%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP067^1 : 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 : n029.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 35.03s 6.26s
% Output : Refutation 35.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 123 ( 36 unt; 0 typ; 6 def)
% Number of atoms : 838 ( 314 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 3239 ( 149 ~; 162 |; 38 &;2823 @)
% ( 7 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 109 ( 106 usr; 20 con; 0-3 aty)
% Number of variables : 175 ( 0 ^; 175 !; 0 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
multiset_a: $tType ).
thf(type_def_7,type,
set_a: $tType ).
thf(type_def_8,type,
tree_a: $tType ).
thf(type_def_9,type,
a: $tType ).
thf(func_def_0,type,
multiset_a: $tType ).
thf(func_def_1,type,
tree_a: $tType ).
thf(func_def_2,type,
set_a: $tType ).
thf(func_def_3,type,
a: $tType ).
thf(func_def_4,type,
minus_1649712171iset_a: multiset_a > multiset_a > multiset_a ).
thf(func_def_5,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(func_def_6,type,
plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
thf(func_def_7,type,
zero_zero_multiset_a: multiset_a ).
thf(func_def_8,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(func_def_9,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(func_def_10,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(func_def_11,type,
e_a: tree_a ).
thf(func_def_12,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(func_def_13,type,
pred_Tree_a: ( a > $o ) > tree_a > $o ).
thf(func_def_14,type,
set_Tree_a: tree_a > set_a ).
thf(func_def_15,type,
in_tree_a: a > tree_a > $o ).
thf(func_def_16,type,
is_heap_a: tree_a > $o ).
thf(func_def_17,type,
multiset_a2: tree_a > multiset_a ).
thf(func_def_18,type,
val_a: tree_a > a ).
thf(func_def_19,type,
lattic146396397_Max_a: set_a > a ).
thf(func_def_20,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(func_def_21,type,
set_mset_a: multiset_a > set_a ).
thf(func_def_22,type,
bot_bot_a_o: a > $o ).
thf(func_def_23,type,
bot_bot_set_a: set_a ).
thf(func_def_24,type,
ord_less_eq_o_o_a: ( $o > $o > a ) > ( $o > $o > a ) > $o ).
thf(func_def_25,type,
ord_less_eq_o_a: ( $o > a ) > ( $o > a ) > $o ).
thf(func_def_26,type,
ord_less_eq_Tree_a_o: ( tree_a > $o ) > ( tree_a > $o ) > $o ).
thf(func_def_27,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_28,type,
ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
thf(func_def_29,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_30,type,
ord_less_eq_a: a > a > $o ).
thf(func_def_31,type,
order_Greatest_o_a: ( ( $o > a ) > $o ) > $o > a ).
thf(func_def_32,type,
order_Greatest_a: ( a > $o ) > a ).
thf(func_def_33,type,
ball_a: set_a > ( a > $o ) > $o ).
thf(func_def_34,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_35,type,
insert_a: a > set_a > set_a ).
thf(func_def_36,type,
is_singleton_a: set_a > $o ).
thf(func_def_37,type,
member_a: a > set_a > $o ).
thf(func_def_38,type,
l1: tree_a ).
thf(func_def_39,type,
l2: tree_a ).
thf(func_def_40,type,
r1: tree_a ).
thf(func_def_41,type,
r2: tree_a ).
thf(func_def_42,type,
t: tree_a ).
thf(func_def_43,type,
v: a ).
thf(func_def_44,type,
v1: a ).
thf(func_def_45,type,
v2: a ).
thf(func_def_46,type,
v3: a ).
thf(func_def_58,type,
sP0: a > a > a > $o ).
thf(func_def_59,type,
sP1: a > a > a > $o ).
thf(func_def_60,type,
sP2: a > a > a > $o ).
thf(func_def_61,type,
sK3: ( a > a > $o ) > a ).
thf(func_def_62,type,
sK4: ( a > a > $o ) > a ).
thf(func_def_63,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_64,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_65,type,
sK7: tree_a > tree_a ).
thf(func_def_66,type,
sK8: tree_a > a ).
thf(func_def_67,type,
sK9: tree_a > tree_a ).
thf(func_def_68,type,
sK10: tree_a > tree_a ).
thf(func_def_69,type,
sK11: tree_a > a ).
thf(func_def_70,type,
sK12: tree_a > a ).
thf(func_def_71,type,
sK13: tree_a > tree_a ).
thf(func_def_72,type,
sK14: tree_a > tree_a ).
thf(func_def_73,type,
sK15: tree_a > a ).
thf(func_def_74,type,
sK16: tree_a > tree_a ).
