1.52 => ( ! [V2: a] :
% 2.63/1.52 ( X
% 2.63/1.52 != ( t_a @ V2 @ e_a @ e_a ) )
% 2.63/1.52 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.63/1.52 ( X
% 2.63/1.52 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 2.63/1.52 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.63/1.52 ( X
% 2.63/1.52 != ( t_a @ V2 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 2.63/1.52 => ~ ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 2.63/1.52 ( X
% 2.63/1.52 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_9_assms_I3_J,axiom,
% 2.63/1.52 ( t
% 2.63/1.52 = ( t_a @ v @ l @ r ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_10_is__heap_Osimps_I2_J,axiom,
% 2.63/1.52 ! [V: a] : ( is_heap_a @ ( t_a @ V @ e_a @ e_a ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_11_siftDown__Node,axiom,
% 2.63/1.52 ! [T: tree_a,V: a,L: tree_a,R: tree_a] :
% 2.63/1.52 ( ( T
% 2.63/1.52 = ( t_a @ V @ L @ R ) )
% 2.63/1.52 => ? [L2: tree_a,V3: a,R2: tree_a] :
% 2.63/1.52 ( ( ( heapIm1091024090Down_a @ T )
% 2.63/1.52 = ( t_a @ V3 @ L2 @ R2 ) )
% 2.63/1.52 & ( ord_less_eq_a @ V @ V3 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_12__C4_Ohyps_C,axiom,
% 2.63/1.52 ! [L: tree_a,R: tree_a,V: a] :
% 2.63/1.52 ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v2 )
% 2.63/1.52 => ( ( is_heap_a @ L )
% 2.63/1.52 => ( ( is_heap_a @ R )
% 2.63/1.52 => ( ( ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
% 2.63/1.52 = ( t_a @ V @ L @ R ) )
% 2.63/1.52 => ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_13_Tree_Oinject,axiom,
% 2.63/1.52 ! [X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 2.63/1.52 ( ( ( t_a @ X21 @ X22 @ X23 )
% 2.63/1.52 = ( t_a @ Y21 @ Y22 @ Y23 ) )
% 2.63/1.52 = ( ( X21 = Y21 )
% 2.63/1.52 & ( X22 = Y22 )
% 2.63/1.52 & ( X23 = Y23 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_14_is__heap_Osimps_I1_J,axiom,
% 2.63/1.52 is_heap_a @ e_a ).
% 2.63/1.52
% 2.63/1.52 thf(fact_15_Tree_Odistinct_I1_J,axiom,
% 2.63/1.52 ! [X21: a,X22: tree_a,X23: tree_a] :
% 2.63/1.52 ( e_a
% 2.63/1.52 != ( t_a @ X21 @ X22 @ X23 ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_16_Tree_Oinduct,axiom,
% 2.63/1.52 ! [P: tree_a > $o,Tree: tree_a] :
% 2.63/1.52 ( ( P @ e_a )
% 2.63/1.52 => ( ! [X1: a,X2: tree_a,X3: tree_a] :
% 2.63/1.52 ( ( P @ X2 )
% 2.63/1.52 => ( ( P @ X3 )
% 2.63/1.52 => ( P @ ( t_a @ X1 @ X2 @ X3 ) ) ) )
% 2.63/1.52 => ( P @ Tree ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_17_Tree_Oexhaust,axiom,
% 2.63/1.52 ! [Y: tree_a] :
% 2.63/1.52 ( ( Y != e_a )
% 2.63/1.52 => ~ ! [X212: a,X222: tree_a,X232: tree_a] :
% 2.63/1.52 ( Y
% 2.63/1.52 != ( t_a @ X212 @ X222 @ X232 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_18_is__heap_Ocases,axiom,
% 2.63/1.52 ! [X: tree_a] :
% 2.63/1.52 ( ( X != e_a )
% 2.63/1.52 => ( ! [V2: a] :
% 2.63/1.52 ( X
% 2.63/1.52 != ( t_a @ V2 @ e_a @ e_a ) )
% 2.63/1.52 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.63/1.52 ( X
% 2.63/1.52 != ( t_a @ V2 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 2.63/1.52 => ( ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.63/1.52 ( X
% 2.63/1.52 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 2.63/1.52 => ~ ! [V2: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 2.63/1.52 ( X
% 2.63/1.52 != ( t_a @ V2 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_19_siftDown__in__tree__set,axiom,
% 2.63/1.52 ( in_tree_a
% 2.63/1.52 = ( ^ [V4: a,T2: tree_a] : ( in_tree_a @ V4 @ ( heapIm1091024090Down_a @ T2 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_20_left_Osimps,axiom,
% 2.63/1.52 ! [V: a,L: tree_a,R: tree_a] :
% 2.63/1.52 ( ( heapIm1140443833left_a @ ( t_a @ V @ L @ R ) )
% 2.63/1.52 = L ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_21_is__heap__max,axiom,
% 2.63/1.52 ! [V: a,T: tree_a] :
% 2.63/1.52 ( ( in_tree_a @ V @ T )
% 2.63/1.52 => ( ( is_heap_a @ T )
% 2.63/1.52 => ( ord_less_eq_a @ V @ ( val_a @ T ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_22_val_Osimps,axiom,
% 2.63/1.52 ! [V: a,Uu: tree_a,Uv: tree_a] :
% 2.63/1.52 ( ( val_a @ ( t_a @ V @ Uu @ Uv ) )
% 2.63/1.52 = V ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_23_in__tree_Osimps_I2_J,axiom,
% 2.63/1.52 ! [V: a,V5: a,L: tree_a,R: tree_a] :
% 2.63/1.52 ( ( in_tree_a @ V @ ( t_a @ V5 @ L @ R ) )
% 2.63/1.52 = ( ( V = V5 )
% 2.63/1.52 | ( in_tree_a @ V @ L )
% 2.63/1.52 | ( in_tree_a @ V @ R ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_24_siftDown_Osimps_I5_J,axiom,
% 2.63/1.52 ! [Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 2.63/1.52 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.63/1.52 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 2.63/1.52 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.63/1.52 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) )
% 2.63/1.52 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.63/1.52 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 2.63/1.52 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.63/1.52 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_25_siftDown_Osimps_I6_J,axiom,
% 2.63/1.52 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a,V: a] :
% 2.63/1.52 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.63/1.52 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.63/1.52 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) )
% 2.63/1.52 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.63/1.52 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.63/1.52 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_26_in__tree_Osimps_I1_J,axiom,
% 2.63/1.52 ! [V: a] :
% 2.63/1.52 ~ ( in_tree_a @ V @ e_a ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_27_is__heap_Osimps_I5_J,axiom,
% 2.63/1.52 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 2.63/1.52 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.63/1.52 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.63/1.52 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) )
% 2.63/1.52 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_28_is__heap_Osimps_I6_J,axiom,
% 2.63/1.52 ! [V: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.63/1.52 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 2.63/1.52 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.63/1.52 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_29_siftDown_Osimps_I3_J,axiom,
% 2.63/1.52 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 2.63/1.52 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.63/1.52 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) ) )
% 2.63/1.52 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.63/1.52 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ e_a ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_30_siftDown_Osimps_I4_J,axiom,
% 2.63/1.52 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 2.63/1.52 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 = ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.63/1.52 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_31_siftDown__in__tree,axiom,
% 2.63/1.52 ! [T: tree_a] :
% 2.63/1.52 ( ( T != e_a )
% 2.63/1.52 => ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ T ) ) @ T ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_32_is__heap_Osimps_I3_J,axiom,
% 2.63/1.52 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.63/1.52 ( ( is_heap_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.63/1.52 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_33_is__heap_Osimps_I4_J,axiom,
% 2.63/1.52 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.63/1.52 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.63/1.52 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.63/1.52 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_34_right_Osimps,axiom,
% 2.63/1.52 ! [V: a,L: tree_a,R: tree_a] :
% 2.63/1.52 ( ( heapIm1257206334ight_a @ ( t_a @ V @ L @ R ) )
% 2.63/1.52 = R ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_35_order__refl,axiom,
% 2.63/1.52 ! [X: $o > a] : ( ord_less_eq_o_a @ X @ X ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_36_order__refl,axiom,
% 2.63/1.52 ! [X: a] : ( ord_less_eq_a @ X @ X ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_37_le__funD,axiom,
% 2.63/1.52 ! [F: $o > a,G: $o > a,X: $o] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ F @ G )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_38_le__funE,axiom,
% 2.63/1.52 ! [F: $o > a,G: $o > a,X: $o] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ F @ G )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_39_le__funI,axiom,
% 2.63/1.52 ! [F: $o > a,G: $o > a] :
% 2.63/1.52 ( ! [X4: $o] : ( ord_less_eq_a @ ( F @ X4 ) @ ( G @ X4 ) )
% 2.63/1.52 => ( ord_less_eq_o_a @ F @ G ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_40_le__fun__def,axiom,
% 2.63/1.52 ( ord_less_eq_o_a
% 2.63/1.52 = ( ^ [F2: $o > a,G2: $o > a] :
% 2.63/1.52 ! [X5: $o] : ( ord_less_eq_a @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_41_order__subst1,axiom,
% 2.63/1.52 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ B @ C )
% 2.63/1.52 => ( ! [X4: $o > a,Y2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_42_order__subst1,axiom,
% 2.63/1.52 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 2.63/1.52 => ( ( ord_less_eq_a @ B @ C )
% 2.63/1.52 => ( ! [X4: a,Y2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_43_order__subst1,axiom,
% 2.63/1.52 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ B @ C )
% 2.63/1.52 => ( ! [X4: $o > a,Y2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_44_order__subst1,axiom,
% 2.63/1.52 ! [A: a,F: a > a,B: a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 2.63/1.52 => ( ( ord_less_eq_a @ B @ C )
% 2.63/1.52 => ( ! [X4: a,Y2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_45_order__subst2,axiom,
% 2.63/1.52 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A @ B )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 2.63/1.52 => ( ! [X4: a,Y2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_46_order__subst2,axiom,
% 2.63/1.52 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A @ B )
% 2.63/1.52 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 2.63/1.52 => ( ! [X4: $o > a,Y2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_47_order__subst2,axiom,
% 2.63/1.52 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A @ B )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 2.63/1.52 => ( ! [X4: $o > a,Y2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_48_order__subst2,axiom,
% 2.63/1.52 ! [A: a,B: a,F: a > a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A @ B )
% 2.63/1.52 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 2.63/1.52 => ( ! [X4: a,Y2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_49_verit__la__disequality,axiom,
% 2.63/1.52 ! [A: a,B: a] :
% 2.63/1.52 ( ( A = B )
% 2.63/1.52 | ~ ( ord_less_eq_a @ A @ B )
% 2.63/1.52 | ~ ( ord_less_eq_a @ B @ A ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_50_ord__eq__le__subst,axiom,
% 2.63/1.52 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 2.63/1.52 ( ( A
% 2.63/1.52 = ( F @ B ) )
% 2.63/1.52 => ( ( ord_less_eq_a @ B @ C )
% 2.63/1.52 => ( ! [X4: a,Y2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_51_ord__eq__le__subst,axiom,
% 2.63/1.52 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 2.63/1.52 ( ( A
% 2.63/1.52 = ( F @ B ) )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ B @ C )
% 2.63/1.52 => ( ! [X4: $o > a,Y2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_52_ord__eq__le__subst,axiom,
% 2.63/1.52 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 2.63/1.52 ( ( A
% 2.63/1.52 = ( F @ B ) )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ B @ C )
% 2.63/1.52 => ( ! [X4: $o > a,Y2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_53_ord__eq__le__subst,axiom,
% 2.63/1.52 ! [A: a,F: a > a,B: a,C: a] :
% 2.63/1.52 ( ( A
% 2.63/1.52 = ( F @ B ) )
% 2.63/1.52 => ( ( ord_less_eq_a @ B @ C )
% 2.63/1.52 => ( ! [X4: a,Y2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_54_ord__le__eq__subst,axiom,
% 2.63/1.52 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A @ B )
% 2.63/1.52 => ( ( ( F @ B )
% 2.63/1.52 = C )
% 2.63/1.52 => ( ! [X4: a,Y2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_55_ord__le__eq__subst,axiom,
% 2.63/1.52 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A @ B )
% 2.63/1.52 => ( ( ( F @ B )
% 2.63/1.52 = C )
% 2.63/1.52 => ( ! [X4: $o > a,Y2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_56_ord__le__eq__subst,axiom,
% 2.63/1.52 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A @ B )
% 2.63/1.52 => ( ( ( F @ B )
% 2.63/1.52 = C )
% 2.63/1.52 => ( ! [X4: $o > a,Y2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_57_ord__le__eq__subst,axiom,
% 2.63/1.52 ! [A: a,B: a,F: a > a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A @ B )
% 2.63/1.52 => ( ( ( F @ B )
% 2.63/1.52 = C )
% 2.63/1.52 => ( ! [X4: a,Y2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X4 @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.63/1.52 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_58_mem__Collect__eq,axiom,
% 2.63/1.52 ! [A: a,P: a > $o] :
% 2.63/1.52 ( ( member_a @ A @ ( collect_a @ P ) )
% 2.63/1.52 = ( P @ A ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_59_Collect__mem__eq,axiom,
% 2.63/1.52 ! [A2: set_a] :
% 2.63/1.52 ( ( collect_a
% 2.63/1.52 @ ^ [X5: a] : ( member_a @ X5 @ A2 ) )
% 2.63/1.52 = A2 ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_60_dual__order_Oantisym,axiom,
% 2.63/1.52 ! [B: $o > a,A: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ B @ A )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ A @ B )
% 2.63/1.52 => ( A = B ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_61_dual__order_Oantisym,axiom,
% 2.63/1.52 ! [B: a,A: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ B @ A )
% 2.63/1.52 => ( ( ord_less_eq_a @ A @ B )
% 2.63/1.52 => ( A = B ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_62_dual__order_Oeq__iff,axiom,
% 2.63/1.52 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 2.63/1.52 = ( ^ [A3: $o > a,B2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ B2 @ A3 )
% 2.63/1.52 & ( ord_less_eq_o_a @ A3 @ B2 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_63_dual__order_Oeq__iff,axiom,
% 2.63/1.52 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 2.63/1.52 = ( ^ [A3: a,B2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ B2 @ A3 )
% 2.63/1.52 & ( ord_less_eq_a @ A3 @ B2 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_64_dual__order_Otrans,axiom,
% 2.63/1.52 ! [B: $o > a,A: $o > a,C: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ B @ A )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ C @ B )
% 2.63/1.52 => ( ord_less_eq_o_a @ C @ A ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_65_dual__order_Otrans,axiom,
% 2.63/1.52 ! [B: a,A: a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ B @ A )
% 2.63/1.52 => ( ( ord_less_eq_a @ C @ B )
% 2.63/1.52 => ( ord_less_eq_a @ C @ A ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_66_linorder__wlog,axiom,
% 2.63/1.52 ! [P: a > a > $o,A: a,B: a] :
% 2.63/1.52 ( ! [A4: a,B3: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A4 @ B3 )
% 2.63/1.52 => ( P @ A4 @ B3 ) )
% 2.63/1.52 => ( ! [A4: a,B3: a] :
% 2.63/1.52 ( ( P @ B3 @ A4 )
% 2.63/1.52 => ( P @ A4 @ B3 ) )
% 2.63/1.52 => ( P @ A @ B ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_67_dual__order_Orefl,axiom,
% 2.63/1.52 ! [A: $o > a] : ( ord_less_eq_o_a @ A @ A ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_68_dual__order_Orefl,axiom,
% 2.63/1.52 ! [A: a] : ( ord_less_eq_a @ A @ A ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_69_order__trans,axiom,
% 2.63/1.52 ! [X: $o > a,Y: $o > a,Z2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X @ Y )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ Y @ Z2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ X @ Z2 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_70_order__trans,axiom,
% 2.63/1.52 ! [X: a,Y: a,Z2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X @ Y )
% 2.63/1.52 => ( ( ord_less_eq_a @ Y @ Z2 )
% 2.63/1.52 => ( ord_less_eq_a @ X @ Z2 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_71_order__class_Oorder_Oantisym,axiom,
% 2.63/1.52 ! [A: $o > a,B: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A @ B )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ B @ A )
% 2.63/1.52 => ( A = B ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_72_order__class_Oorder_Oantisym,axiom,
% 2.63/1.52 ! [A: a,B: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A @ B )
% 2.63/1.52 => ( ( ord_less_eq_a @ B @ A )
% 2.63/1.52 => ( A = B ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_73_ord__le__eq__trans,axiom,
% 2.63/1.52 ! [A: $o > a,B: $o > a,C: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A @ B )
% 2.63/1.52 => ( ( B = C )
% 2.63/1.52 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_74_ord__le__eq__trans,axiom,
% 2.63/1.52 ! [A: a,B: a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A @ B )
% 2.63/1.52 => ( ( B = C )
% 2.63/1.52 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_75_ord__eq__le__trans,axiom,
% 2.63/1.52 ! [A: $o > a,B: $o > a,C: $o > a] :
% 2.63/1.52 ( ( A = B )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ B @ C )
% 2.63/1.52 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_76_ord__eq__le__trans,axiom,
% 2.63/1.52 ! [A: a,B: a,C: a] :
% 2.63/1.52 ( ( A = B )
% 2.63/1.52 => ( ( ord_less_eq_a @ B @ C )
% 2.63/1.52 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_77_order__class_Oorder_Oeq__iff,axiom,
% 2.63/1.52 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 2.63/1.52 = ( ^ [A3: $o > a,B2: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A3 @ B2 )
% 2.63/1.52 & ( ord_less_eq_o_a @ B2 @ A3 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_78_order__class_Oorder_Oeq__iff,axiom,
% 2.63/1.52 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 2.63/1.52 = ( ^ [A3: a,B2: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A3 @ B2 )
% 2.63/1.52 & ( ord_less_eq_a @ B2 @ A3 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_79_antisym__conv,axiom,
% 2.63/1.52 ! [Y: $o > a,X: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ Y @ X )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ X @ Y )
% 2.63/1.52 = ( X = Y ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_80_antisym__conv,axiom,
% 2.63/1.52 ! [Y: a,X: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ Y @ X )
% 2.63/1.52 => ( ( ord_less_eq_a @ X @ Y )
% 2.63/1.52 = ( X = Y ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_81_le__cases3,axiom,
% 2.63/1.52 ! [X: a,Y: a,Z2: a] :
% 2.63/1.52 ( ( ( ord_less_eq_a @ X @ Y )
% 2.63/1.52 => ~ ( ord_less_eq_a @ Y @ Z2 ) )
% 2.63/1.52 => ( ( ( ord_less_eq_a @ Y @ X )
% 2.63/1.52 => ~ ( ord_less_eq_a @ X @ Z2 ) )
% 2.63/1.52 => ( ( ( ord_less_eq_a @ X @ Z2 )
% 2.63/1.52 => ~ ( ord_less_eq_a @ Z2 @ Y ) )
% 2.63/1.52 => ( ( ( ord_less_eq_a @ Z2 @ Y )
% 2.63/1.52 => ~ ( ord_less_eq_a @ Y @ X ) )
% 2.63/1.52 => ( ( ( ord_less_eq_a @ Y @ Z2 )
% 2.63/1.52 => ~ ( ord_less_eq_a @ Z2 @ X ) )
% 2.63/1.52 => ~ ( ( ord_less_eq_a @ Z2 @ X )
% 2.63/1.52 => ~ ( ord_less_eq_a @ X @ Y ) ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_82_order_Otrans,axiom,
% 2.63/1.52 ! [A: $o > a,B: $o > a,C: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ A @ B )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ B @ C )
% 2.63/1.52 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_83_order_Otrans,axiom,
% 2.63/1.52 ! [A: a,B: a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ A @ B )
% 2.63/1.52 => ( ( ord_less_eq_a @ B @ C )
% 2.63/1.52 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_84_le__cases,axiom,
% 2.63/1.52 ! [X: a,Y: a] :
% 2.63/1.52 ( ~ ( ord_less_eq_a @ X @ Y )
% 2.63/1.52 => ( ord_less_eq_a @ Y @ X ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_85_eq__refl,axiom,
% 2.63/1.52 ! [X: $o > a,Y: $o > a] :
% 2.63/1.52 ( ( X = Y )
% 2.63/1.52 => ( ord_less_eq_o_a @ X @ Y ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_86_eq__refl,axiom,
% 2.63/1.52 ! [X: a,Y: a] :
% 2.63/1.52 ( ( X = Y )
% 2.63/1.52 => ( ord_less_eq_a @ X @ Y ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_87_linear,axiom,
% 2.63/1.52 ! [X: a,Y: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X @ Y )
% 2.63/1.52 | ( ord_less_eq_a @ Y @ X ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_88_antisym,axiom,
% 2.63/1.52 ! [X: $o > a,Y: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X @ Y )
% 2.63/1.52 => ( ( ord_less_eq_o_a @ Y @ X )
% 2.63/1.52 => ( X = Y ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_89_antisym,axiom,
% 2.63/1.52 ! [X: a,Y: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X @ Y )
% 2.63/1.52 => ( ( ord_less_eq_a @ Y @ X )
% 2.63/1.52 => ( X = Y ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_90_eq__iff,axiom,
% 2.63/1.52 ( ( ^ [Y3: $o > a,Z: $o > a] : ( Y3 = Z ) )
% 2.63/1.52 = ( ^ [X5: $o > a,Y4: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 2.63/1.52 & ( ord_less_eq_o_a @ Y4 @ X5 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_91_eq__iff,axiom,
% 2.63/1.52 ( ( ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 2.63/1.52 = ( ^ [X5: a,Y4: a] :
% 2.63/1.52 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.63/1.52 & ( ord_less_eq_a @ Y4 @ X5 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_92_Greatest__equality,axiom,
% 2.63/1.52 ! [P: ( $o > a ) > $o,X: $o > a] :
% 2.63/1.52 ( ( P @ X )
% 2.63/1.52 => ( ! [Y2: $o > a] :
% 2.63/1.52 ( ( P @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ Y2 @ X ) )
% 2.63/1.52 => ( ( order_Greatest_o_a @ P )
% 2.63/1.52 = X ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_93_Greatest__equality,axiom,
% 2.63/1.52 ! [P: a > $o,X: a] :
% 2.63/1.52 ( ( P @ X )
% 2.63/1.52 => ( ! [Y2: a] :
% 2.63/1.52 ( ( P @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ Y2 @ X ) )
% 2.63/1.52 => ( ( order_Greatest_a @ P )
% 2.63/1.52 = X ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_94_GreatestI2__order,axiom,
% 2.63/1.52 ! [P: ( $o > a ) > $o,X: $o > a,Q: ( $o > a ) > $o] :
% 2.63/1.52 ( ( P @ X )
% 2.63/1.52 => ( ! [Y2: $o > a] :
% 2.63/1.52 ( ( P @ Y2 )
% 2.63/1.52 => ( ord_less_eq_o_a @ Y2 @ X ) )
% 2.63/1.52 => ( ! [X4: $o > a] :
% 2.63/1.52 ( ( P @ X4 )
% 2.63/1.52 => ( ! [Y5: $o > a] :
% 2.63/1.52 ( ( P @ Y5 )
% 2.63/1.52 => ( ord_less_eq_o_a @ Y5 @ X4 ) )
% 2.63/1.52 => ( Q @ X4 ) ) )
% 2.63/1.52 => ( Q @ ( order_Greatest_o_a @ P ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_95_GreatestI2__order,axiom,
% 2.63/1.52 ! [P: a > $o,X: a,Q: a > $o] :
% 2.63/1.52 ( ( P @ X )
% 2.63/1.52 => ( ! [Y2: a] :
% 2.63/1.52 ( ( P @ Y2 )
% 2.63/1.52 => ( ord_less_eq_a @ Y2 @ X ) )
% 2.63/1.52 => ( ! [X4: a] :
% 2.63/1.52 ( ( P @ X4 )
% 2.63/1.52 => ( ! [Y5: a] :
% 2.63/1.52 ( ( P @ Y5 )
% 2.63/1.52 => ( ord_less_eq_a @ Y5 @ X4 ) )
% 2.63/1.52 => ( Q @ X4 ) ) )
% 2.63/1.52 => ( Q @ ( order_Greatest_a @ P ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_96_le__rel__bool__arg__iff,axiom,
% 2.63/1.52 ( ord_less_eq_o_o_a
% 2.63/1.52 = ( ^ [X6: $o > $o > a,Y6: $o > $o > a] :
% 2.63/1.52 ( ( ord_less_eq_o_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 2.63/1.52 & ( ord_less_eq_o_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_97_le__rel__bool__arg__iff,axiom,
% 2.63/1.52 ( ord_less_eq_o_a
% 2.63/1.52 = ( ^ [X6: $o > a,Y6: $o > a] :
% 2.63/1.52 ( ( ord_less_eq_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 2.63/1.52 & ( ord_less_eq_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_98_Tree_Orel__induct,axiom,
% 2.63/1.52 ! [R3: a > a > $o,X: tree_a,Y: tree_a,Q: tree_a > tree_a > $o] :
% 2.63/1.52 ( ( rel_Tree_a_a @ R3 @ X @ Y )
% 2.63/1.52 => ( ( Q @ e_a @ e_a )
% 2.63/1.52 => ( ! [A21: a,A22: tree_a,A23: tree_a,B21: a,B22: tree_a,B23: tree_a] :
% 2.63/1.52 ( ( R3 @ A21 @ B21 )
% 2.63/1.52 => ( ( Q @ A22 @ B22 )
% 2.63/1.52 => ( ( Q @ A23 @ B23 )
% 2.63/1.52 => ( Q @ ( t_a @ A21 @ A22 @ A23 ) @ ( t_a @ B21 @ B22 @ B23 ) ) ) ) )
% 2.63/1.52 => ( Q @ X @ Y ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_99_Tree_Orel__mono,axiom,
% 2.63/1.52 ! [R3: a > a > $o,Ra: a > a > $o] :
% 2.63/1.52 ( ( ord_less_eq_a_a_o @ R3 @ Ra )
% 2.63/1.52 => ( ord_le1530450702ee_a_o @ ( rel_Tree_a_a @ R3 ) @ ( rel_Tree_a_a @ Ra ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_100_Tree_Orel__eq,axiom,
% 2.63/1.52 ( ( rel_Tree_a_a
% 2.63/1.52 @ ^ [Y3: a,Z: a] : ( Y3 = Z ) )
% 2.63/1.52 = ( ^ [Y3: tree_a,Z: tree_a] : ( Y3 = Z ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_101_Tree_Orel__refl,axiom,
% 2.63/1.52 ! [Ra: a > a > $o,X: tree_a] :
% 2.63/1.52 ( ! [X4: a] : ( Ra @ X4 @ X4 )
% 2.63/1.52 => ( rel_Tree_a_a @ Ra @ X @ X ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_102_Tree_Orel__inject_I2_J,axiom,
% 2.63/1.52 ! [R3: a > a > $o,X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 2.63/1.52 ( ( rel_Tree_a_a @ R3 @ ( t_a @ X21 @ X22 @ X23 ) @ ( t_a @ Y21 @ Y22 @ Y23 ) )
% 2.63/1.52 = ( ( R3 @ X21 @ Y21 )
% 2.63/1.52 & ( rel_Tree_a_a @ R3 @ X22 @ Y22 )
% 2.63/1.52 & ( rel_Tree_a_a @ R3 @ X23 @ Y23 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_103_Tree_Orel__intros_I2_J,axiom,
% 2.63/1.52 ! [R3: a > a > $o,X21: a,Y21: a,X22: tree_a,Y22: tree_a,X23: tree_a,Y23: tree_a] :
% 2.63/1.52 ( ( R3 @ X21 @ Y21 )
% 2.63/1.52 => ( ( rel_Tree_a_a @ R3 @ X22 @ Y22 )
% 2.63/1.52 => ( ( rel_Tree_a_a @ R3 @ X23 @ Y23 )
% 2.63/1.52 => ( rel_Tree_a_a @ R3 @ ( t_a @ X21 @ X22 @ X23 ) @ ( t_a @ Y21 @ Y22 @ Y23 ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_104_Tree_Octr__transfer_I1_J,axiom,
% 2.63/1.52 ! [R3: a > a > $o] : ( rel_Tree_a_a @ R3 @ e_a @ e_a ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_105_Tree_Orel__distinct_I2_J,axiom,
% 2.63/1.52 ! [R3: a > a > $o,Y21: a,Y22: tree_a,Y23: tree_a] :
% 2.63/1.52 ~ ( rel_Tree_a_a @ R3 @ ( t_a @ Y21 @ Y22 @ Y23 ) @ e_a ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_106_Tree_Orel__distinct_I1_J,axiom,
% 2.63/1.52 ! [R3: a > a > $o,Y21: a,Y22: tree_a,Y23: tree_a] :
% 2.63/1.52 ~ ( rel_Tree_a_a @ R3 @ e_a @ ( t_a @ Y21 @ Y22 @ Y23 ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_107_Tree_Orel__cases,axiom,
% 2.63/1.52 ! [R3: a > a > $o,A: tree_a,B: tree_a] :
% 2.63/1.52 ( ( rel_Tree_a_a @ R3 @ A @ B )
% 2.63/1.52 => ( ( ( A = e_a )
% 2.63/1.52 => ( B != e_a ) )
% 2.63/1.52 => ~ ! [X1: a,X2: tree_a,X3: tree_a] :
% 2.63/1.52 ( ( A
% 2.63/1.52 = ( t_a @ X1 @ X2 @ X3 ) )
% 2.63/1.52 => ! [Y1: a,Y24: tree_a,Y32: tree_a] :
% 2.63/1.52 ( ( B
% 2.63/1.52 = ( t_a @ Y1 @ Y24 @ Y32 ) )
% 2.63/1.52 => ( ( R3 @ X1 @ Y1 )
% 2.63/1.52 => ( ( rel_Tree_a_a @ R3 @ X2 @ Y24 )
% 2.63/1.52 => ~ ( rel_Tree_a_a @ R3 @ X3 @ Y32 ) ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_108_heap__top__geq,axiom,
% 2.63/1.52 ! [A: a,T: tree_a] :
% 2.63/1.52 ( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ T ) ) )
% 2.63/1.52 => ( ( is_heap_a @ T )
% 2.63/1.52 => ( ord_less_eq_a @ A @ ( val_a @ T ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_109_add__mset__add__mset__same__iff,axiom,
% 2.63/1.52 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 2.63/1.52 ( ( ( add_mset_a @ A @ A2 )
% 2.63/1.52 = ( add_mset_a @ A @ B4 ) )
% 2.63/1.52 = ( A2 = B4 ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_110_multi__self__add__other__not__self,axiom,
% 2.63/1.52 ! [M: multiset_a,X: a] :
% 2.63/1.52 ( M
% 2.63/1.52 != ( add_mset_a @ X @ M ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_111_mset__add,axiom,
% 2.63/1.52 ! [A: a,A2: multiset_a] :
% 2.63/1.52 ( ( member_a @ A @ ( set_mset_a @ A2 ) )
% 2.63/1.52 => ~ ! [B5: multiset_a] :
% 2.63/1.52 ( A2
% 2.63/1.52 != ( add_mset_a @ A @ B5 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_112_multi__member__split,axiom,
% 2.63/1.52 ! [X: a,M: multiset_a] :
% 2.63/1.52 ( ( member_a @ X @ ( set_mset_a @ M ) )
% 2.63/1.52 => ? [A5: multiset_a] :
% 2.63/1.52 ( M
% 2.63/1.52 = ( add_mset_a @ X @ A5 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_113_add__mset__commute,axiom,
% 2.63/1.52 ! [X: a,Y: a,M: multiset_a] :
% 2.63/1.52 ( ( add_mset_a @ X @ ( add_mset_a @ Y @ M ) )
% 2.63/1.52 = ( add_mset_a @ Y @ ( add_mset_a @ X @ M ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_114_add__eq__conv__ex,axiom,
% 2.63/1.52 ! [A: a,M: multiset_a,B: a,N: multiset_a] :
% 2.63/1.52 ( ( ( add_mset_a @ A @ M )
% 2.63/1.52 = ( add_mset_a @ B @ N ) )
% 2.63/1.52 = ( ( ( M = N )
% 2.63/1.52 & ( A = B ) )
% 2.63/1.52 | ? [K: multiset_a] :
% 2.63/1.52 ( ( M
% 2.63/1.52 = ( add_mset_a @ B @ K ) )
% 2.63/1.52 & ( N
% 2.63/1.52 = ( add_mset_a @ A @ K ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_115_union__single__eq__member,axiom,
% 2.63/1.52 ! [X: a,M: multiset_a,N: multiset_a] :
% 2.63/1.52 ( ( ( add_mset_a @ X @ M )
% 2.63/1.52 = N )
% 2.63/1.52 => ( member_a @ X @ ( set_mset_a @ N ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_116_insert__noteq__member,axiom,
% 2.63/1.52 ! [B: a,B4: multiset_a,C: a,C2: multiset_a] :
% 2.63/1.52 ( ( ( add_mset_a @ B @ B4 )
% 2.63/1.52 = ( add_mset_a @ C @ C2 ) )
% 2.63/1.52 => ( ( B != C )
% 2.63/1.52 => ( member_a @ C @ ( set_mset_a @ B4 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_117_heap__top__max,axiom,
% 2.63/1.52 ! [T: tree_a] :
% 2.63/1.52 ( ( T != e_a )
% 2.63/1.52 => ( ( is_heap_a @ T )
% 2.63/1.52 => ( ( val_a @ T )
% 2.63/1.52 = ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ T ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_118_multiset__induct__max,axiom,
% 2.63/1.52 ! [P: multiset_a > $o,M: multiset_a] :
% 2.63/1.52 ( ( P @ zero_zero_multiset_a )
% 2.63/1.52 => ( ! [X4: a,M2: multiset_a] :
% 2.63/1.52 ( ( P @ M2 )
% 2.63/1.52 => ( ! [Xa: a] :
% 2.63/1.52 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 2.63/1.52 => ( ord_less_eq_a @ Xa @ X4 ) )
% 2.63/1.52 => ( P @ ( add_mset_a @ X4 @ M2 ) ) ) )
% 2.63/1.52 => ( P @ M ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_119_multiset__induct__min,axiom,
% 2.63/1.52 ! [P: multiset_a > $o,M: multiset_a] :
% 2.63/1.52 ( ( P @ zero_zero_multiset_a )
% 2.63/1.52 => ( ! [X4: a,M2: multiset_a] :
% 2.63/1.52 ( ( P @ M2 )
% 2.63/1.52 => ( ! [Xa: a] :
% 2.63/1.52 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 2.63/1.52 => ( ord_less_eq_a @ X4 @ Xa ) )
% 2.63/1.52 => ( P @ ( add_mset_a @ X4 @ M2 ) ) ) )
% 2.63/1.52 => ( P @ M ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_120_add__mset__eq__singleton__iff,axiom,
% 2.63/1.52 ! [X: a,M: multiset_a,Y: a] :
% 2.63/1.52 ( ( ( add_mset_a @ X @ M )
% 2.63/1.52 = ( add_mset_a @ Y @ zero_zero_multiset_a ) )
% 2.63/1.52 = ( ( M = zero_zero_multiset_a )
% 2.63/1.52 & ( X = Y ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_121_single__eq__add__mset,axiom,
% 2.63/1.52 ! [A: a,B: a,M: multiset_a] :
% 2.63/1.52 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 2.63/1.52 = ( add_mset_a @ B @ M ) )
% 2.63/1.52 = ( ( B = A )
% 2.63/1.52 & ( M = zero_zero_multiset_a ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_122_add__mset__eq__single,axiom,
% 2.63/1.52 ! [B: a,M: multiset_a,A: a] :
% 2.63/1.52 ( ( ( add_mset_a @ B @ M )
% 2.63/1.52 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 2.63/1.52 = ( ( B = A )
% 2.63/1.52 & ( M = zero_zero_multiset_a ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_123_single__eq__single,axiom,
% 2.63/1.52 ! [A: a,B: a] :
% 2.63/1.52 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 2.63/1.52 = ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 2.63/1.52 = ( A = B ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_124_multiset__cases,axiom,
% 2.63/1.52 ! [M: multiset_a] :
% 2.63/1.52 ( ( M != zero_zero_multiset_a )
% 2.63/1.52 => ~ ! [X4: a,N2: multiset_a] :
% 2.63/1.52 ( M
% 2.63/1.52 != ( add_mset_a @ X4 @ N2 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_125_multiset__induct,axiom,
% 2.63/1.52 ! [P: multiset_a > $o,M: multiset_a] :
% 2.63/1.52 ( ( P @ zero_zero_multiset_a )
% 2.63/1.52 => ( ! [X4: a,M2: multiset_a] :
% 2.63/1.52 ( ( P @ M2 )
% 2.63/1.52 => ( P @ ( add_mset_a @ X4 @ M2 ) ) )
% 2.63/1.52 => ( P @ M ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_126_multiset__induct2,axiom,
% 2.63/1.52 ! [P: multiset_a > multiset_a > $o,M: multiset_a,N: multiset_a] :
% 2.63/1.52 ( ( P @ zero_zero_multiset_a @ zero_zero_multiset_a )
% 2.63/1.52 => ( ! [A4: a,M2: multiset_a,N2: multiset_a] :
% 2.63/1.52 ( ( P @ M2 @ N2 )
% 2.63/1.52 => ( P @ ( add_mset_a @ A4 @ M2 ) @ N2 ) )