thf(func_def_75,type,
sK17: tree_a > a ).
thf(func_def_76,type,
sK18: tree_a > a ).
thf(func_def_77,type,
sK19: tree_a > tree_a ).
thf(func_def_78,type,
sK20: tree_a > tree_a ).
thf(func_def_79,type,
sK21: tree_a > a ).
thf(func_def_80,type,
sK22: tree_a > a ).
thf(func_def_81,type,
sK23: tree_a > tree_a ).
thf(func_def_82,type,
sK24: tree_a > tree_a ).
thf(func_def_83,type,
sK25: tree_a > a ).
thf(func_def_84,type,
sK26: ( a > a ) > a ).
thf(func_def_85,type,
sK27: ( a > a ) > a ).
thf(func_def_86,type,
sK28: ( a > a ) > a ).
thf(func_def_87,type,
sK29: ( a > a ) > a ).
thf(func_def_88,type,
sK30: ( a > a ) > a ).
thf(func_def_89,type,
sK31: ( a > a ) > a ).
thf(func_def_90,type,
sK32: ( a > a ) > a ).
thf(func_def_91,type,
sK33: ( a > a ) > a ).
thf(func_def_92,type,
sK34: ( tree_a > $o ) > tree_a ).
thf(func_def_93,type,
sK35: ( tree_a > $o ) > a ).
thf(func_def_94,type,
sK36: ( tree_a > $o ) > tree_a ).
thf(func_def_95,type,
sK37: tree_a > a ).
thf(func_def_96,type,
sK38: tree_a > a ).
thf(func_def_97,type,
sK39: tree_a > tree_a ).
thf(func_def_98,type,
sK40: tree_a > a ).
thf(func_def_99,type,
sK41: tree_a > tree_a ).
thf(func_def_100,type,
sK42: tree_a > tree_a ).
thf(func_def_101,type,
sK43: tree_a > a ).
thf(func_def_102,type,
sK44: tree_a > tree_a ).
thf(func_def_103,type,
sK45: tree_a > a ).
thf(func_def_104,type,
sK46: tree_a > tree_a ).
thf(func_def_105,type,
sK47: tree_a > a ).
thf(func_def_106,type,
sK48: tree_a > a ).
thf(func_def_107,type,
sK49: tree_a > tree_a ).
thf(func_def_108,type,
sK50: tree_a > a ).
thf(func_def_109,type,
sK51: tree_a > tree_a ).
thf(func_def_110,type,
sK52: tree_a > tree_a ).
thf(func_def_111,type,
sK53: tree_a > a > tree_a ).
thf(func_def_112,type,
sK54: tree_a > a > a ).
thf(func_def_113,type,
sK55: tree_a > a > tree_a ).
thf(func_def_115,type,
ph57:
!>[X0: $tType] : X0 ).
thf(f5174,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3919,f4271,f4454,f4468,f4789,f5012,f5173]) ).
thf(f5173,plain,
( spl56_3
| ~ spl56_25 ),
inference(avatar_split_clause,[status(thm)],[f5172,f4465,f833]) ).
thf(f833,definition,
( spl56_3
<=> ( v = v3 ) ),
introduced(definition,[new_symbols(naming,[spl56_3])],[avatar_definition]) ).
thf(f4465,definition,
( spl56_25
<=> ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl56_25])],[avatar_definition]) ).
thf(f5172,plain,
( ( v = v3 )
| ~ spl56_25 ),
inference(trivial_inequality_removal,[status(thm)],[f5171]) ).
thf(f5171,plain,
( ( v = v3 )
| ( $true = $false )
| ~ spl56_25 ),
inference(forward_demodulation,[status(thm)],[f5170,f758]) ).
thf(f758,plain,
( ( in_tree_a @ v @ r1 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f749]) ).
thf(f749,plain,
( ( $true != $true )
| ( ( in_tree_a @ v @ r1 )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f741]) ).
thf(f741,plain,
( ( in_tree_a @ v @ r1 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f734]) ).
thf(f734,plain,
( ( $true != $true )
| ( ( in_tree_a @ v @ r1 )
!= $true ) ),
inference(superposition,[status(thm)],[f729,f657]) ).
thf(f657,plain,
! [X2: tree_a,X3: tree_a,X0: a,X1: a] :
( ( ( in_tree_a @ X0 @ X2 )
!= $true )
| ( ( in_tree_a @ X0 @ ( t_a @ X1 @ X3 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f580]) ).