% 2.63/1.52 => ( ! [A4: a,M2: multiset_a,N2: multiset_a] :
% 2.63/1.52 ( ( P @ M2 @ N2 )
% 2.63/1.52 => ( P @ M2 @ ( add_mset_a @ A4 @ N2 ) ) )
% 2.63/1.52 => ( P @ M @ N ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_127_empty__not__add__mset,axiom,
% 2.63/1.52 ! [A: a,A2: multiset_a] :
% 2.63/1.52 ( zero_zero_multiset_a
% 2.63/1.52 != ( add_mset_a @ A @ A2 ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_128_multiset__nonemptyE,axiom,
% 2.63/1.52 ! [A2: multiset_a] :
% 2.63/1.52 ( ( A2 != zero_zero_multiset_a )
% 2.63/1.52 => ~ ! [X4: a] :
% 2.63/1.52 ~ ( member_a @ X4 @ ( set_mset_a @ A2 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_129_multi__nonempty__split,axiom,
% 2.63/1.52 ! [M: multiset_a] :
% 2.63/1.52 ( ( M != zero_zero_multiset_a )
% 2.63/1.52 => ? [A5: multiset_a,A4: a] :
% 2.63/1.52 ( M
% 2.63/1.52 = ( add_mset_a @ A4 @ A5 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_130_multi__member__last,axiom,
% 2.63/1.52 ! [X: a] : ( member_a @ X @ ( set_mset_a @ ( add_mset_a @ X @ zero_zero_multiset_a ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_131_multiset_Osimps_I1_J,axiom,
% 2.63/1.52 ( ( multiset_a2 @ e_a )
% 2.63/1.52 = zero_zero_multiset_a ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_132_multiset_Osimps_I2_J,axiom,
% 2.63/1.52 ! [V: a,L: tree_a,R: tree_a] :
% 2.63/1.52 ( ( multiset_a2 @ ( t_a @ V @ L @ R ) )
% 2.63/1.52 = ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ L ) @ ( add_mset_a @ V @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ R ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_133_single__subset__iff,axiom,
% 2.63/1.52 ! [A: a,M: multiset_a] :
% 2.63/1.52 ( ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ M )
% 2.63/1.52 = ( member_a @ A @ ( set_mset_a @ M ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_134_union__mset__add__mset__left,axiom,
% 2.63/1.52 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 2.63/1.52 ( ( plus_plus_multiset_a @ ( add_mset_a @ A @ A2 ) @ B4 )
% 2.63/1.52 = ( add_mset_a @ A @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_135_union__mset__add__mset__right,axiom,
% 2.63/1.52 ! [A2: multiset_a,A: a,B4: multiset_a] :
% 2.63/1.52 ( ( plus_plus_multiset_a @ A2 @ ( add_mset_a @ A @ B4 ) )
% 2.63/1.52 = ( add_mset_a @ A @ ( plus_plus_multiset_a @ A2 @ B4 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_136_add__mset__subseteq__single__iff,axiom,
% 2.63/1.52 ! [A: a,M: multiset_a,B: a] :
% 2.63/1.52 ( ( subseteq_mset_a @ ( add_mset_a @ A @ M ) @ ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 2.63/1.52 = ( ( M = zero_zero_multiset_a )
% 2.63/1.52 & ( A = B ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_137_verit__sum__simplify,axiom,
% 2.63/1.52 ! [A: multiset_a] :
% 2.63/1.52 ( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
% 2.63/1.52 = A ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_138_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.63/1.52 ! [I: multiset_a,J: multiset_a,K2: multiset_a,L: multiset_a] :
% 2.63/1.52 ( ( ( ord_le1199012836iset_a @ I @ J )
% 2.63/1.52 & ( K2 = L ) )
% 2.63/1.52 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K2 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_139_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.63/1.52 ! [I: multiset_a,J: multiset_a,K2: multiset_a,L: multiset_a] :
% 2.63/1.52 ( ( ( I = J )
% 2.63/1.52 & ( ord_le1199012836iset_a @ K2 @ L ) )
% 2.63/1.52 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K2 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_140_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.63/1.52 ! [I: multiset_a,J: multiset_a,K2: multiset_a,L: multiset_a] :
% 2.63/1.52 ( ( ( ord_le1199012836iset_a @ I @ J )
% 2.63/1.52 & ( ord_le1199012836iset_a @ K2 @ L ) )
% 2.63/1.52 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K2 ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_141_add__mono,axiom,
% 2.63/1.52 ! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
% 2.63/1.52 ( ( ord_le1199012836iset_a @ A @ B )
% 2.63/1.52 => ( ( ord_le1199012836iset_a @ C @ D )
% 2.63/1.52 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_142_add__left__mono,axiom,
% 2.63/1.52 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 2.63/1.52 ( ( ord_le1199012836iset_a @ A @ B )
% 2.63/1.52 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_143_add__right__mono,axiom,
% 2.63/1.52 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 2.63/1.52 ( ( ord_le1199012836iset_a @ A @ B )
% 2.63/1.52 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_144_union__iff,axiom,
% 2.63/1.52 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 2.63/1.52 ( ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ A2 @ B4 ) ) )
% 2.63/1.52 = ( ( member_a @ A @ ( set_mset_a @ A2 ) )
% 2.63/1.52 | ( member_a @ A @ ( set_mset_a @ B4 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_145_mset__subset__eqD,axiom,
% 2.63/1.52 ! [A2: multiset_a,B4: multiset_a,X: a] :
% 2.63/1.52 ( ( subseteq_mset_a @ A2 @ B4 )
% 2.63/1.52 => ( ( member_a @ X @ ( set_mset_a @ A2 ) )
% 2.63/1.52 => ( member_a @ X @ ( set_mset_a @ B4 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_146_mset__subset__eq__add__mset__cancel,axiom,
% 2.63/1.52 ! [A: a,A2: multiset_a,B4: multiset_a] :
% 2.63/1.52 ( ( subseteq_mset_a @ ( add_mset_a @ A @ A2 ) @ ( add_mset_a @ A @ B4 ) )
% 2.63/1.52 = ( subseteq_mset_a @ A2 @ B4 ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_147_set__mset__mono,axiom,
% 2.63/1.52 ! [A2: multiset_a,B4: multiset_a] :
% 2.63/1.52 ( ( subseteq_mset_a @ A2 @ B4 )
% 2.63/1.52 => ( ord_less_eq_set_a @ ( set_mset_a @ A2 ) @ ( set_mset_a @ B4 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_148_single__is__union,axiom,
% 2.63/1.52 ! [A: a,M: multiset_a,N: multiset_a] :
% 2.63/1.52 ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 2.63/1.52 = ( plus_plus_multiset_a @ M @ N ) )
% 2.63/1.52 = ( ( ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 2.63/1.52 = M )
% 2.63/1.52 & ( N = zero_zero_multiset_a ) )
% 2.63/1.52 | ( ( M = zero_zero_multiset_a )
% 2.63/1.52 & ( ( add_mset_a @ A @ zero_zero_multiset_a )
% 2.63/1.52 = N ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_149_union__is__single,axiom,
% 2.63/1.52 ! [M: multiset_a,N: multiset_a,A: a] :
% 2.63/1.52 ( ( ( plus_plus_multiset_a @ M @ N )
% 2.63/1.52 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 2.63/1.52 = ( ( ( M
% 2.63/1.52 = ( add_mset_a @ A @ zero_zero_multiset_a ) )
% 2.63/1.52 & ( N = zero_zero_multiset_a ) )
% 2.63/1.52 | ( ( M = zero_zero_multiset_a )
% 2.63/1.52 & ( N
% 2.63/1.52 = ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_150_add__mset__add__single,axiom,
% 2.63/1.52 ( add_mset_a
% 2.63/1.52 = ( ^ [A3: a,A6: multiset_a] : ( plus_plus_multiset_a @ A6 @ ( add_mset_a @ A3 @ zero_zero_multiset_a ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_151_multi__subset__induct,axiom,
% 2.63/1.52 ! [F3: multiset_a,A2: multiset_a,P: multiset_a > $o] :
% 2.63/1.52 ( ( subseteq_mset_a @ F3 @ A2 )
% 2.63/1.52 => ( ( P @ zero_zero_multiset_a )
% 2.63/1.52 => ( ! [A4: a,F4: multiset_a] :
% 2.63/1.52 ( ( member_a @ A4 @ ( set_mset_a @ A2 ) )
% 2.63/1.52 => ( ( P @ F4 )
% 2.63/1.52 => ( P @ ( add_mset_a @ A4 @ F4 ) ) ) )
% 2.63/1.52 => ( P @ F3 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_152_mset__subset__eq__single,axiom,
% 2.63/1.52 ! [A: a,B4: multiset_a] :
% 2.63/1.52 ( ( member_a @ A @ ( set_mset_a @ B4 ) )
% 2.63/1.52 => ( subseteq_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B4 ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_153_multi__member__skip,axiom,
% 2.63/1.52 ! [X: a,XS: multiset_a,Y: a] :
% 2.63/1.52 ( ( member_a @ X @ ( set_mset_a @ XS ) )
% 2.63/1.52 => ( member_a @ X @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ Y @ zero_zero_multiset_a ) @ XS ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_154_multi__member__this,axiom,
% 2.63/1.52 ! [X: a,XS: multiset_a] : ( member_a @ X @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ X @ zero_zero_multiset_a ) @ XS ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_155_mult1E,axiom,
% 2.63/1.52 ! [N: multiset_a,M: multiset_a,R: set_Product_prod_a_a] :
% 2.63/1.52 ( ( member340150864iset_a @ ( produc2037245207iset_a @ N @ M ) @ ( mult1_a @ R ) )
% 2.63/1.52 => ~ ! [A4: a,M0: multiset_a] :
% 2.63/1.52 ( ( M
% 2.63/1.52 = ( add_mset_a @ A4 @ M0 ) )
% 2.63/1.52 => ! [K3: multiset_a] :
% 2.63/1.52 ( ( N
% 2.63/1.52 = ( plus_plus_multiset_a @ M0 @ K3 ) )
% 2.63/1.52 => ~ ! [B6: a] :
% 2.63/1.52 ( ( member_a @ B6 @ ( set_mset_a @ K3 ) )
% 2.63/1.52 => ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A4 ) @ R ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_156_mult1I,axiom,
% 2.63/1.52 ! [M: multiset_a,A: a,M02: multiset_a,N: multiset_a,K4: multiset_a,R: set_Product_prod_a_a] :
% 2.63/1.52 ( ( M
% 2.63/1.52 = ( add_mset_a @ A @ M02 ) )
% 2.63/1.52 => ( ( N
% 2.63/1.52 = ( plus_plus_multiset_a @ M02 @ K4 ) )
% 2.63/1.52 => ( ! [B3: a] :
% 2.63/1.52 ( ( member_a @ B3 @ ( set_mset_a @ K4 ) )
% 2.63/1.52 => ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A ) @ R ) )
% 2.63/1.52 => ( member340150864iset_a @ ( produc2037245207iset_a @ N @ M ) @ ( mult1_a @ R ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_157_less__add,axiom,
% 2.63/1.52 ! [N: multiset_a,A: a,M02: multiset_a,R: set_Product_prod_a_a] :
% 2.63/1.52 ( ( member340150864iset_a @ ( produc2037245207iset_a @ N @ ( add_mset_a @ A @ M02 ) ) @ ( mult1_a @ R ) )
% 2.63/1.52 => ( ? [M2: multiset_a] :
% 2.63/1.52 ( ( member340150864iset_a @ ( produc2037245207iset_a @ M2 @ M02 ) @ ( mult1_a @ R ) )
% 2.63/1.52 & ( N
% 2.63/1.52 = ( add_mset_a @ A @ M2 ) ) )
% 2.63/1.52 | ? [K3: multiset_a] :
% 2.63/1.52 ( ! [B6: a] :
% 2.63/1.52 ( ( member_a @ B6 @ ( set_mset_a @ K3 ) )
% 2.63/1.52 => ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A ) @ R ) )
% 2.63/1.52 & ( N
% 2.63/1.52 = ( plus_plus_multiset_a @ M02 @ K3 ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_158_subsetI,axiom,
% 2.63/1.52 ! [A2: set_a,B4: set_a] :
% 2.63/1.52 ( ! [X4: a] :
% 2.63/1.52 ( ( member_a @ X4 @ A2 )
% 2.63/1.52 => ( member_a @ X4 @ B4 ) )
% 2.63/1.52 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_159_in__mono,axiom,
% 2.63/1.52 ! [A2: set_a,B4: set_a,X: a] :
% 2.63/1.52 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.63/1.52 => ( ( member_a @ X @ A2 )
% 2.63/1.52 => ( member_a @ X @ B4 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_160_subsetD,axiom,
% 2.63/1.52 ! [A2: set_a,B4: set_a,C: a] :
% 2.63/1.52 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.63/1.52 => ( ( member_a @ C @ A2 )
% 2.63/1.52 => ( member_a @ C @ B4 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_161_subset__eq,axiom,
% 2.63/1.52 ( ord_less_eq_set_a
% 2.63/1.52 = ( ^ [A6: set_a,B7: set_a] :
% 2.63/1.52 ! [X5: a] :
% 2.63/1.52 ( ( member_a @ X5 @ A6 )
% 2.63/1.52 => ( member_a @ X5 @ B7 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_162_subset__iff,axiom,
% 2.63/1.52 ( ord_less_eq_set_a
% 2.63/1.52 = ( ^ [A6: set_a,B7: set_a] :
% 2.63/1.52 ! [T2: a] :
% 2.63/1.52 ( ( member_a @ T2 @ A6 )
% 2.63/1.52 => ( member_a @ T2 @ B7 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_163_one__step__implies__mult,axiom,
% 2.63/1.52 ! [J2: multiset_a,K4: multiset_a,R: set_Product_prod_a_a,I2: multiset_a] :
% 2.63/1.52 ( ( J2 != zero_zero_multiset_a )
% 2.63/1.52 => ( ! [X4: a] :
% 2.63/1.52 ( ( member_a @ X4 @ ( set_mset_a @ K4 ) )
% 2.63/1.52 => ? [Xa: a] :
% 2.63/1.52 ( ( member_a @ Xa @ ( set_mset_a @ J2 ) )
% 2.63/1.52 & ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Xa ) @ R ) ) )
% 2.63/1.52 => ( member340150864iset_a @ ( produc2037245207iset_a @ ( plus_plus_multiset_a @ I2 @ K4 ) @ ( plus_plus_multiset_a @ I2 @ J2 ) ) @ ( mult_a @ R ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_164_mult__implies__one__step,axiom,
% 2.63/1.52 ! [R: set_Product_prod_a_a,M: multiset_a,N: multiset_a] :
% 2.63/1.52 ( ( trans_a @ R )
% 2.63/1.52 => ( ( member340150864iset_a @ ( produc2037245207iset_a @ M @ N ) @ ( mult_a @ R ) )
% 2.63/1.52 => ? [I3: multiset_a,J3: multiset_a] :
% 2.63/1.52 ( ( N
% 2.63/1.52 = ( plus_plus_multiset_a @ I3 @ J3 ) )
% 2.63/1.52 & ? [K3: multiset_a] :
% 2.63/1.52 ( ( M
% 2.63/1.52 = ( plus_plus_multiset_a @ I3 @ K3 ) )
% 2.63/1.52 & ( J3 != zero_zero_multiset_a )
% 2.63/1.52 & ! [X7: a] :
% 2.63/1.52 ( ( member_a @ X7 @ ( set_mset_a @ K3 ) )
% 2.63/1.52 => ? [Xa2: a] :
% 2.63/1.52 ( ( member_a @ Xa2 @ ( set_mset_a @ J3 ) )
% 2.63/1.52 & ( member449909584od_a_a @ ( product_Pair_a_a @ X7 @ Xa2 ) @ R ) ) ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_165_subset__mset_Osum__mset__0__iff,axiom,
% 2.63/1.52 ! [M: multiset_multiset_a] :
% 2.63/1.52 ( ( ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ M )
% 2.63/1.52 = zero_zero_multiset_a )
% 2.63/1.52 = ( ! [X5: multiset_a] :
% 2.63/1.52 ( ( member_multiset_a @ X5 @ ( set_mset_multiset_a @ M ) )
% 2.63/1.52 => ( X5 = zero_zero_multiset_a ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_166_mult__cancel__add__mset,axiom,
% 2.63/1.52 ! [S: set_Product_prod_a_a,Uu: a,X8: multiset_a,Y7: multiset_a] :
% 2.63/1.52 ( ( trans_a @ S )
% 2.63/1.52 => ( ( irrefl_a @ S )
% 2.63/1.52 => ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( add_mset_a @ Uu @ X8 ) @ ( add_mset_a @ Uu @ Y7 ) ) @ ( mult_a @ S ) )
% 2.63/1.52 = ( member340150864iset_a @ ( produc2037245207iset_a @ X8 @ Y7 ) @ ( mult_a @ S ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_167_in__mset__fold__plus__iff,axiom,
% 2.63/1.52 ! [X: a,M: multiset_a,NN: multiset_multiset_a] :
% 2.63/1.52 ( ( member_a @ X @ ( set_mset_a @ ( fold_m382157835iset_a @ plus_plus_multiset_a @ M @ NN ) ) )
% 2.63/1.52 = ( ( member_a @ X @ ( set_mset_a @ M ) )
% 2.63/1.52 | ? [N3: multiset_a] :
% 2.63/1.52 ( ( member_multiset_a @ N3 @ ( set_mset_multiset_a @ NN ) )
% 2.63/1.52 & ( member_a @ X @ ( set_mset_a @ N3 ) ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_168_union__fold__mset__add__mset,axiom,
% 2.63/1.52 ( plus_plus_multiset_a
% 2.63/1.52 = ( fold_m364285649iset_a @ add_mset_a ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_169_add__mset__replicate__mset__safe,axiom,
% 2.63/1.52 ! [M: multiset_a,A: a] :
% 2.63/1.52 ( ( nO_MAT1617603563iset_a @ zero_zero_multiset_a @ M )
% 2.63/1.52 => ( ( add_mset_a @ A @ M )
% 2.63/1.52 = ( plus_plus_multiset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ M ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_170_subset__mset_Osum__mset__mono,axiom,
% 2.63/1.52 ! [K4: multiset_a,F: a > multiset_a,G: a > multiset_a] :
% 2.63/1.52 ( ! [I4: a] :
% 2.63/1.52 ( ( member_a @ I4 @ ( set_mset_a @ K4 ) )
% 2.63/1.52 => ( subseteq_mset_a @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 2.63/1.52 => ( subseteq_mset_a @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ F @ K4 ) ) @ ( comm_m315775925iset_a @ plus_plus_multiset_a @ zero_zero_multiset_a @ ( image_929116801iset_a @ G @ K4 ) ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_171_image__mset__add__mset,axiom,
% 2.63/1.52 ! [F: a > a,A: a,M: multiset_a] :
% 2.63/1.52 ( ( image_mset_a_a @ F @ ( add_mset_a @ A @ M ) )
% 2.63/1.52 = ( add_mset_a @ ( F @ A ) @ ( image_mset_a_a @ F @ M ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_172_msed__map__invR,axiom,
% 2.63/1.52 ! [F: a > a,M: multiset_a,B: a,N: multiset_a] :
% 2.63/1.52 ( ( ( image_mset_a_a @ F @ M )
% 2.63/1.52 = ( add_mset_a @ B @ N ) )
% 2.63/1.52 => ? [M1: multiset_a,A4: a] :
% 2.63/1.52 ( ( M
% 2.63/1.52 = ( add_mset_a @ A4 @ M1 ) )
% 2.63/1.52 & ( ( F @ A4 )
% 2.63/1.52 = B )
% 2.63/1.52 & ( ( image_mset_a_a @ F @ M1 )
% 2.63/1.52 = N ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_173_msed__map__invL,axiom,
% 2.63/1.52 ! [F: a > a,A: a,M: multiset_a,N: multiset_a] :
% 2.63/1.52 ( ( ( image_mset_a_a @ F @ ( add_mset_a @ A @ M ) )
% 2.63/1.52 = N )
% 2.63/1.52 => ? [N1: multiset_a] :
% 2.63/1.52 ( ( N
% 2.63/1.52 = ( add_mset_a @ ( F @ A ) @ N1 ) )
% 2.63/1.52 & ( ( image_mset_a_a @ F @ M )
% 2.63/1.52 = N1 ) ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(fact_174_image__mset__single,axiom,
% 2.63/1.52 ! [F: a > a,X: a] :
% 2.63/1.52 ( ( image_mset_a_a @ F @ ( add_mset_a @ X @ zero_zero_multiset_a ) )
% 2.63/1.52 = ( add_mset_a @ ( F @ X ) @ zero_zero_multiset_a ) ) ).
% 2.63/1.52
% 2.63/1.52 thf(conj_0,conjecture,
% 2.63/1.52 is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ).
% 2.63/1.52 ------------------------
% 2.63/1.54 % (30685)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/2Mi)
% 2.63/1.54 % (30682)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/183Mi)
% 2.63/1.54 % (30683)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/4Mi)
% 2.63/1.55 % (30685)Instruction limit reached!
% 2.63/1.55 % (30685)------------------------------
% 2.63/1.55 % (30685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.55 % (30685)Termination reason: Unknown
% 2.63/1.55 % (30685)Termination phase: shuffling
% 2.63/1.55
% 2.63/1.55 % (30685)Memory used [KB]: 1407
% 2.63/1.55 % (30685)Time elapsed: 0.003 s
% 2.63/1.55 % (30685)Instructions burned: 4 (million)
% 2.63/1.55 % (30685)------------------------------
% 2.63/1.55 % (30685)------------------------------
% 2.63/1.55 % (30683)Instruction limit reached!
% 2.63/1.55 % (30683)------------------------------
% 2.63/1.55 % (30683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.55 % (30683)Termination reason: Unknown
% 2.63/1.55 % (30683)Termination phase: shuffling
% 2.63/1.55
% 2.63/1.55 % (30683)Memory used [KB]: 1407
% 2.63/1.55 % (30683)Time elapsed: 0.003 s
% 2.63/1.55 % (30683)Instructions burned: 6 (million)
% 2.63/1.55 % (30683)------------------------------
% 2.63/1.55 % (30683)------------------------------
% 2.63/1.55 % (30684)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/27Mi)
% 2.63/1.55 % (30686)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/2Mi)
% 2.63/1.55 % (30687)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/275Mi)
% 2.63/1.55 % (30688)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/18Mi)
% 2.63/1.55 % (30686)Instruction limit reached!
% 2.63/1.55 % (30686)------------------------------
% 2.63/1.55 % (30686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.55 % (30686)Termination reason: Unknown
% 2.63/1.55 % (30686)Termination phase: shuffling
% 2.63/1.55
% 2.63/1.55 % (30686)Memory used [KB]: 1279
% 2.63/1.55 % (30686)Time elapsed: 0.004 s
% 2.63/1.55 % (30686)Instructions burned: 3 (million)
% 2.63/1.55 % (30686)------------------------------
% 2.63/1.55 % (30686)------------------------------
% 2.63/1.56 % (30689)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/3Mi)
% 2.63/1.56 % (30689)Instruction limit reached!
% 2.63/1.56 % (30689)------------------------------
% 2.63/1.56 % (30689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.56 % (30689)Termination reason: Unknown
% 2.63/1.56 % (30689)Termination phase: shuffling
% 2.63/1.56
% 2.63/1.56 % (30689)Memory used [KB]: 1279
% 2.63/1.56 % (30689)Time elapsed: 0.002 s
% 2.63/1.56 % (30689)Instructions burned: 3 (million)
% 2.63/1.56 % (30689)------------------------------
% 2.63/1.56 % (30689)------------------------------
% 2.63/1.56 % (30690)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/37Mi)
% 2.63/1.56 % (30688)Instruction limit reached!
% 2.63/1.56 % (30688)------------------------------
% 2.63/1.56 % (30688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.56 % (30688)Termination reason: Unknown
% 2.63/1.56 % (30688)Termination phase: shuffling
% 2.63/1.56
% 2.63/1.56 % (30688)Memory used [KB]: 1535
% 2.63/1.56 % (30688)Time elapsed: 0.013 s
% 2.63/1.56 % (30688)Instructions burned: 18 (million)
% 2.63/1.56 % (30688)------------------------------
% 2.63/1.56 % (30688)------------------------------
% 2.63/1.57 % (30692)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/3Mi)
% 2.63/1.57 % (30692)Instruction limit reached!
% 2.63/1.57 % (30692)------------------------------
% 2.63/1.57 % (30692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.57 % (30692)Termination reason: Unknown
% 2.63/1.57 % (30692)Termination phase: shuffling
% 2.63/1.57
% 2.63/1.57 % (30692)Memory used [KB]: 1279
% 2.63/1.57 % (30692)Time elapsed: 0.002 s
% 2.63/1.57 % (30692)Instructions burned: 3 (million)
% 2.63/1.57 % (30692)------------------------------
% 2.63/1.57 % (30692)------------------------------
% 2.63/1.57 % (30684)Instruction limit reached!
% 2.63/1.57 % (30684)------------------------------
% 2.63/1.57 % (30684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.57 % (30684)Termination reason: Unknown
% 2.63/1.57 % (30684)Termination phase: Property scanning
% 2.63/1.57
% 2.63/1.57 % (30684)Memory used [KB]: 1663
% 2.63/1.57 % (30684)Time elapsed: 0.018 s
% 2.63/1.57 % (30684)Instructions burned: 27 (million)
% 2.63/1.57 % (30684)------------------------------
% 2.63/1.57 % (30684)------------------------------
% 2.63/1.57 % (30690)Instruction limit reached!
% 2.63/1.57 % (30690)------------------------------
% 2.63/1.57 % (30690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.57 % (30690)Termination reason: Unknown
% 2.63/1.57 % (30690)Termination phase: Property scanning
% 2.63/1.57
% 2.63/1.57 % (30690)Memory used [KB]: 2046
% 2.63/1.57 % (30690)Time elapsed: 0.013 s
% 2.63/1.57 % (30690)Instructions burned: 38 (million)
% 2.63/1.57 % (30690)------------------------------
% 2.63/1.57 % (30690)------------------------------
% 2.63/1.57 % (30691)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/15Mi)
% 2.63/1.58 % (30694)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/7Mi)
% 2.63/1.58 % (30693)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/1041Mi)
% 2.63/1.58 % (30696)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/3Mi)
% 2.63/1.58 % (30694)Instruction limit reached!
% 2.63/1.58 % (30694)------------------------------
% 2.63/1.58 % (30694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.58 % (30694)Termination reason: Unknown
% 2.63/1.58 % (30694)Termination phase: shuffling
% 2.63/1.58
% 2.63/1.58 % (30694)Memory used [KB]: 1407
% 2.63/1.58 % (30694)Time elapsed: 0.004 s
% 2.63/1.58 % (30694)Instructions burned: 9 (million)
% 2.63/1.58 % (30694)------------------------------
% 2.63/1.58 % (30694)------------------------------
% 2.63/1.58 % (30696)Instruction limit reached!
% 2.63/1.58 % (30696)------------------------------
% 2.63/1.58 % (30696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.58 % (30696)Termination reason: Unknown
% 2.63/1.58 % (30696)Termination phase: shuffling
% 2.63/1.58
% 2.63/1.58 % (30696)Memory used [KB]: 1279
% 2.63/1.58 % (30696)Time elapsed: 0.003 s
% 2.63/1.58 % (30696)Instructions burned: 3 (million)
% 2.63/1.58 % (30696)------------------------------
% 2.63/1.58 % (30696)------------------------------
% 2.63/1.58 % (30691)Instruction limit reached!
% 2.63/1.58 % (30691)------------------------------
% 2.63/1.58 % (30691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.58 % (30691)Termination reason: Unknown
% 2.63/1.58 % (30691)Termination phase: shuffling
% 2.63/1.58
% 2.63/1.58 % (30691)Memory used [KB]: 1535
% 2.63/1.58 % (30691)Time elapsed: 0.011 s
% 2.63/1.58 % (30691)Instructions burned: 15 (million)
% 2.63/1.58 % (30691)------------------------------
% 2.63/1.58 % (30691)------------------------------
% 2.63/1.59 % (30695)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/16Mi)
% 2.63/1.59 % (30687)Refutation not found, incomplete strategy
% 2.63/1.59 % (30687)------------------------------
% 2.63/1.59 % (30687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.59 % (30687)Termination reason: Refutation not found, incomplete strategy
% 2.63/1.59
% 2.63/1.59
% 2.63/1.59 % (30687)Memory used [KB]: 6396
% 2.63/1.59 % (30687)Time elapsed: 0.037 s
% 2.63/1.59 % (30687)Instructions burned: 63 (million)
% 2.63/1.59 % (30687)------------------------------
% 2.63/1.59 % (30687)------------------------------
% 2.63/1.59 % (30697)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/3Mi)
% 2.63/1.59 % (30697)Instruction limit reached!
% 2.63/1.59 % (30697)------------------------------
% 2.63/1.59 % (30697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.59 % (30697)Termination reason: Unknown
% 2.63/1.59 % (30697)Termination phase: shuffling
% 2.63/1.59
% 2.63/1.59 % (30697)Memory used [KB]: 1279
% 2.63/1.59 % (30697)Time elapsed: 0.002 s
% 2.63/1.59 % (30697)Instructions burned: 3 (million)
% 2.63/1.59 % (30697)------------------------------
% 2.63/1.59 % (30697)------------------------------
% 2.63/1.59 % (30698)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/7Mi)
% 2.63/1.59 % (30698)Instruction limit reached!
% 2.63/1.59 % (30698)------------------------------
% 2.63/1.59 % (30698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.59 % (30698)Termination reason: Unknown
% 2.63/1.59 % (30698)Termination phase: shuffling
% 2.63/1.59
% 2.63/1.59 % (30698)Memory used [KB]: 1407
% 2.63/1.59 % (30698)Time elapsed: 0.004 s
% 2.63/1.59 % (30698)Instructions burned: 7 (million)
% 2.63/1.59 % (30698)------------------------------
% 2.63/1.59 % (30698)------------------------------
% 2.63/1.59 % (30695)Instruction limit reached!
% 2.63/1.59 % (30695)------------------------------
% 2.63/1.59 % (30695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.59 % (30695)Termination reason: Unknown
% 2.63/1.59 % (30695)Termination phase: shuffling
% 2.63/1.59
% 2.63/1.59 % (30695)Memory used [KB]: 1535
% 2.63/1.59 % (30695)Time elapsed: 0.011 s
% 2.63/1.59 % (30695)Instructions burned: 16 (million)
% 2.63/1.59 % (30695)------------------------------
% 2.63/1.59 % (30695)------------------------------
% 2.63/1.59 % (30699)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/3Mi)
% 2.63/1.60 % (30699)Instruction limit reached!
% 2.63/1.60 % (30699)------------------------------
% 2.63/1.60 % (30699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.60 % (30699)Termination reason: Unknown
% 2.63/1.60 % (30699)Termination phase: shuffling
% 2.63/1.60
% 2.63/1.60 % (30699)Memory used [KB]: 1279
% 2.63/1.60 % (30699)Time elapsed: 0.002 s
% 2.63/1.60 % (30699)Instructions burned: 3 (million)
% 2.63/1.60 % (30699)------------------------------
% 2.63/1.60 % (30699)------------------------------
% 2.67/1.60 % (30702)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/710Mi)
% 2.67/1.60 % (30682)Instruction limit reached!
% 2.67/1.60 % (30682)------------------------------
% 2.67/1.60 % (30682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.60 % (30682)Termination reason: Unknown
% 2.67/1.60 % (30682)Termination phase: Saturation
% 2.67/1.60
% 2.67/1.60 % (30682)Memory used [KB]: 7164
% 2.67/1.60 % (30682)Time elapsed: 0.059 s
% 2.67/1.60 % (30682)Instructions burned: 183 (million)
% 2.67/1.60 % (30682)------------------------------
% 2.67/1.60 % (30682)------------------------------
% 2.67/1.61 % (30700)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/4Mi)
% 2.67/1.61 % (30704)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/902Mi)
% 2.67/1.61 % (30701)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/18Mi)
% 2.67/1.61 % (30700)Instruction limit reached!
% 2.67/1.61 % (30700)------------------------------
% 2.67/1.61 % (30700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.61 % (30700)Termination reason: Unknown
% 2.67/1.61 % (30700)Termination phase: shuffling
% 2.67/1.61
% 2.67/1.61 % (30700)Memory used [KB]: 1407
% 2.67/1.61 % (30700)Time elapsed: 0.005 s
% 2.67/1.61 % (30700)Instructions burned: 5 (million)
% 2.67/1.61 % (30700)------------------------------
% 2.67/1.61 % (30700)------------------------------
% 2.67/1.61 % (30703)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/6Mi)
% 2.67/1.61 % (30703)Instruction limit reached!
% 2.67/1.61 % (30703)------------------------------
% 2.67/1.61 % (30703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.61 % (30703)Termination reason: Unknown
% 2.67/1.61 % (30703)Termination phase: shuffling
% 2.67/1.61
% 2.67/1.61 % (30703)Memory used [KB]: 1407
% 2.67/1.61 % (30703)Time elapsed: 0.005 s
% 2.67/1.61 % (30703)Instructions burned: 8 (million)
% 2.67/1.61 % (30703)------------------------------
% 2.67/1.61 % (30703)------------------------------
% 2.67/1.61 % (30705)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/21Mi)
% 2.67/1.62 % (30701)Instruction limit reached!
% 2.67/1.62 % (30701)------------------------------
% 2.67/1.62 % (30701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.62 % (30701)Termination reason: Unknown
% 2.67/1.62 % (30701)Termination phase: shuffling
% 2.67/1.62
% 2.67/1.62 % (30701)Memory used [KB]: 1535
% 2.67/1.62 % (30701)Time elapsed: 0.013 s
% 2.67/1.62 % (30701)Instructions burned: 18 (million)
% 2.67/1.62 % (30701)------------------------------
% 2.67/1.62 % (30701)------------------------------
% 2.67/1.62 % (30705)Instruction limit reached!
% 2.67/1.62 % (30705)------------------------------
% 2.67/1.62 % (30705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.62 % (30705)Termination reason: Unknown
% 2.67/1.62 % (30705)Termination phase: shuffling
% 2.67/1.62
% 2.67/1.62 % (30705)Memory used [KB]: 1663
% 2.67/1.62 % (30705)Time elapsed: 0.009 s
% 2.67/1.62 % (30705)Instructions burned: 21 (million)
% 2.67/1.62 % (30705)------------------------------
% 2.67/1.62 % (30705)------------------------------
% 2.67/1.62 % (30707)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/6Mi)
% 2.67/1.62 % (30707)Instruction limit reached!
% 2.67/1.62 % (30707)------------------------------
% 2.67/1.62 % (30707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.62 % (30707)Termination reason: Unknown
% 2.67/1.62 % (30707)Termination phase: shuffling
% 2.67/1.62
% 2.67/1.62 % (30707)Memory used [KB]: 1407
% 2.67/1.62 % (30707)Time elapsed: 0.004 s
% 2.67/1.62 % (30707)Instructions burned: 8 (million)
% 2.67/1.62 % (30707)------------------------------
% 2.67/1.62 % (30707)------------------------------
% 2.67/1.63 % (30706)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/5Mi)
% 2.67/1.63 % (30706)Instruction limit reached!
% 2.67/1.63 % (30706)------------------------------
% 2.67/1.63 % (30706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.63 % (30706)Termination reason: Unknown
% 2.67/1.63 % (30706)Termination phase: shuffling
% 2.67/1.63
% 2.67/1.63 % (30706)Memory used [KB]: 1407
% 2.67/1.63 % (30706)Time elapsed: 0.005 s
% 2.67/1.63 % (30706)Instructions burned: 6 (million)
% 2.67/1.63 % (30706)------------------------------
% 2.67/1.63 % (30706)------------------------------
% 2.67/1.63 % (30709)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/779Mi)
% 2.67/1.63 % (30710)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/19Mi)
% 2.67/1.64 % (30708)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/377Mi)
% 2.67/1.64 % (30704)Refutation not found, incomplete strategy
% 2.67/1.64 % (30704)------------------------------
% 2.67/1.64 % (30704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.64 % (30704)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.64
% 2.67/1.64
% 2.67/1.64 % (30704)Memory used [KB]: 6908
% 2.67/1.64 % (30704)Time elapsed: 0.032 s
% 2.67/1.64 % (30704)Instructions burned: 104 (million)
% 2.67/1.64 % (30704)------------------------------
% 2.67/1.64 % (30704)------------------------------
% 2.67/1.64 % (30710)Instruction limit reached!
% 2.67/1.64 % (30710)------------------------------
% 2.67/1.64 % (30710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.64 % (30710)Termination reason: Unknown
% 2.67/1.64 % (30710)Termination phase: shuffling
% 2.67/1.64
% 2.67/1.64 % (30710)Memory used [KB]: 1791
% 2.67/1.64 % (30710)Time elapsed: 0.008 s
% 2.67/1.64 % (30710)Instructions burned: 21 (million)
% 2.67/1.64 % (30710)------------------------------
% 2.67/1.64 % (30710)------------------------------
% 2.67/1.65 % (30711)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30403 for (2999ds/879Mi)
% 2.67/1.65 % (30712)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30403 for (2998ds/17Mi)
% 2.67/1.65 % (30713)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30403 for (2998ds/3Mi)
% 2.67/1.65 % (30712)Instruction limit reached!
% 2.67/1.65 % (30712)------------------------------
% 2.67/1.65 % (30712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.65 % (30712)Termination reason: Unknown
% 2.67/1.65 % (30712)Termination phase: shuffling
% 2.67/1.65
% 2.67/1.65 % (30712)Memory used [KB]: 1535
% 2.67/1.65 % (30712)Time elapsed: 0.007 s
% 2.67/1.65 % (30712)Instructions burned: 20 (million)
% 2.67/1.65 % (30712)------------------------------
% 2.67/1.65 % (30712)------------------------------
% 2.67/1.65 % (30713)Instruction limit reached!