thf(f580,plain,
! [X0: a,X1: a,X2: tree_a,X3: tree_a] :
( ( ( $true
= ( in_tree_a @ X0 @ X3 ) )
| ( ( in_tree_a @ X0 @ X2 )
= $true )
| ( X0 = X1 )
| ( ( in_tree_a @ X0 @ ( t_a @ X1 @ X3 @ X2 ) )
!= $true ) )
& ( ( ( in_tree_a @ X0 @ ( t_a @ X1 @ X3 @ X2 ) )
= $true )
| ( ( $true
!= ( in_tree_a @ X0 @ X3 ) )
& ( ( in_tree_a @ X0 @ X2 )
!= $true )
& ( X0 != X1 ) ) ) ),
inference(flattening,[status(thm)],[f579]) ).
thf(f579,plain,
! [X0: a,X1: a,X2: tree_a,X3: tree_a] :
( ( ( $true
= ( in_tree_a @ X0 @ X3 ) )
| ( ( in_tree_a @ X0 @ X2 )
= $true )
| ( X0 = X1 )
| ( ( in_tree_a @ X0 @ ( t_a @ X1 @ X3 @ X2 ) )
!= $true ) )
& ( ( ( in_tree_a @ X0 @ ( t_a @ X1 @ X3 @ X2 ) )
= $true )
| ( ( $true
!= ( in_tree_a @ X0 @ X3 ) )
& ( ( in_tree_a @ X0 @ X2 )
!= $true )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f219]) ).
thf(f219,plain,
! [X0: a,X1: a,X2: tree_a,X3: tree_a] :
( ( ( $true
= ( in_tree_a @ X0 @ X3 ) )
| ( ( in_tree_a @ X0 @ X2 )
= $true )
| ( X0 = X1 ) )
<=> ( ( in_tree_a @ X0 @ ( t_a @ X1 @ X3 @ X2 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f218]) ).
thf(f218,plain,
! [X0: a,X1: a,X2: tree_a,X3: tree_a] :
( ( ( in_tree_a @ X0 @ ( t_a @ X1 @ X3 @ X2 ) )
= ( X0 = X1 ) )
| ( in_tree_a @ X0 @ X2 )
| ( in_tree_a @ X0 @ X3 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X6: a,X7: a,X9: tree_a,X8: tree_a] :
( ( ( in_tree_a @ X6 @ ( t_a @ X7 @ X8 @ X9 ) )
= ( X6 = X7 ) )
| ( in_tree_a @ X6 @ X9 )
| ( in_tree_a @ X6 @ X8 ) ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_5_in__tree_Osimps_I2_J) ).
thf(f729,plain,
( $true
!= ( in_tree_a @ v @ ( t_a @ v1 @ l1 @ r1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f719]) ).
thf(f719,plain,
( ( $true
!= ( in_tree_a @ v @ ( t_a @ v1 @ l1 @ r1 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f602,f658]) ).
thf(f658,plain,
! [X2: tree_a,X3: tree_a,X0: a,X1: a] :
( ( ( in_tree_a @ X0 @ ( t_a @ X1 @ X3 @ X2 ) )
= $true )
| ( $true
!= ( in_tree_a @ X0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f580]) ).
thf(f602,plain,
( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f474]) ).
thf(f474,plain,
( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
!= $true ),
inference(flattening,[status(thm)],[f191]) ).
thf(f191,plain,
( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f190]) ).
thf(f190,plain,
~ ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(rectify,[status(thm)],[f170]) ).
thf(f170,negated_conjecture,
~ ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(negated_conjecture,[status(cth)],[f169]) ).
thf(f169,conjecture,
in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',conj_0) ).
thf(f5170,plain,
( ( v = v3 )
| ( ( in_tree_a @ v @ r1 )
= $true )
| ~ spl56_25 ),
inference(trivial_inequality_removal,[status(thm)],[f5169]) ).
thf(f5169,plain,
( ( v = v3 )
| ( $true = $false )
| ( ( in_tree_a @ v @ r1 )
= $true )
| ~ spl56_25 ),
inference(forward_demodulation,[status(thm)],[f5159,f788]) ).
thf(f788,plain,
( $false
= ( in_tree_a @ v @ l1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f777]) ).
thf(f777,plain,
( ( $false
= ( in_tree_a @ v @ l1 ) )
| ( $true != $true ) ),
inference(fool_paramodulation,[status(thm)],[f744]) ).
thf(f744,plain,
( $true
!= ( in_tree_a @ v @ l1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f735]) ).
thf(f735,plain,
( ( $true
!= ( in_tree_a @ v @ l1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f729,f658]) ).
thf(f5159,plain,
( ( v = v3 )
| ( $true
= ( in_tree_a @ v @ l1 ) )
| ( ( in_tree_a @ v @ r1 )
= $true )
| ~ spl56_25 ),
inference(trivial_inequality_removal,[status(thm)],[f5155]) ).
thf(f5155,plain,
( ( ( in_tree_a @ v @ r1 )
= $true )
| ( $true
= ( in_tree_a @ v @ l1 ) )
| ( v = v3 )
| ( $true != $true )
| ~ spl56_25 ),
inference(superposition,[status(thm)],[f659,f4467]) ).
thf(f4467,plain,
( ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true )
| ~ spl56_25 ),
inference(avatar_component_clause,[status(thm)],[f4465]) ).
thf(f659,plain,
! [X2: tree_a,X3: tree_a,X0: a,X1: a] :
( ( ( in_tree_a @ X0 @ X2 )
= $true )
| ( X0 = X1 )
| ( ( in_tree_a @ X0 @ ( t_a @ X1 @ X3 @ X2 ) )
!= $true )
| ( $true
= ( in_tree_a @ X0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f580]) ).
thf(f5012,plain,
~ spl56_26,
inference(avatar_contradiction_clause,[status(thm)],[f5011]) ).
thf(f5011,plain,
( $false
| ~ spl56_26 ),
inference(trivial_inequality_removal,[status(thm)],[f5010]) ).
thf(f5010,plain,
( ( $true = $false )
| ~ spl56_26 ),
inference(forward_demodulation,[status(thm)],[f4495,f726]) ).
thf(f726,plain,
( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f717]) ).
thf(f717,plain,
( ( $true != $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f602]) ).
thf(f4495,plain,
( ( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $true )
| ~ spl56_26 ),
inference(avatar_component_clause,[status(thm)],[f4493]) ).
thf(f4493,definition,
( spl56_26
<=> ( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl56_26])],[avatar_definition]) ).
thf(f4789,plain,
( ~ spl56_12
| spl56_26 ),
inference(avatar_split_clause,[status(thm)],[f4788,f4493,f3912]) ).
thf(f3912,definition,
( spl56_12
<=> ( $true
= ( ord_less_eq_a @ v1 @ v3 ) ) ),
introduced(definition,[new_symbols(naming,[spl56_12])],[avatar_definition]) ).
thf(f4788,plain,
( ( $true
!= ( ord_less_eq_a @ v1 @ v3 ) )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f4787,f677]) ).
thf(f677,plain,
! [X2: tree_a,X0: a,X1: tree_a] :
( ( val_a @ ( t_a @ X0 @ X1 @ X2 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f483]) ).
thf(f483,plain,
! [X0: a,X1: tree_a,X2: tree_a] :
( ( val_a @ ( t_a @ X0 @ X1 @ X2 ) )
= X0 ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,axiom,
! [X6: a,X43: tree_a,X44: tree_a] :
( ( val_a @ ( t_a @ X6 @ X43 @ X44 ) )
= X6 ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_29_val_Osimps) ).
thf(f4787,plain,
( ( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4786]) ).
thf(f4786,plain,
( ( $true != $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
!= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f4785,f686]) ).
thf(f686,plain,
( ( ord_less_eq_a @ v2 @ v1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f247]) ).
thf(f247,plain,
( ( ord_less_eq_a @ v2 @ v1 )
= $true ),
inference(fool_elimination,[status(thm)],[f246]) ).
thf(f246,plain,
ord_less_eq_a @ v2 @ v1,
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
ord_less_eq_a @ v2 @ v1,
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_2_True) ).
thf(f4785,plain,
( ( ( ord_less_eq_a @ v2 @ v1 )
!= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f4784,f677]) ).
thf(f4784,plain,
( ( $true
!= ( ord_less_eq_a @ v2 @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f4771,f677]) ).
thf(f4771,plain,
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
!= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
!= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f608,f672]) ).
thf(f672,plain,
! [X2: a,X3: a,X0: tree_a,X1: tree_a,X6: a,X4: tree_a,X5: tree_a] :
( ( ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X2 )
!= $true )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f500]) ).
thf(f500,plain,
! [X0: tree_a,X1: tree_a,X2: a,X3: a,X4: tree_a,X5: tree_a,X6: a] :
( ( ( ( ( ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ X2 ) ) )
& ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ X2 ) )
| ( ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( t_a @ X3 @ X0 @ X1 ) @ ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( heapIm1140443833left_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) ) ) ) )
| ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) )
& ( ( ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X2 )
= $true )
| ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) )
& ( ( ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X2 )
!= $true ) ) )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f489]) ).