% 2.67/1.65 % (30713)------------------------------
% 2.67/1.65 % (30713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.65 % (30713)Termination reason: Unknown
% 2.67/1.65 % (30713)Termination phase: shuffling
% 2.67/1.65
% 2.67/1.65 % (30713)Memory used [KB]: 1279
% 2.67/1.65 % (30713)Time elapsed: 0.003 s
% 2.67/1.65 % (30713)Instructions burned: 4 (million)
% 2.67/1.65 % (30713)------------------------------
% 2.67/1.65 % (30713)------------------------------
% 2.67/1.66 % (30714)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_30403 for (2998ds/30Mi)
% 2.67/1.66 % (30715)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_30403 for (2998ds/127Mi)
% 2.67/1.67 % (30714)Instruction limit reached!
% 2.67/1.67 % (30714)------------------------------
% 2.67/1.67 % (30714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.67 % (30714)Termination reason: Unknown
% 2.67/1.67 % (30714)Termination phase: Property scanning
% 2.67/1.67
% 2.67/1.67 % (30714)Memory used [KB]: 1663
% 2.67/1.67 % (30714)Time elapsed: 0.011 s
% 2.67/1.67 % (30714)Instructions burned: 32 (million)
% 2.67/1.67 % (30714)------------------------------
% 2.67/1.67 % (30714)------------------------------
% 2.67/1.68 % (30716)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_30403 for (2998ds/100Mi)
% 2.67/1.70 % (30715)Instruction limit reached!
% 2.67/1.70 % (30715)------------------------------
% 2.67/1.70 % (30715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.70 % (30715)Termination reason: Unknown
% 2.67/1.70 % (30715)Termination phase: Saturation
% 2.67/1.70
% 2.67/1.70 % (30715)Memory used [KB]: 6908
% 2.67/1.70 % (30715)Time elapsed: 0.041 s
% 2.67/1.70 % (30715)Instructions burned: 128 (million)
% 2.67/1.70 % (30715)------------------------------
% 2.67/1.70 % (30715)------------------------------
% 2.67/1.71 % (30716)Instruction limit reached!
% 2.67/1.71 % (30716)------------------------------
% 2.67/1.71 % (30716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.71 % (30716)Termination reason: Unknown
% 2.67/1.71 % (30716)Termination phase: Property scanning
% 2.67/1.71
% 2.67/1.71 % (30716)Memory used [KB]: 2174
% 2.67/1.71 % (30716)Time elapsed: 0.028 s
% 2.67/1.71 % (30716)Instructions burned: 103 (million)
% 2.67/1.71 % (30716)------------------------------
% 2.67/1.71 % (30716)------------------------------
% 2.67/1.71 % (30717)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_30403 for (2998ds/3Mi)
% 2.67/1.71 % (30717)Instruction limit reached!
% 2.67/1.71 % (30717)------------------------------
% 2.67/1.71 % (30717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.71 % (30717)Termination reason: Unknown
% 2.67/1.71 % (30717)Termination phase: shuffling
% 2.67/1.71
% 2.67/1.71 % (30717)Memory used [KB]: 1279
% 2.67/1.71 % (30717)Time elapsed: 0.003 s
% 2.67/1.71 % (30717)Instructions burned: 4 (million)
% 2.67/1.71 % (30717)------------------------------
% 2.67/1.71 % (30717)------------------------------
% 2.67/1.72 % (30718)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_30403 for (2998ds/20Mi)
% 2.67/1.72 % (30719)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_30403 for (2998ds/86Mi)
% 2.67/1.72 % (30718)Instruction limit reached!
% 2.67/1.72 % (30718)------------------------------
% 2.67/1.72 % (30718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.72 % (30718)Termination reason: Unknown
% 2.67/1.72 % (30718)Termination phase: Property scanning
% 2.67/1.72
% 2.67/1.72 % (30718)Memory used [KB]: 1535
% 2.67/1.72 % (30718)Time elapsed: 0.008 s
% 2.67/1.72 % (30718)Instructions burned: 23 (million)
% 2.67/1.72 % (30718)------------------------------
% 2.67/1.72 % (30718)------------------------------
% 2.67/1.73 % (30720)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_30403 for (2997ds/107Mi)
% 2.67/1.75 % (30719)Instruction limit reached!
% 2.67/1.75 % (30719)------------------------------
% 2.67/1.75 % (30719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.75 % (30719)Termination reason: Unknown
% 2.67/1.75 % (30719)Termination phase: Saturation
% 2.67/1.75
% 2.67/1.75 % (30719)Memory used [KB]: 6524
% 2.67/1.75 % (30719)Time elapsed: 0.027 s
% 2.67/1.75 % (30719)Instructions burned: 86 (million)
% 2.67/1.75 % (30719)------------------------------
% 2.67/1.75 % (30719)------------------------------
% 2.67/1.76 % (30721)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_30403 for (2997ds/39Mi)
% 2.67/1.76 % (30720)Instruction limit reached!
% 2.67/1.76 % (30720)------------------------------
% 2.67/1.76 % (30720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.76 % (30720)Termination reason: Unknown
% 2.67/1.76 % (30720)Termination phase: Saturation
% 2.67/1.76
% 2.67/1.76 % (30720)Memory used [KB]: 6780
% 2.67/1.76 % (30720)Time elapsed: 0.032 s
% 2.67/1.76 % (30720)Instructions burned: 109 (million)
% 2.67/1.76 % (30720)------------------------------
% 2.67/1.76 % (30720)------------------------------
% 2.67/1.77 % (30721)Instruction limit reached!
% 2.67/1.77 % (30721)------------------------------
% 2.67/1.77 % (30721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.77 % (30721)Termination reason: Unknown
% 2.67/1.77 % (30721)Termination phase: Property scanning
% 2.67/1.77
% 2.67/1.77 % (30721)Memory used [KB]: 2046
% 2.67/1.77 % (30721)Time elapsed: 0.013 s
% 2.67/1.77 % (30721)Instructions burned: 40 (million)
% 2.67/1.77 % (30721)------------------------------
% 2.67/1.77 % (30721)------------------------------
% 2.67/1.77 % (30722)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_30403 for (2997ds/448Mi)
% 2.67/1.78 % (30723)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_30403 for (2997ds/46Mi)
% 2.67/1.79 % (30708)Instruction limit reached!
% 2.67/1.79 % (30708)------------------------------
% 2.67/1.79 % (30708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.79 % (30708)Termination reason: Unknown
% 2.67/1.79 % (30708)Termination phase: Saturation
% 2.67/1.79
% 2.67/1.79 % (30708)Memory used [KB]: 7803
% 2.67/1.79 % (30708)Time elapsed: 0.155 s
% 2.67/1.79 % (30708)Instructions burned: 378 (million)
% 2.67/1.79 % (30708)------------------------------
% 2.67/1.79 % (30708)------------------------------
% 2.67/1.79 % (30723)Instruction limit reached!
% 2.67/1.79 % (30723)------------------------------
% 2.67/1.79 % (30723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.79 % (30723)Termination reason: Unknown
% 2.67/1.79 % (30723)Termination phase: Preprocessing 3
% 2.67/1.79
% 2.67/1.79 % (30723)Memory used [KB]: 1791
% 2.67/1.79 % (30723)Time elapsed: 0.016 s
% 2.67/1.79 % (30723)Instructions burned: 46 (million)
% 2.67/1.79 % (30723)------------------------------
% 2.67/1.79 % (30723)------------------------------
% 2.67/1.80 % (30724)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_30403 for (2997ds/98Mi)
% 2.67/1.80 % (30725)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_30403 for (2997ds/507Mi)
% 2.67/1.82 % (30702)Instruction limit reached!
% 2.67/1.82 % (30702)------------------------------
% 2.67/1.82 % (30702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.82 % (30702)Termination reason: Unknown
% 2.67/1.82 % (30702)Termination phase: Saturation
% 2.67/1.82
% 2.67/1.82 % (30702)Memory used [KB]: 7675
% 2.67/1.82 % (30702)Time elapsed: 0.223 s
% 2.67/1.82 % (30702)Instructions burned: 710 (million)
% 2.67/1.82 % (30702)------------------------------
% 2.67/1.82 % (30702)------------------------------
% 2.67/1.83 % (30724)Instruction limit reached!
% 2.67/1.83 % (30724)------------------------------
% 2.67/1.83 % (30724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.83 % (30724)Termination reason: Unknown
% 2.67/1.83 % (30724)Termination phase: Property scanning
% 2.67/1.83
% 2.67/1.83 % (30724)Memory used [KB]: 2174
% 2.67/1.83 % (30724)Time elapsed: 0.029 s
% 2.67/1.83 % (30724)Instructions burned: 100 (million)
% 2.67/1.83 % (30724)------------------------------
% 2.67/1.83 % (30724)------------------------------
% 2.67/1.83 % (30726)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/149Mi)
% 2.67/1.84 % (30727)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/39Mi)
% 2.67/1.84 % (30725)Refutation not found, incomplete strategy
% 2.67/1.84 % (30725)------------------------------
% 2.67/1.84 % (30725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.84 % (30725)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.84
% 2.67/1.84
% 2.67/1.84 % (30725)Memory used [KB]: 7291
% 2.67/1.84 % (30725)Time elapsed: 0.039 s
% 2.67/1.84 % (30725)Instructions burned: 120 (million)
% 2.67/1.84 % (30725)------------------------------
% 2.67/1.84 % (30725)------------------------------
% 2.67/1.85 % (30727)Instruction limit reached!
% 2.67/1.85 % (30727)------------------------------
% 2.67/1.85 % (30727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.85 % (30727)Termination reason: Unknown
% 2.67/1.85 % (30727)Termination phase: Preprocessing 3
% 2.67/1.85
% 2.67/1.85 % (30727)Memory used [KB]: 1918
% 2.67/1.85 % (30727)Time elapsed: 0.015 s
% 2.67/1.85 % (30727)Instructions burned: 42 (million)
% 2.67/1.85 % (30727)------------------------------
% 2.67/1.85 % (30727)------------------------------
% 2.67/1.85 % (30728)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/6Mi)
% 2.67/1.86 % (30728)Instruction limit reached!
% 2.67/1.86 % (30728)------------------------------
% 2.67/1.86 % (30728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.86 % (30728)Termination reason: Unknown
% 2.67/1.86 % (30728)Termination phase: shuffling
% 2.67/1.86
% 2.67/1.86 % (30728)Memory used [KB]: 1407
% 2.67/1.86 % (30728)Time elapsed: 0.004 s
% 2.67/1.86 % (30728)Instructions burned: 8 (million)
% 2.67/1.86 % (30728)------------------------------
% 2.67/1.86 % (30728)------------------------------
% 2.67/1.86 % (30729)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/1087Mi)
% 2.67/1.87 % (30730)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/47Mi)
% 2.67/1.87 % (30709)Instruction limit reached!
% 2.67/1.87 % (30709)------------------------------
% 2.67/1.87 % (30709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.87 % (30709)Termination reason: Unknown
% 2.67/1.87 % (30709)Termination phase: Saturation
% 2.67/1.87
% 2.67/1.87 % (30709)Memory used [KB]: 7931
% 2.67/1.87 % (30709)Time elapsed: 0.240 s
% 2.67/1.87 % (30709)Instructions burned: 781 (million)
% 2.67/1.87 % (30709)------------------------------
% 2.67/1.87 % (30709)------------------------------
% 2.67/1.88 % (30726)Instruction limit reached!
% 2.67/1.88 % (30726)------------------------------
% 2.67/1.88 % (30726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.88 % (30726)Termination reason: Unknown
% 2.67/1.88 % (30726)Termination phase: Saturation
% 2.67/1.88
% 2.67/1.88 % (30726)Memory used [KB]: 7036
% 2.67/1.88 % (30726)Time elapsed: 0.045 s
% 2.67/1.88 % (30726)Instructions burned: 151 (million)
% 2.67/1.88 % (30726)------------------------------
% 2.67/1.88 % (30726)------------------------------
% 2.67/1.88 % (30731)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/44Mi)
% 2.67/1.88 % (30730)Instruction limit reached!
% 2.67/1.88 % (30730)------------------------------
% 2.67/1.88 % (30730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.88 % (30730)Termination reason: Unknown
% 2.67/1.88 % (30730)Termination phase: Property scanning
% 2.67/1.88
% 2.67/1.88 % (30730)Memory used [KB]: 1918
% 2.67/1.88 % (30730)Time elapsed: 0.017 s
% 2.67/1.88 % (30730)Instructions burned: 49 (million)
% 2.67/1.88 % (30730)------------------------------
% 2.67/1.88 % (30730)------------------------------
% 2.67/1.89 % (30732)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/432Mi)
% 2.67/1.89 % (30731)Instruction limit reached!
% 2.67/1.89 % (30731)------------------------------
% 2.67/1.89 % (30731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.89 % (30731)Termination reason: Unknown
% 2.67/1.89 % (30731)Termination phase: Property scanning
% 2.67/1.89
% 2.67/1.89 % (30731)Memory used [KB]: 2046
% 2.67/1.89 % (30731)Time elapsed: 0.013 s
% 2.67/1.89 % (30731)Instructions burned: 45 (million)
% 2.67/1.89 % (30731)------------------------------
% 2.67/1.89 % (30731)------------------------------
% 2.67/1.89 % (30733)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/62Mi)
% 2.67/1.90 % (30734)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/31Mi)
% 2.67/1.90 % (30722)Instruction limit reached!
% 2.67/1.90 % (30722)------------------------------
% 2.67/1.90 % (30722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.90 % (30722)Termination reason: Unknown
% 2.67/1.90 % (30722)Termination phase: Saturation
% 2.67/1.90
% 2.67/1.90 % (30722)Memory used [KB]: 8571
% 2.67/1.90 % (30722)Time elapsed: 0.131 s
% 2.67/1.90 % (30722)Instructions burned: 449 (million)
% 2.67/1.90 % (30722)------------------------------
% 2.67/1.90 % (30722)------------------------------
% 2.67/1.91 % (30733)Instruction limit reached!
% 2.67/1.91 % (30733)------------------------------
% 2.67/1.91 % (30733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.91 % (30733)Termination reason: Unknown
% 2.67/1.91 % (30733)Termination phase: Property scanning
% 2.67/1.91
% 2.67/1.91 % (30733)Memory used [KB]: 2046
% 2.67/1.91 % (30733)Time elapsed: 0.019 s
% 2.67/1.91 % (30733)Instructions burned: 62 (million)
% 2.67/1.91 % (30733)------------------------------
% 2.67/1.91 % (30733)------------------------------
% 2.67/1.91 % (30734)Instruction limit reached!
% 2.67/1.91 % (30734)------------------------------
% 2.67/1.91 % (30734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.91 % (30734)Termination reason: Unknown
% 2.67/1.91 % (30734)Termination phase: Preprocessing 1
% 2.67/1.91
% 2.67/1.91 % (30734)Memory used [KB]: 1535
% 2.67/1.91 % (30734)Time elapsed: 0.011 s
% 2.67/1.91 % (30734)Instructions burned: 33 (million)
% 2.67/1.91 % (30734)------------------------------
% 2.67/1.91 % (30734)------------------------------
% 2.67/1.91 % (30735)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/96Mi)
% 2.67/1.92 % (30736)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/453Mi)
% 2.67/1.92 % (30737)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_30403 for (2996ds/71Mi)
% 2.67/1.92 % (30693)Instruction limit reached!
% 2.67/1.92 % (30693)------------------------------
% 2.67/1.92 % (30693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.92 % (30693)Termination reason: Unknown
% 2.67/1.92 % (30693)Termination phase: Saturation
% 2.67/1.92
% 2.67/1.92 % (30693)Memory used [KB]: 8443
% 2.67/1.92 % (30693)Time elapsed: 0.348 s
% 2.67/1.92 % (30693)Instructions burned: 1041 (million)
% 2.67/1.92 % (30693)------------------------------
% 2.67/1.92 % (30693)------------------------------
% 2.67/1.94 % (30738)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/83Mi)
% 2.67/1.94 % (30737)Instruction limit reached!
% 2.67/1.94 % (30737)------------------------------
% 2.67/1.94 % (30737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.94 % (30737)Termination reason: Unknown
% 2.67/1.94 % (30737)Termination phase: Property scanning
% 2.67/1.94
% 2.67/1.94 % (30737)Memory used [KB]: 2046
% 2.67/1.94 % (30737)Time elapsed: 0.021 s
% 2.67/1.94 % (30737)Instructions burned: 72 (million)
% 2.67/1.94 % (30737)------------------------------
% 2.67/1.94 % (30737)------------------------------
% 2.67/1.94 % (30711)Instruction limit reached!
% 2.67/1.94 % (30711)------------------------------
% 2.67/1.94 % (30711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.94 % (30711)Termination reason: Unknown
% 2.67/1.94 % (30711)Termination phase: Saturation
% 2.67/1.94
% 2.67/1.94 % (30711)Memory used [KB]: 7931
% 2.67/1.94 % (30711)Time elapsed: 0.295 s
% 2.67/1.94 % (30711)Instructions burned: 879 (million)
% 2.67/1.94 % (30711)------------------------------
% 2.67/1.94 % (30711)------------------------------
% 2.67/1.94 % (30735)Instruction limit reached!
% 2.67/1.94 % (30735)------------------------------
% 2.67/1.94 % (30735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.94 % (30735)Termination reason: Unknown
% 2.67/1.94 % (30735)Termination phase: Saturation
% 2.67/1.94
% 2.67/1.94 % (30735)Memory used [KB]: 6524
% 2.67/1.94 % (30735)Time elapsed: 0.028 s
% 2.67/1.94 % (30735)Instructions burned: 99 (million)
% 2.67/1.94 % (30735)------------------------------
% 2.67/1.94 % (30735)------------------------------
% 2.67/1.95 % (30739)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/11Mi)
% 2.67/1.95 % (30740)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/41Mi)
% 2.67/1.95 % (30741)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/6Mi)
% 2.67/1.95 % (30739)Instruction limit reached!
% 2.67/1.95 % (30739)------------------------------
% 2.67/1.95 % (30739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.95 % (30739)Termination reason: Unknown
% 2.67/1.95 % (30739)Termination phase: shuffling
% 2.67/1.95
% 2.67/1.95 % (30739)Memory used [KB]: 1535
% 2.67/1.95 % (30739)Time elapsed: 0.005 s
% 2.67/1.95 % (30739)Instructions burned: 13 (million)
% 2.67/1.95 % (30739)------------------------------
% 2.67/1.95 % (30739)------------------------------
% 2.67/1.95 % (30741)Instruction limit reached!
% 2.67/1.95 % (30741)------------------------------
% 2.67/1.95 % (30741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.95 % (30741)Termination reason: Unknown
% 2.67/1.95 % (30741)Termination phase: shuffling
% 2.67/1.95
% 2.67/1.95 % (30741)Memory used [KB]: 1407
% 2.67/1.95 % (30741)Time elapsed: 0.004 s
% 2.67/1.95 % (30741)Instructions burned: 8 (million)
% 2.67/1.95 % (30741)------------------------------
% 2.67/1.95 % (30741)------------------------------
% 2.67/1.96 % (30740)Instruction limit reached!
% 2.67/1.96 % (30740)------------------------------
% 2.67/1.96 % (30740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.96 % (30740)Termination reason: Unknown
% 2.67/1.96 % (30740)Termination phase: Property scanning
% 2.67/1.96
% 2.67/1.96 % (30740)Memory used [KB]: 2046
% 2.67/1.96 % (30740)Time elapsed: 0.014 s
% 2.67/1.96 % (30740)Instructions burned: 43 (million)
% 2.67/1.96 % (30740)------------------------------
% 2.67/1.96 % (30740)------------------------------
% 2.67/1.96 % (30738)Instruction limit reached!
% 2.67/1.96 % (30738)------------------------------
% 2.67/1.96 % (30738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.96 % (30738)Termination reason: Unknown
% 2.67/1.96 % (30738)Termination phase: Saturation
% 2.67/1.96
% 2.67/1.96 % (30742)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/150Mi)
% 2.67/1.96 % (30738)Memory used [KB]: 6396
% 2.67/1.96 % (30738)Time elapsed: 0.028 s
% 2.67/1.96 % (30738)Instructions burned: 85 (million)
% 2.67/1.96 % (30738)------------------------------
% 2.67/1.96 % (30738)------------------------------
% 2.67/1.96 % (30743)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/343Mi)
% 2.67/1.97 % (30745)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/253Mi)
% 2.67/1.97 % (30744)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/109Mi)
% 2.67/2.00 % (30742)Instruction limit reached!
% 2.67/2.00 % (30742)------------------------------
% 2.67/2.00 % (30742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/2.00 % (30742)Termination reason: Unknown
% 2.67/2.00 % (30742)Termination phase: Saturation
% 2.67/2.00
% 2.67/2.00 % (30742)Memory used [KB]: 7036
% 2.67/2.00 % (30742)Time elapsed: 0.044 s
% 2.67/2.00 % (30742)Instructions burned: 150 (million)
% 2.67/2.00 % (30742)------------------------------
% 2.67/2.00 % (30742)------------------------------
% 2.67/2.00 % (30744)Instruction limit reached!
% 2.67/2.00 % (30744)------------------------------
% 2.67/2.00 % (30744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/2.00 % (30744)Termination reason: Unknown
% 2.67/2.00 % (30744)Termination phase: Saturation
% 2.67/2.00
% 2.67/2.00 % (30744)Memory used [KB]: 6780
% 2.67/2.00 % (30744)Time elapsed: 0.035 s
% 2.67/2.00 % (30744)Instructions burned: 111 (million)
% 2.67/2.00 % (30744)------------------------------
% 2.67/2.00 % (30744)------------------------------
% 5.96/2.01 % (30732)Instruction limit reached!
% 5.96/2.01 % (30732)------------------------------
% 5.96/2.01 % (30732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.01 % (30732)Termination reason: Unknown
% 5.96/2.01 % (30732)Termination phase: Saturation
% 5.96/2.01
% 5.96/2.01 % (30732)Memory used [KB]: 4221
% 5.96/2.01 % (30732)Time elapsed: 0.127 s
% 5.96/2.01 % (30732)Instructions burned: 434 (million)
% 5.96/2.01 % (30732)------------------------------
% 5.96/2.01 % (30732)------------------------------
% 5.96/2.01 % (30746)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/140Mi)
% 5.96/2.01 % (30747)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/614Mi)
% 5.96/2.02 % (30748)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_30403 for (2995ds/202Mi)
% 5.96/2.04 % (30748)Refutation not found, incomplete strategy
% 5.96/2.04 % (30748)------------------------------
% 5.96/2.04 % (30748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.04 % (30748)Termination reason: Refutation not found, incomplete strategy
% 5.96/2.04
% 5.96/2.04
% 5.96/2.04 % (30748)Memory used [KB]: 6396
% 5.96/2.04 % (30748)Time elapsed: 0.018 s
% 5.96/2.04 % (30748)Instructions burned: 60 (million)
% 5.96/2.04 % (30748)------------------------------
% 5.96/2.04 % (30748)------------------------------
% 5.96/2.05 % (30749)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_30403 for (2994ds/339Mi)
% 5.96/2.06 % (30736)Instruction limit reached!
% 5.96/2.06 % (30736)------------------------------
% 5.96/2.06 % (30736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.06 % (30736)Termination reason: Unknown
% 5.96/2.06 % (30736)Termination phase: Saturation
% 5.96/2.06
% 5.96/2.06 % (30736)Memory used [KB]: 7675
% 5.96/2.06 % (30736)Time elapsed: 0.139 s
% 5.96/2.06 % (30736)Instructions burned: 453 (million)
% 5.96/2.06 % (30736)------------------------------
% 5.96/2.06 % (30736)------------------------------
% 5.96/2.06 % (30746)Instruction limit reached!
% 5.96/2.06 % (30746)------------------------------
% 5.96/2.06 % (30746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.06 % (30746)Termination reason: Unknown
% 5.96/2.06 % (30746)Termination phase: Saturation
% 5.96/2.06
% 5.96/2.06 % (30746)Memory used [KB]: 6524
% 5.96/2.06 % (30746)Time elapsed: 0.065 s
% 5.96/2.06 % (30746)Instructions burned: 141 (million)
% 5.96/2.06 % (30746)------------------------------
% 5.96/2.06 % (30746)------------------------------
% 5.96/2.06 % (30750)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_30403 for (2994ds/283Mi)
% 5.96/2.07 % (30751)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_30403 for (2994ds/134Mi)
% 5.96/2.07 % (30743)Instruction limit reached!
% 5.96/2.07 % (30743)------------------------------
% 5.96/2.07 % (30743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.07 % (30743)Termination reason: Unknown
% 5.96/2.07 % (30743)Termination phase: Saturation
% 5.96/2.07
% 5.96/2.07 % (30743)Memory used [KB]: 7164
% 5.96/2.07 % (30743)Time elapsed: 0.106 s
% 5.96/2.07 % (30743)Instructions burned: 343 (million)
% 5.96/2.07 % (30743)------------------------------
% 5.96/2.07 % (30743)------------------------------
% 5.96/2.08 % (30752)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_30403 for (2994ds/298Mi)
% 5.96/2.08 % (30745)Instruction limit reached!
% 5.96/2.08 % (30745)------------------------------
% 5.96/2.08 % (30745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.08 % (30745)Termination reason: Unknown
% 5.96/2.08 % (30745)Termination phase: Saturation
% 5.96/2.08
% 5.96/2.08 % (30745)Memory used [KB]: 6780
% 5.96/2.08 % (30745)Time elapsed: 0.115 s
% 5.96/2.08 % (30745)Instructions burned: 254 (million)
% 5.96/2.08 % (30745)------------------------------
% 5.96/2.08 % (30745)------------------------------
% 5.96/2.09 % (30753)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_30403 for (2994ds/192Mi)
% 5.96/2.11 % (30751)Instruction limit reached!
% 5.96/2.11 % (30751)------------------------------
% 5.96/2.11 % (30751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.11 % (30751)Termination reason: Unknown
% 5.96/2.11 % (30751)Termination phase: Saturation
% 5.96/2.11
% 5.96/2.11 % (30751)Memory used [KB]: 7036
% 5.96/2.11 % (30751)Time elapsed: 0.064 s
% 5.96/2.11 % (30751)Instructions burned: 136 (million)
% 5.96/2.11 % (30751)------------------------------
% 5.96/2.11 % (30751)------------------------------
% 6.40/2.12 % (30754)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_30403 for (2994ds/258Mi)
% 6.40/2.15 % (30749)Instruction limit reached!
% 6.40/2.15 % (30749)------------------------------
% 6.40/2.15 % (30749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.15 % (30749)Termination reason: Unknown
% 6.40/2.15 % (30749)Termination phase: Saturation
% 6.40/2.15
% 6.40/2.15 % (30749)Memory used [KB]: 7675
% 6.40/2.15 % (30749)Time elapsed: 0.098 s
% 6.40/2.15 % (30749)Instructions burned: 340 (million)
% 6.40/2.15 % (30749)------------------------------
% 6.40/2.15 % (30749)------------------------------
% 6.40/2.15 % (30750)Instruction limit reached!
% 6.40/2.15 % (30750)------------------------------
% 6.40/2.15 % (30750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.15 % (30750)Termination reason: Unknown
% 6.40/2.15 % (30750)Termination phase: Saturation
% 6.40/2.15
% 6.40/2.15 % (30750)Memory used [KB]: 7291
% 6.40/2.15 % (30750)Time elapsed: 0.106 s
% 6.40/2.15 % (30750)Instructions burned: 284 (million)
% 6.40/2.15 % (30750)------------------------------
% 6.40/2.15 % (30750)------------------------------
% 6.40/2.15 % (30754)Refutation not found, incomplete strategy
% 6.40/2.15 % (30754)------------------------------
% 6.40/2.15 % (30754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.15 % (30754)Termination reason: Refutation not found, incomplete strategy
% 6.40/2.15
% 6.40/2.15
% 6.40/2.15 % (30754)Memory used [KB]: 7164
% 6.40/2.15 % (30754)Time elapsed: 0.036 s
% 6.40/2.15 % (30754)Instructions burned: 124 (million)
% 6.40/2.15 % (30754)------------------------------
% 6.40/2.15 % (30754)------------------------------
% 6.40/2.15 % (30753)Instruction limit reached!
% 6.40/2.15 % (30753)------------------------------
% 6.40/2.15 % (30753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.15 % (30753)Termination reason: Unknown
% 6.40/2.15 % (30753)Termination phase: Saturation
% 6.40/2.15
% 6.40/2.15 % (30753)Memory used [KB]: 7931
% 6.40/2.15 % (30753)Time elapsed: 0.062 s
% 6.40/2.15 % (30753)Instructions burned: 192 (million)
% 6.40/2.15 % (30753)------------------------------
% 6.40/2.15 % (30753)------------------------------
% 6.40/2.16 % (30755)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_30403 for (2993ds/90Mi)
% 6.40/2.16 % (30756)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_30403 for (2993ds/231Mi)
% 6.40/2.16 % (30752)Instruction limit reached!
% 6.40/2.16 % (30752)------------------------------
% 6.40/2.16 % (30752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.16 % (30752)Termination reason: Unknown
% 6.40/2.16 % (30752)Termination phase: Saturation
% 6.40/2.16
% 6.40/2.16 % (30752)Memory used [KB]: 8315
% 6.40/2.16 % (30752)Time elapsed: 0.081 s
% 6.40/2.16 % (30752)Instructions burned: 300 (million)
% 6.40/2.16 % (30752)------------------------------
% 6.40/2.16 % (30752)------------------------------
% 6.40/2.16 % (30757)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_30403 for (2993ds/458Mi)
% 6.40/2.17 % (30758)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_30403 for (2993ds/31Mi)
% 6.40/2.17 % (30759)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_30403 for (2993ds/297Mi)
% 6.40/2.18 % (30758)Instruction limit reached!
% 6.40/2.18 % (30758)------------------------------
% 6.40/2.18 % (30758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.18 % (30758)Termination reason: Unknown
% 6.40/2.18 % (30758)Termination phase: Preprocessing 1
% 6.40/2.18
% 6.40/2.18 % (30758)Memory used [KB]: 1663
% 6.40/2.18 % (30758)Time elapsed: 0.012 s
% 6.40/2.18 % (30758)Instructions burned: 33 (million)
% 6.40/2.18 % (30758)------------------------------
% 6.40/2.18 % (30758)------------------------------
% 6.40/2.18 % (30755)Instruction limit reached!
% 6.40/2.18 % (30755)------------------------------
% 6.40/2.18 % (30755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.18 % (30755)Termination reason: Unknown
% 6.40/2.18 % (30755)Termination phase: Saturation
% 6.40/2.18
% 6.40/2.18 % (30755)Memory used [KB]: 6524
% 6.40/2.18 % (30755)Time elapsed: 0.026 s
% 6.40/2.18 % (30755)Instructions burned: 91 (million)
% 6.40/2.18 % (30755)------------------------------
% 6.40/2.18 % (30755)------------------------------
% 6.40/2.19 % (30760)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_30403 for (2993ds/987Mi)
% 6.40/2.19 % (30761)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_30403 for (2993ds/182Mi)
% 6.94/2.20 % (30747)Instruction limit reached!
% 6.94/2.20 % (30747)------------------------------
% 6.94/2.20 % (30747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.20 % (30747)Termination reason: Unknown
% 6.94/2.20 % (30747)Termination phase: Saturation
% 6.94/2.20
% 6.94/2.20 % (30747)Memory used [KB]: 8443
% 6.94/2.20 % (30747)Time elapsed: 0.209 s
% 6.94/2.20 % (30747)Instructions burned: 617 (million)
% 6.94/2.20 % (30747)------------------------------
% 6.94/2.20 % (30747)------------------------------
% 6.94/2.21 % (30729)Instruction limit reached!
% 6.94/2.21 % (30729)------------------------------
% 6.94/2.21 % (30729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.21 % (30729)Termination reason: Unknown
% 6.94/2.21 % (30729)Termination phase: Saturation
% 6.94/2.21
% 6.94/2.21 % (30729)Memory used [KB]: 8059
% 6.94/2.21 % (30729)Time elapsed: 0.349 s
% 6.94/2.21 % (30729)Instructions burned: 1087 (million)
% 6.94/2.21 % (30729)------------------------------
% 6.94/2.21 % (30729)------------------------------
% 6.94/2.21 % (30762)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_30403 for (2993ds/182Mi)
% 6.94/2.22 % (30763)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_30403 for (2993ds/154Mi)
% 6.94/2.22 % (30756)Instruction limit reached!
% 6.94/2.22 % (30756)------------------------------
% 6.94/2.22 % (30756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.22 % (30756)Termination reason: Unknown
% 6.94/2.22 % (30756)Termination phase: Saturation
% 6.94/2.22
% 6.94/2.22 % (30756)Memory used [KB]: 7547
% 6.94/2.22 % (30756)Time elapsed: 0.068 s
% 6.94/2.22 % (30756)Instructions burned: 231 (million)
% 6.94/2.22 % (30756)------------------------------
% 6.94/2.22 % (30756)------------------------------
% 6.94/2.23 % (30764)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/79Mi)
% 6.94/2.24 % (30761)Instruction limit reached!
% 6.94/2.24 % (30761)------------------------------
% 6.94/2.24 % (30761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.24 % (30761)Termination reason: Unknown
% 6.94/2.24 % (30761)Termination phase: Saturation
% 6.94/2.24
% 6.94/2.24 % (30761)Memory used [KB]: 7164
% 6.94/2.24 % (30761)Time elapsed: 0.055 s
% 6.94/2.24 % (30761)Instructions burned: 183 (million)
% 6.94/2.24 % (30761)------------------------------
% 6.94/2.24 % (30761)------------------------------
% 6.94/2.25 % (30759)Instruction limit reached!
% 6.94/2.25 % (30759)------------------------------
% 6.94/2.25 % (30759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.25 % (30759)Termination reason: Unknown
% 6.94/2.25 % (30759)Termination phase: Saturation
% 6.94/2.25
% 6.94/2.25 % (30759)Memory used [KB]: 7164
% 6.94/2.25 % (30759)Time elapsed: 0.087 s
% 6.94/2.25 % (30759)Instructions burned: 297 (million)
% 6.94/2.25 % (30759)------------------------------
% 6.94/2.25 % (30759)------------------------------
% 6.94/2.25 % (30765)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/216Mi)
% 6.94/2.25 % (30764)Instruction limit reached!
% 6.94/2.25 % (30764)------------------------------
% 6.94/2.25 % (30764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.25 % (30764)Termination reason: Unknown
% 6.94/2.25 % (30764)Termination phase: Property scanning
% 6.94/2.25
% 6.94/2.25 % (30764)Memory used [KB]: 2046
% 6.94/2.25 % (30764)Time elapsed: 0.023 s
% 6.94/2.25 % (30764)Instructions burned: 80 (million)
% 6.94/2.25 % (30764)------------------------------
% 6.94/2.25 % (30764)------------------------------
% 6.94/2.26 % (30763)Refutation not found, incomplete strategy
% 6.94/2.26 % (30763)------------------------------
% 6.94/2.26 % (30763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.26 % (30763)Termination reason: Refutation not found, incomplete strategy
% 6.94/2.26
% 6.94/2.26
% 6.94/2.26 % (30763)Memory used [KB]: 6908
% 6.94/2.26 % (30763)Time elapsed: 0.041 s
% 6.94/2.26 % (30763)Instructions burned: 149 (million)
% 6.94/2.26 % (30763)------------------------------
% 6.94/2.26 % (30763)------------------------------
% 6.94/2.26 % (30766)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/114Mi)
% 6.94/2.26 % (30767)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/922Mi)
% 6.94/2.27 % (30762)Instruction limit reached!
% 6.94/2.27 % (30762)------------------------------
% 6.94/2.27 % (30762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.27 % (30768)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/182Mi)
% 6.94/2.27 % (30762)Termination reason: Unknown
% 6.94/2.27 % (30762)Termination phase: Saturation
% 6.94/2.27
% 6.94/2.27 % (30762)Memory used [KB]: 7036
% 6.94/2.27 % (30762)Time elapsed: 0.056 s
% 6.94/2.27 % (30762)Instructions burned: 182 (million)
% 6.94/2.27 % (30762)------------------------------
% 6.94/2.27 % (30762)------------------------------
% 6.94/2.28 % (30769)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/164Mi)
% 6.94/2.29 % (30766)Instruction limit reached!
% 6.94/2.29 % (30766)------------------------------
% 6.94/2.29 % (30766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.29 % (30766)Termination reason: Unknown
% 6.94/2.29 % (30766)Termination phase: Saturation
% 6.94/2.29
% 6.94/2.29 % (30766)Memory used [KB]: 6908
% 6.94/2.29 % (30766)Time elapsed: 0.033 s
% 6.94/2.29 % (30766)Instructions burned: 116 (million)
% 6.94/2.29 % (30766)------------------------------
% 6.94/2.29 % (30766)------------------------------
% 6.94/2.30 % (30757)Refutation not found, non-redundant clauses discarded% (30757)------------------------------
% 6.94/2.30 % (30757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.30 % (30757)Termination reason: Refutation not found, non-redundant clauses discarded
% 6.94/2.30
% 6.94/2.30 % (30757)Memory used [KB]: 7675
% 6.94/2.30 % (30757)Time elapsed: 0.135 s
% 6.94/2.30 % (30757)Instructions burned: 446 (million)
% 6.94/2.30 % (30757)------------------------------
% 6.94/2.30 % (30757)------------------------------
% 7.73/2.30 % (30770)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/50Mi)
% 7.73/2.31 % (30771)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/368Mi)
% 7.73/2.31 % (30765)Instruction limit reached!
% 7.73/2.31 % (30765)------------------------------
% 7.73/2.31 % (30765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.31 % (30765)Termination reason: Unknown
% 7.73/2.31 % (30765)Termination phase: Saturation
% 7.73/2.31
% 7.73/2.31 % (30765)Memory used [KB]: 7164
% 7.73/2.31 % (30765)Time elapsed: 0.059 s
% 7.73/2.31 % (30765)Instructions burned: 219 (million)
% 7.73/2.31 % (30765)------------------------------
% 7.73/2.31 % (30765)------------------------------
% 7.73/2.31 % (30768)Instruction limit reached!
% 7.73/2.31 % (30768)------------------------------
% 7.73/2.31 % (30768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.31 % (30768)Termination reason: Unknown
% 7.73/2.31 % (30768)Termination phase: Saturation
% 7.73/2.31
% 7.73/2.31 % (30768)Memory used [KB]: 7036
% 7.73/2.31 % (30768)Time elapsed: 0.050 s
% 7.73/2.31 % (30768)Instructions burned: 184 (million)
% 7.73/2.31 % (30768)------------------------------
% 7.73/2.31 % (30768)------------------------------
% 7.73/2.32 % (30770)Instruction limit reached!
% 7.73/2.32 % (30770)------------------------------
% 7.73/2.32 % (30770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.32 % (30770)Termination reason: Unknown
% 7.73/2.32 % (30770)Termination phase: Property scanning
% 7.73/2.32
% 7.73/2.32 % (30770)Memory used [KB]: 2046
% 7.73/2.32 % (30770)Time elapsed: 0.015 s
% 7.73/2.32 % (30770)Instructions burned: 52 (million)
% 7.73/2.32 % (30770)------------------------------
% 7.73/2.32 % (30770)------------------------------
% 7.73/2.32 % (30769)Instruction limit reached!
% 7.73/2.32 % (30769)------------------------------
% 7.73/2.32 % (30769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.32 % (30769)Termination reason: Unknown
% 7.73/2.32 % (30769)Termination phase: Saturation
% 7.73/2.32
% 7.73/2.32 % (30769)Memory used [KB]: 2558
% 7.73/2.32 % (30769)Time elapsed: 0.045 s
% 7.73/2.32 % (30769)Instructions burned: 165 (million)
% 7.73/2.32 % (30769)------------------------------
% 7.73/2.32 % (30769)------------------------------
% 7.73/2.32 % (30772)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/1021Mi)
% 7.73/2.32 % (30773)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/267Mi)
% 7.73/2.33 % (30774)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/204Mi)
% 7.73/2.33 % (30775)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_30403 for (2992ds/26Mi)
% 7.73/2.34 % (30775)Instruction limit reached!
% 7.73/2.34 % (30775)------------------------------
% 7.73/2.34 % (30775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.34 % (30775)Termination reason: Unknown
% 7.73/2.34 % (30775)Termination phase: shuffling
% 7.73/2.34
% 7.73/2.34 % (30775)Memory used [KB]: 1918
% 7.73/2.34 % (30775)Time elapsed: 0.008 s
% 7.73/2.34 % (30775)Instructions burned: 26 (million)
% 7.73/2.34 % (30775)------------------------------
% 7.73/2.34 % (30775)------------------------------
% 7.73/2.35 % (30776)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_30403 for (2991ds/53Mi)
% 7.73/2.35 % (30767)First to succeed.
% 7.73/2.35 % (30767)Refutation found. Thanks to Tanya!
% 7.73/2.35 % SZS status Theorem for DTF2THF_30403
% 7.73/2.35 % SZS output start Proof for DTF2THF_30403
% 7.73/2.35 thf(type_def_5, type, multiset_a: $tType).
% 7.73/2.35 thf(type_def_7, type, tree_a: $tType).
% 7.73/2.35 thf(type_def_8, type, a: $tType).
% 7.73/2.35 thf(type_def_9, type, set_a: $tType).
% 7.73/2.35 thf(type_def_10, type, multiset_multiset_a: $tType).
% 7.73/2.35 thf(type_def_11, type, set_Product_prod_a_a: $tType).
% 7.73/2.35 thf(type_def_12, type, set_Pr158363655iset_a: $tType).
% 7.73/2.35 thf(type_def_13, type, set_multiset_a: $tType).
% 7.73/2.35 thf(type_def_14, type, produc1127127335iset_a: $tType).
% 7.73/2.35 thf(type_def_15, type, product_prod_a_a: $tType).
% 7.73/2.35 thf(func_def_0, type, set_Pr158363655iset_a: $tType).
% 7.73/2.35 thf(func_def_1, type, produc1127127335iset_a: $tType).
% 7.73/2.35 thf(func_def_2, type, set_Product_prod_a_a: $tType).
% 7.73/2.35 thf(func_def_3, type, multiset_multiset_a: $tType).
% 7.73/2.35 thf(func_def_4, type, set_multiset_a: $tType).
% 7.73/2.35 thf(func_def_5, type, product_prod_a_a: $tType).
% 7.73/2.35 thf(func_def_6, type, multiset_a: $tType).
% 7.73/2.35 thf(func_def_7, type, tree_a: $tType).
% 7.73/2.35 thf(func_def_8, type, set_a: $tType).
% 7.73/2.35 thf(func_def_9, type, a: $tType).
% 7.73/2.35 thf(func_def_10, type, plus_plus_multiset_a: multiset_a > multiset_a > multiset_a).
% 7.73/2.35 thf(func_def_11, type, zero_zero_multiset_a: multiset_a).
% 7.73/2.35 thf(func_def_12, type, nO_MAT1617603563iset_a: multiset_a > multiset_a > $o).
% 7.73/2.35 thf(func_def_13, type, heapIm1140443833left_a: tree_a > tree_a).
% 7.73/2.35 thf(func_def_14, type, heapIm1257206334ight_a: tree_a > tree_a).
% 7.73/2.35 thf(func_def_15, type, heapIm1091024090Down_a: tree_a > tree_a).
% 7.73/2.35 thf(func_def_16, type, e_a: tree_a).
% 7.73/2.35 thf(func_def_17, type, t_a: a > tree_a > tree_a > tree_a).
% 7.73/2.35 thf(func_def_18, type, rel_Tree_a_a: (a > a > $o) > tree_a > tree_a > $o).
% 7.73/2.35 thf(func_def_19, type, in_tree_a: a > tree_a > $o).
% 7.73/2.35 thf(func_def_20, type, is_heap_a: tree_a > $o).
% 7.73/2.35 thf(func_def_21, type, multiset_a2: tree_a > multiset_a).
% 7.73/2.35 thf(func_def_22, type, val_a: tree_a > a).
% 7.73/2.35 thf(func_def_23, type, lattic146396397_Max_a: set_a > a).
% 7.73/2.35 thf(func_def_24, type, add_mset_a: a > multiset_a > multiset_a).
% 7.73/2.35 thf(func_def_25, type, comm_m315775925iset_a: (multiset_a > multiset_a > multiset_a) > multiset_a > multiset_multiset_a > multiset_a).
% 7.73/2.35 thf(func_def_26, type, fold_m382157835iset_a: (multiset_a > multiset_a > multiset_a) > multiset_a > multiset_multiset_a > multiset_a).
% 7.73/2.35 thf(func_def_27, type, fold_m364285649iset_a: (a > multiset_a > multiset_a) > multiset_a > multiset_a > multiset_a).
% 7.73/2.35 thf(func_def_28, type, image_929116801iset_a: (a > multiset_a) > multiset_a > multiset_multiset_a).
% 7.73/2.35 thf(func_def_29, type, image_mset_a_a: (a > a) > multiset_a > multiset_a).
% 7.73/2.35 thf(func_def_30, type, mult1_a: set_Product_prod_a_a > set_Pr158363655iset_a).
% 7.73/2.35 thf(func_def_31, type, mult_a: set_Product_prod_a_a > set_Pr158363655iset_a).
% 7.73/2.35 thf(func_def_32, type, set_mset_multiset_a: multiset_multiset_a > set_multiset_a).
% 7.73/2.35 thf(func_def_33, type, set_mset_a: multiset_a > set_a).
% 7.73/2.35 thf(func_def_34, type, subseteq_mset_a: multiset_a > multiset_a > $o).
% 7.73/2.35 thf(func_def_35, type, ord_less_eq_o_o_a: ($o > $o > a) > ($o > $o > a) > $o).
% 7.73/2.35 thf(func_def_36, type, ord_less_eq_o_a: ($o > a) > ($o > a) > $o).
% 7.73/2.35 thf(func_def_37, type, ord_le1530450702ee_a_o: (tree_a > tree_a > $o) > (tree_a > tree_a > $o) > $o).
% 7.73/2.35 thf(func_def_38, type, ord_less_eq_a_a_o: (a > a > $o) > (a > a > $o) > $o).
% 7.73/2.35 thf(func_def_39, type, ord_le1199012836iset_a: multiset_a > multiset_a > $o).
% 7.73/2.35 thf(func_def_40, type, ord_less_eq_set_a: set_a > set_a > $o).
% 7.73/2.35 thf(func_def_41, type, ord_less_eq_a: a > a > $o).
% 7.73/2.35 thf(func_def_42, type, order_Greatest_o_a: (($o > a) > $o) > $o > a).
% 7.73/2.35 thf(func_def_43, type, order_Greatest_a: (a > $o) > a).
% 7.73/2.35 thf(func_def_44, type, produc2037245207iset_a: multiset_a > multiset_a > produc1127127335iset_a).
% 7.73/2.35 thf(func_def_45, type, product_Pair_a_a: a > a > product_prod_a_a).
% 7.73/2.35 thf(func_def_46, type, irrefl_a: set_Product_prod_a_a > $o).
% 7.73/2.35 thf(func_def_47, type, trans_a: set_Product_prod_a_a > $o).
% 7.73/2.35 thf(func_def_48, type, collect_a: (a > $o) > set_a).
% 7.73/2.35 thf(func_def_49, type, member_multiset_a: multiset_a > set_multiset_a > $o).
% 7.73/2.35 thf(func_def_50, type, member340150864iset_a: produc1127127335iset_a > set_Pr158363655iset_a > $o).
% 7.73/2.35 thf(func_def_51, type, member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o).
% 7.73/2.35 thf(func_def_52, type, member_a: a > set_a > $o).
% 7.73/2.35 thf(func_def_53, type, l: tree_a).
% 7.73/2.35 thf(func_def_54, type, l1: tree_a).
% 7.73/2.35 thf(func_def_55, type, la: tree_a).
% 7.73/2.35 thf(func_def_56, type, r: tree_a).
% 7.73/2.35 thf(func_def_57, type, r1: tree_a).
% 7.73/2.35 thf(func_def_58, type, ra: tree_a).
% 7.73/2.35 thf(func_def_59, type, t: tree_a).
% 7.73/2.35 thf(func_def_60, type, v: a).
% 7.73/2.35 thf(func_def_61, type, v1: a).
% 7.73/2.35 thf(func_def_62, type, v2: a).
% 7.73/2.35 thf(func_def_63, type, va: a).
% 7.73/2.35 thf(func_def_75, type, sP0: a > a > a > $o).
% 7.73/2.35 thf(func_def_76, type, sP1: a > a > a > $o).
% 7.73/2.35 thf(func_def_77, type, sP2: a > a > a > $o).
% 7.73/2.35 thf(func_def_78, type, sK3: (a > a > $o) > a).
% 7.73/2.35 thf(func_def_79, type, sK4: (a > a > $o) > a).
% 7.73/2.35 thf(func_def_80, type, sK5: (a > a > $o) > a).
% 7.73/2.35 thf(func_def_81, type, sK6: (a > a > $o) > a).
% 7.73/2.35 thf(func_def_82, type, sK7: tree_a > tree_a).
% 7.73/2.35 thf(func_def_83, type, sK8: tree_a > tree_a).
% 7.73/2.35 thf(func_def_84, type, sK9: tree_a > a).
% 7.73/2.35 thf(func_def_85, type, sK10: tree_a > a).
% 7.73/2.35 thf(func_def_86, type, sK11: tree_a > a).
% 7.73/2.35 thf(func_def_87, type, sK12: tree_a > a).
% 7.73/2.35 thf(func_def_88, type, sK13: tree_a > tree_a).
% 7.73/2.35 thf(func_def_89, type, sK14: tree_a > tree_a).
% 7.73/2.35 thf(func_def_90, type, sK15: tree_a > tree_a).
% 7.73/2.35 thf(func_def_91, type, sK16: tree_a > tree_a).
% 7.73/2.35 thf(func_def_92, type, sK17: tree_a > a).
% 7.73/2.35 thf(func_def_93, type, sK18: tree_a > a).
% 7.73/2.35 thf(func_def_94, type, sK19: tree_a > tree_a).
% 7.73/2.35 thf(func_def_95, type, sK20: tree_a > a).
% 7.73/2.35 thf(func_def_96, type, sK21: tree_a > tree_a).
% 7.73/2.35 thf(func_def_97, type, sK22: tree_a > tree_a).
% 7.73/2.35 thf(func_def_98, type, sK23: tree_a > a).
% 7.73/2.35 thf(func_def_99, type, sK24: tree_a > a).
% 7.73/2.35 thf(func_def_100, type, sK25: tree_a > tree_a).
% 7.73/2.35 thf(func_def_101, type, sK26: (tree_a > $o) > a).
% 7.73/2.35 thf(func_def_102, type, sK27: (tree_a > $o) > tree_a).
% 7.73/2.35 thf(func_def_103, type, sK28: (tree_a > $o) > tree_a).
% 7.73/2.35 thf(func_def_104, type, sK29: tree_a > a > tree_a).
% 7.73/2.35 thf(func_def_105, type, sK30: tree_a > a > tree_a).
% 7.73/2.35 thf(func_def_106, type, sK31: tree_a > a > a).
% 7.73/2.35 thf(func_def_107, type, sK32: (a > a) > a).
% 7.73/2.35 thf(func_def_108, type, sK33: (a > a) > a).
% 7.73/2.35 thf(func_def_109, type, sK34: (a > a) > a).
% 7.73/2.35 thf(func_def_110, type, sK35: (a > a) > a).
% 7.73/2.35 thf(func_def_111, type, sK36: (a > a) > a).
% 7.73/2.35 thf(func_def_112, type, sK37: (a > a) > a).
% 7.73/2.35 thf(func_def_113, type, sK38: tree_a > a).
% 7.73/2.35 thf(func_def_114, type, sK39: tree_a > tree_a).
% 7.73/2.35 thf(func_def_115, type, sK40: tree_a > a).
% 7.73/2.35 thf(func_def_116, type, sK41: tree_a > tree_a).
% 7.73/2.35 thf(func_def_117, type, sK42: tree_a > tree_a).
% 7.73/2.35 thf(func_def_118, type, sK43: tree_a > a).
% 7.73/2.35 thf(func_def_119, type, sK44: tree_a > tree_a).
% 7.73/2.35 thf(func_def_120, type, sK45: tree_a > tree_a).
% 7.73/2.35 thf(func_def_121, type, sK46: tree_a > a).
% 7.73/2.35 thf(func_def_122, type, sK47: tree_a > a).
% 7.73/2.35 thf(func_def_123, type, sK48: tree_a > tree_a).
% 7.73/2.35 thf(func_def_124, type, sK49: tree_a > a).
% 7.73/2.35 thf(func_def_125, type, sK50: tree_a > tree_a).
% 7.73/2.35 thf(func_def_126, type, sK51: tree_a > a).
% 7.73/2.35 thf(func_def_127, type, sK52: tree_a > tree_a).
% 7.73/2.35 thf(func_def_128, type, sK53: tree_a > a).
% 7.73/2.35 thf(func_def_129, type, sK54: (a > a) > a).
% 7.73/2.35 thf(func_def_130, type, sK55: (a > a) > a).
% 7.73/2.35 thf(func_def_133, type, ph57: !>[X0: $tType]:(X0)).
% 7.73/2.35 thf(f1538,plain,(
% 7.73/2.35 $false),
% 7.73/2.35 inference(avatar_sat_refutation,[status(thm)],[f704,f719,f736,f741,f1031,f1496,f1531])).
% 7.73/2.35 thf(f1531,plain,(
% 7.73/2.35 ~spl56_48 | ~spl56_1 | spl56_8 | ~spl56_9),
% 7.73/2.35 inference(avatar_split_clause,[status(thm)],[f1530,f738,f733,f701,f1488])).
% 7.73/2.35 thf(f1488,definition,(
% 7.73/2.35 spl56_48 <=> ($true = (is_heap_a @ (t_a @ va @ la @ ra)))),
% 7.73/2.35 introduced(definition,[new_symbols(naming,[spl56_48])],[avatar_definition])).
% 7.73/2.35 thf(f701,definition,(
% 7.73/2.35 spl56_1 <=> ((t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)) = (t_a @ va @ la @ ra))),
% 7.73/2.35 introduced(definition,[new_symbols(naming,[spl56_1])],[avatar_definition])).
% 7.73/2.35 thf(f733,definition,(
% 7.73/2.35 spl56_8 <=> ((is_heap_a @ (heapIm1091024090Down_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)))) = $true)),
% 7.73/2.35 introduced(definition,[new_symbols(naming,[spl56_8])],[avatar_definition])).
% 7.73/2.35 thf(f738,definition,(
% 7.73/2.35 spl56_9 <=> ((ord_less_eq_a @ v1 @ v2) = $true)),
% 7.73/2.35 introduced(definition,[new_symbols(naming,[spl56_9])],[avatar_definition])).
% 7.73/2.35 thf(f1530,plain,(
% 7.73/2.35 ($true != (is_heap_a @ (t_a @ va @ la @ ra))) | (~spl56_1 | spl56_8 | ~spl56_9)),
% 7.73/2.35 inference(forward_demodulation,[status(thm)],[f1529,f703])).
% 7.73/2.35 thf(f703,plain,(
% 7.73/2.35 ((t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)) = (t_a @ va @ la @ ra)) | ~spl56_1),
% 7.73/2.35 inference(avatar_component_clause,[status(thm)],[f701])).
% 7.73/2.35 thf(f1529,plain,(
% 7.73/2.35 ($true != (is_heap_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)))) | (spl56_8 | ~spl56_9)),
% 7.73/2.35 inference(subsumption_resolution,[status(thm)],[f1528,f740])).
% 7.73/2.35 thf(f740,plain,(
% 7.73/2.35 ((ord_less_eq_a @ v1 @ v2) = $true) | ~spl56_9),
% 7.73/2.35 inference(avatar_component_clause,[status(thm)],[f738])).
% 7.73/2.35 thf(f1528,plain,(
% 7.73/2.35 ($true != (is_heap_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)))) | ((ord_less_eq_a @ v1 @ v2) != $true) | spl56_8),
% 7.73/2.35 inference(superposition,[status(thm)],[f735,f1523])).
% 7.73/2.35 thf(f1523,plain,(
% 7.73/2.35 ( ! [X2 : tree_a,X3 : a,X0 : tree_a,X1 : a] : (((heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))) = (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))) | ((ord_less_eq_a @ X3 @ X1) != $true)) )),
% 7.73/2.35 inference(forward_demodulation,[status(thm)],[f601,f607])).
% 7.73/2.35 thf(f607,plain,(
% 7.73/2.35 ( ! [X2 : tree_a,X0 : tree_a,X1 : a] : (((val_a @ (t_a @ X1 @ X2 @ X0)) = X1)) )),
% 7.73/2.35 inference(cnf_transformation,[status(thm)],[f488])).
% 7.73/2.35 thf(f488,plain,(
% 7.73/2.35 ! [X0 : tree_a,X1 : a,X2 : tree_a] : ((val_a @ (t_a @ X1 @ X2 @ X0)) = X1)),
% 7.73/2.35 inference(rectify,[status(thm)],[f23])).
% 7.73/2.35 thf(f23,axiom,(
% 7.73/2.35 ! [X33 : tree_a,X0 : a,X32 : tree_a] : ((val_a @ (t_a @ X0 @ X32 @ X33)) = X0)),
% 7.73/2.35 file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_22_val_Osimps)).
% 7.73/2.35 thf(f601,plain,(
% 7.73/2.35 ( ! [X2 : tree_a,X3 : a,X0 : tree_a,X1 : a] : (((heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))) = (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))) | ((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ X1) != $true)) )),
% 7.73/2.35 inference(cnf_transformation,[status(thm)],[f527])).
% 7.73/2.35 thf(f527,plain,(
% 7.73/2.35 ! [X0 : tree_a,X1 : a,X2 : tree_a,X3 : a] : ((((heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))) = (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))) | ((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ X1) != $true)) & (((t_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ e_a @ (heapIm1091024090Down_a @ (t_a @ X1 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X2)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X2))))) = (heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2)))) | ((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ X1) = $true)))),
% 7.73/2.35 inference(ennf_transformation,[status(thm)],[f484])).
% 7.73/2.35 thf(f484,plain,(
% 7.73/2.35 ! [X0 : tree_a,X1 : a,X2 : tree_a,X3 : a] : ((((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ X1) = $true) => ((heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))) = (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2)))) & (((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ X1) != $true) => ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ e_a @ (heapIm1091024090Down_a @ (t_a @ X1 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X2)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X2))))) = (heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))))))),
% 7.73/2.35 inference(flattening,[status(thm)],[f312])).
% 7.73/2.35 thf(f312,plain,(
% 7.73/2.35 ! [X0 : tree_a,X1 : a,X2 : tree_a,X3 : a] : ((((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ X1) = $true) => ((heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))) = (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2)))) & (~((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ X1) = $true) => ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ e_a @ (heapIm1091024090Down_a @ (t_a @ X1 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X2)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X2))))) = (heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))))))),
% 7.73/2.35 inference(fool_elimination,[status(thm)],[f311])).
% 7.73/2.35 thf(f311,plain,(
% 7.73/2.35 ! [X0 : tree_a,X1 : a,X2 : tree_a,X3 : a] : (((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ X1) => ((heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))) = (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2)))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ X1) => ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X2)) @ e_a @ (heapIm1091024090Down_a @ (t_a @ X1 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X2)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X2))))) = (heapIm1091024090Down_a @ (t_a @ X1 @ e_a @ (t_a @ X3 @ X0 @ X2))))))),
% 7.73/2.35 inference(rectify,[status(thm)],[f31])).
% 7.73/2.35 thf(f31,axiom,(
% 7.73/2.35 ! [X39 : tree_a,X0 : a,X40 : tree_a,X38 : a] : (((ord_less_eq_a @ (val_a @ (t_a @ X38 @ X39 @ X40)) @ X0) => ((t_a @ X0 @ e_a @ (t_a @ X38 @ X39 @ X40)) = (heapIm1091024090Down_a @ (t_a @ X0 @ e_a @ (t_a @ X38 @ X39 @ X40))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X38 @ X39 @ X40)) @ X0) => ((heapIm1091024090Down_a @ (t_a @ X0 @ e_a @ (t_a @ X38 @ X39 @ X40))) = (t_a @ (val_a @ (t_a @ X38 @ X39 @ X40)) @ e_a @ (heapIm1091024090Down_a @ (t_a @ X0 @ (heapIm1140443833left_a @ (t_a @ X38 @ X39 @ X40)) @ (heapIm1257206334ight_a @ (t_a @ X38 @ X39 @ X40))))))))),
% 7.73/2.35 file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_30_siftDown_Osimps_I4_J)).
% 7.73/2.35 thf(f735,plain,(
% 7.73/2.35 ((is_heap_a @ (heapIm1091024090Down_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)))) != $true) | spl56_8),
% 7.73/2.35 inference(avatar_component_clause,[status(thm)],[f733])).
% 7.73/2.35 thf(f1496,plain,(
% 7.73/2.35 spl56_48 | ~spl56_1 | ~spl56_4 | ~spl56_9 | ~spl56_18),
% 7.73/2.35 inference(avatar_split_clause,[status(thm)],[f1495,f1028,f738,f716,f701,f1488])).
% 7.73/2.35 thf(f716,definition,(
% 7.73/2.35 spl56_4 <=> ((is_heap_a @ ra) = $true)),
% 7.73/2.35 introduced(definition,[new_symbols(naming,[spl56_4])],[avatar_definition])).
% 7.73/2.35 thf(f1028,definition,(
% 7.73/2.35 spl56_18 <=> (ra = (t_a @ v1 @ l1 @ r1))),
% 7.73/2.35 introduced(definition,[new_symbols(naming,[spl56_18])],[avatar_definition])).
% 7.73/2.35 thf(f1495,plain,(
% 7.73/2.35 ($true = (is_heap_a @ (t_a @ va @ la @ ra))) | (~spl56_1 | ~spl56_4 | ~spl56_9 | ~spl56_18)),
% 7.73/2.35 inference(subsumption_resolution,[status(thm)],[f1494,f718])).
% 7.73/2.35 thf(f718,plain,(
% 7.73/2.35 ((is_heap_a @ ra) = $true) | ~spl56_4),
% 7.73/2.35 inference(avatar_component_clause,[status(thm)],[f716])).
% 7.73/2.35 thf(f1494,plain,(
% 7.73/2.35 ($true = (is_heap_a @ (t_a @ va @ la @ ra))) | ((is_heap_a @ ra) != $true) | (~spl56_1 | ~spl56_9 | ~spl56_18)),
% 7.73/2.35 inference(forward_demodulation,[status(thm)],[f1493,f1030])).
% 7.73/2.35 thf(f1030,plain,(
% 7.73/2.35 (ra = (t_a @ v1 @ l1 @ r1)) | ~spl56_18),
% 7.73/2.35 inference(avatar_component_clause,[status(thm)],[f1028])).
% 7.73/2.35 thf(f1493,plain,(
% 7.73/2.35 ($true = (is_heap_a @ (t_a @ va @ la @ ra))) | ($true != (is_heap_a @ (t_a @ v1 @ l1 @ r1))) | (~spl56_1 | ~spl56_9)),
% 7.73/2.35 inference(subsumption_resolution,[status(thm)],[f1481,f740])).
% 7.73/2.35 thf(f1481,plain,(
% 7.73/2.35 ($true = (is_heap_a @ (t_a @ va @ la @ ra))) | ((ord_less_eq_a @ v1 @ v2) != $true) | ($true != (is_heap_a @ (t_a @ v1 @ l1 @ r1))) | ~spl56_1),
% 7.73/2.35 inference(superposition,[status(thm)],[f1477,f703])).
% 7.73/2.35 thf(f1477,plain,(
% 7.73/2.35 ( ! [X2 : tree_a,X3 : a,X0 : tree_a,X1 : a] : (((is_heap_a @ (t_a @ X3 @ e_a @ (t_a @ X1 @ X2 @ X0))) = $true) | ($true != (is_heap_a @ (t_a @ X1 @ X2 @ X0))) | ((ord_less_eq_a @ X1 @ X3) != $true)) )),
% 7.73/2.35 inference(forward_demodulation,[status(thm)],[f651,f607])).
% 7.73/2.35 thf(f651,plain,(
% 7.73/2.35 ( ! [X2 : tree_a,X3 : a,X0 : tree_a,X1 : a] : (($true != (is_heap_a @ (t_a @ X1 @ X2 @ X0))) | ((is_heap_a @ (t_a @ X3 @ e_a @ (t_a @ X1 @ X2 @ X0))) = $true) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ X1 @ X2 @ X0)) @ X3))) )),
% 7.73/2.35 inference(cnf_transformation,[status(thm)],[f574])).
% 7.73/2.35 thf(f574,plain,(
% 7.73/2.35 ! [X0 : tree_a,X1 : a,X2 : tree_a,X3 : a] : ((((is_heap_a @ (t_a @ X3 @ e_a @ (t_a @ X1 @ X2 @ X0))) = $true) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ X1 @ X2 @ X0)) @ X3)) | ($true != (is_heap_a @ (t_a @ X1 @ X2 @ X0)))) & ((($true = (ord_less_eq_a @ (val_a @ (t_a @ X1 @ X2 @ X0)) @ X3)) & ($true = (is_heap_a @ (t_a @ X1 @ X2 @ X0)))) | ((is_heap_a @ (t_a @ X3 @ e_a @ (t_a @ X1 @ X2 @ X0))) != $true)))),
% 7.73/2.35 inference(flattening,[status(thm)],[f573])).
% 7.73/2.35 thf(f573,plain,(
% 7.73/2.35 ! [X0 : tree_a,X1 : a,X2 : tree_a,X3 : a] : ((((is_heap_a @ (t_a @ X3 @ e_a @ (t_a @ X1 @ X2 @ X0))) = $true) | (($true != (ord_less_eq_a @ (val_a @ (t_a @ X1 @ X2 @ X0)) @ X3)) | ($true != (is_heap_a @ (t_a @ X1 @ X2 @ X0))))) & ((($true = (ord_less_eq_a @ (val_a @ (t_a @ X1 @ X2 @ X0)) @ X3)) & ($true = (is_heap_a @ (t_a @ X1 @ X2 @ X0)))) | ((is_heap_a @ (t_a @ X3 @ e_a @ (t_a @ X1 @ X2 @ X0))) != $true)))),
% 7.73/2.35 inference(nnf_transformation,[status(thm)],[f342])).
% 7.73/2.35 thf(f342,plain,(
% 7.73/2.35 ! [X0 : tree_a,X1 : a,X2 : tree_a,X3 : a] : (((is_heap_a @ (t_a @ X3 @ e_a @ (t_a @ X1 @ X2 @ X0))) = $true) <=> (($true = (ord_less_eq_a @ (val_a @ (t_a @ X1 @ X2 @ X0)) @ X3)) & ($true = (is_heap_a @ (t_a @ X1 @ X2 @ X0)))))),
% 7.73/2.35 inference(fool_elimination,[status(thm)],[f341])).
% 7.73/2.35 thf(f341,plain,(
% 7.73/2.35 ! [X0 : tree_a,X1 : a,X2 : tree_a,X3 : a] : ((is_heap_a @ (t_a @ X3 @ e_a @ (t_a @ X1 @ X2 @ X0))) = (ord_less_eq_a @ (val_a @ (t_a @ X1 @ X2 @ X0)) @ X3) & (is_heap_a @ (t_a @ X1 @ X2 @ X0)))),
% 7.73/2.35 inference(rectify,[status(thm)],[f33])).
% 7.73/2.35 thf(f33,axiom,(
% 7.73/2.35 ! [X40 : tree_a,X38 : a,X39 : tree_a,X0 : a] : ((is_heap_a @ (t_a @ X0 @ e_a @ (t_a @ X38 @ X39 @ X40))) = (ord_less_eq_a @ (val_a @ (t_a @ X38 @ X39 @ X40)) @ X0) & (is_heap_a @ (t_a @ X38 @ X39 @ X40)))),
% 7.73/2.35 file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_32_is__heap_Osimps_I3_J)).
% 7.73/2.35 thf(f1031,plain,(
% 7.73/2.35 spl56_18 | ~spl56_1),
% 7.73/2.35 inference(avatar_split_clause,[status(thm)],[f1026,f701,f1028])).
% 7.73/2.35 thf(f1026,plain,(
% 7.73/2.35 (ra = (t_a @ v1 @ l1 @ r1)) | ~spl56_1),
% 7.73/2.35 inference(forward_demodulation,[status(thm)],[f1011,f622])).
% 7.73/2.35 thf(f622,plain,(
% 7.73/2.35 ( ! [X2 : tree_a,X0 : a,X1 : tree_a] : (((heapIm1257206334ight_a @ (t_a @ X0 @ X2 @ X1)) = X1)) )),
% 7.73/2.35 inference(cnf_transformation,[status(thm)],[f487])).
% 7.73/2.35 thf(f487,plain,(
% 7.73/2.35 ! [X0 : a,X1 : tree_a,X2 : tree_a] : ((heapIm1257206334ight_a @ (t_a @ X0 @ X2 @ X1)) = X1)),
% 7.73/2.35 inference(rectify,[status(thm)],[f35])).
% 7.73/2.35 thf(f35,axiom,(
% 7.73/2.35 ! [X0 : a,X11 : tree_a,X10 : tree_a] : ((heapIm1257206334ight_a @ (t_a @ X0 @ X10 @ X11)) = X11)),
% 7.73/2.35 file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_34_right_Osimps)).
% 7.73/2.35 thf(f1011,plain,(
% 7.73/2.35 ((t_a @ v1 @ l1 @ r1) = (heapIm1257206334ight_a @ (t_a @ va @ la @ ra))) | ~spl56_1),
% 7.73/2.35 inference(superposition,[status(thm)],[f622,f703])).
% 7.73/2.35 thf(f741,plain,(
% 7.73/2.35 spl56_9),
% 7.73/2.35 inference(avatar_split_clause,[status(thm)],[f680,f738])).
% 7.73/2.35 thf(f680,plain,(
% 7.73/2.35 ((ord_less_eq_a @ v1 @ v2) = $true)),
% 7.73/2.35 inference(cnf_transformation,[status(thm)],[f276])).
% 7.73/2.35 thf(f276,plain,(
% 7.73/2.35 ((ord_less_eq_a @ v1 @ v2) = $true)),
% 7.73/2.35 inference(fool_elimination,[status(thm)],[f275])).
% 7.73/2.35 thf(f275,plain,(
% 7.73/2.35 (ord_less_eq_a @ v1 @ v2)),
% 7.73/2.35 inference(rectify,[status(thm)],[f5])).
% 7.73/2.35 thf(f5,axiom,(
% 7.73/2.35 (ord_less_eq_a @ v1 @ v2)),
% 7.73/2.35 file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_4_True)).
% 7.73/2.35 thf(f736,plain,(
% 7.73/2.35 ~spl56_8),
% 7.73/2.35 inference(avatar_split_clause,[status(thm)],[f638,f733])).
% 7.73/2.35 thf(f638,plain,(
% 7.73/2.35 ((is_heap_a @ (heapIm1091024090Down_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)))) != $true)),
% 7.73/2.35 inference(cnf_transformation,[status(thm)],[f473])).
% 7.73/2.35 thf(f473,plain,(
% 7.73/2.35 ((is_heap_a @ (heapIm1091024090Down_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)))) != $true)),
% 7.73/2.35 inference(flattening,[status(thm)],[f256])).
% 7.73/2.35 thf(f256,plain,(
% 7.73/2.35 ~((is_heap_a @ (heapIm1091024090Down_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)))) = $true)),
% 7.73/2.35 inference(fool_elimination,[status(thm)],[f255])).
% 7.73/2.35 thf(f255,plain,(
% 7.73/2.35 ~(is_heap_a @ (heapIm1091024090Down_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1))))),
% 7.73/2.35 inference(rectify,[status(thm)],[f177])).
% 7.73/2.35 thf(f177,negated_conjecture,(
% 7.73/2.35 ~(is_heap_a @ (heapIm1091024090Down_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1))))),
% 7.73/2.35 inference(negated_conjecture,[status(cth)],[f176])).
% 7.73/2.35 thf(f176,conjecture,(
% 7.73/2.35 (is_heap_a @ (heapIm1091024090Down_a @ (t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1))))),
% 7.73/2.35 file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',conj_0)).
% 7.73/2.35 thf(f719,plain,(
% 7.73/2.35 spl56_4),
% 7.73/2.35 inference(avatar_split_clause,[status(thm)],[f602,f716])).
% 7.73/2.35 thf(f602,plain,(
% 7.73/2.35 ((is_heap_a @ ra) = $true)),
% 7.73/2.35 inference(cnf_transformation,[status(thm)],[f348])).
% 7.73/2.35 thf(f348,plain,(
% 7.73/2.35 ((is_heap_a @ ra) = $true)),
% 7.73/2.35 inference(fool_elimination,[status(thm)],[f347])).
% 7.73/2.35 thf(f347,plain,(
% 7.73/2.35 (is_heap_a @ ra)),
% 7.73/2.35 inference(rectify,[status(thm)],[f1])).
% 7.73/2.35 thf(f1,axiom,(
% 7.73/2.35 (is_heap_a @ ra)),
% 7.73/2.35 file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_0__C4_Oprems_C_I2_J)).
% 7.73/2.35 thf(f704,plain,(
% 7.73/2.35 spl56_1),
% 7.73/2.35 inference(avatar_split_clause,[status(thm)],[f593,f701])).
% 7.73/2.35 thf(f593,plain,(
% 7.73/2.35 ((t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)) = (t_a @ va @ la @ ra))),
% 7.73/2.35 inference(cnf_transformation,[status(thm)],[f6])).
% 7.73/2.35 thf(f6,axiom,(
% 7.73/2.35 ((t_a @ v2 @ e_a @ (t_a @ v1 @ l1 @ r1)) = (t_a @ va @ la @ ra))),
% 7.73/2.35 file('/export/starexec/sandbox/tmp/tmp.HDh29X2AMh/DTF2THF_30403.p',fact_5__C4_Oprems_C_I3_J)).
% 7.73/2.35 % SZS output end Proof for DTF2THF_30403
% 7.73/2.35 % (30767)------------------------------
% 7.73/2.35 % (30767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.35 % (30767)Termination reason: Refutation
% 7.73/2.35
% 7.73/2.35 % (30767)Memory used [KB]: 7036
% 7.73/2.35 % (30767)Time elapsed: 0.085 s
% 7.73/2.35 % (30767)Instructions burned: 261 (million)
% 7.73/2.35 % (30767)------------------------------
% 7.73/2.35 % (30767)------------------------------
% 7.73/2.35 % (30681)Success in time 0.822 s
%------------------------------------------------------------------------------