thf(f489,plain,
! [X0: tree_a,X1: tree_a,X2: a,X3: a,X4: tree_a,X5: tree_a,X6: a] :
( ( ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) )
=> ( ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ X2 ) )
=> ( ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) )
& ( ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ X2 ) )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( t_a @ X3 @ X0 @ X1 ) @ ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( heapIm1140443833left_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) ) ) ) ) )
& ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) )
=> ( ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X2 )
= $true )
=> ( ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) )
& ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X2 )
!= $true )
=> ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f287]) ).
thf(f287,plain,
! [X0: tree_a,X1: tree_a,X2: a,X3: a,X4: tree_a,X5: tree_a,X6: a] :
( ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) )
=> ( ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X2 )
= $true )
=> ( ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) )
& ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X2 )
!= $true )
=> ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) ) ) )
& ( ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) )
=> ( ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ X2 ) )
=> ( ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) )
& ( ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ X2 ) )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( t_a @ X3 @ X0 @ X1 ) @ ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( heapIm1140443833left_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f286]) ).
thf(f286,plain,
! [X0: tree_a,X1: tree_a,X2: a,X3: a,X4: tree_a,X5: tree_a,X6: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X2 )
=> ( ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X2 )
=> ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ X2 )
=> ( ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ X2 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( t_a @ X3 @ X0 @ X1 ) @ ( t_a @ X6 @ X5 @ X4 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( t_a @ X3 @ X0 @ X1 ) @ ( heapIm1091024090Down_a @ ( t_a @ X2 @ ( heapIm1140443833left_a @ ( t_a @ X6 @ X5 @ X4 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X6 @ X5 @ X4 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X27: tree_a,X28: tree_a,X6: a,X26: a,X25: tree_a,X24: tree_a,X23: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ X6 )
=> ( ( t_a @ X6 @ ( t_a @ X26 @ X27 @ X28 ) @ ( t_a @ X23 @ X24 @ X25 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X26 @ X27 @ X28 ) @ ( t_a @ X23 @ X24 @ X25 ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ X6 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X26 @ X27 @ X28 ) @ ( t_a @ X23 @ X24 @ X25 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X26 @ X27 @ X28 ) ) ) ) @ ( t_a @ X23 @ X24 @ X25 ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ X6 )
=> ( ( t_a @ X6 @ ( t_a @ X26 @ X27 @ X28 ) @ ( t_a @ X23 @ X24 @ X25 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X26 @ X27 @ X28 ) @ ( t_a @ X23 @ X24 @ X25 ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ X6 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X26 @ X27 @ X28 ) @ ( t_a @ X23 @ X24 @ X25 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ ( t_a @ X26 @ X27 @ X28 ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X23 @ X24 @ X25 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_15_siftDown_Osimps_I6_J) ).
thf(f608,plain,
( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f273]) ).
thf(f273,plain,
( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f272]) ).
thf(f272,plain,
in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_3__C5__1_Oprems_C) ).
thf(f4468,plain,
( spl56_12
| spl56_25
| ~ spl56_11 ),
inference(avatar_split_clause,[status(thm)],[f4463,f3908,f4465,f3912]) ).
thf(f3908,definition,
( spl56_11
<=> ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl56_11])],[avatar_definition]) ).
thf(f4463,plain,
( ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
!= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true )
| ( $true
= ( ord_less_eq_a @ v1 @ v3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f4462]) ).
thf(f4462,plain,
( ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
!= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true )
| ( $true != $true )
| ( $true
= ( ord_less_eq_a @ v1 @ v3 ) ) ),
inference(forward_demodulation,[status(thm)],[f4461,f686]) ).
thf(f4461,plain,
( ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true )
| ( $true
= ( ord_less_eq_a @ v1 @ v3 ) )
| ( ( ord_less_eq_a @ v2 @ v1 )
!= $true )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f4460,f677]) ).
thf(f4460,plain,
( ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true )
| ( $true
!= ( ord_less_eq_a @ v2 @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
| ( $true
= ( ord_less_eq_a @ v1 @ v3 ) )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f4459,f677]) ).
thf(f4459,plain,
( ( $true
= ( ord_less_eq_a @ v1 @ v3 ) )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
!= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f4458,f687]) ).
thf(f687,plain,
! [X2: tree_a,X0: a,X1: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X0 @ X1 @ X2 ) )
= X2 ),
inference(cnf_transformation,[status(thm)],[f492]) ).
thf(f492,plain,
! [X0: a,X1: tree_a,X2: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X0 @ X1 @ X2 ) )
= X2 ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X6: a,X8: tree_a,X9: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X6 @ X8 @ X9 ) )
= X9 ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_9_right_Osimps) ).
thf(f4458,plain,
( ( $true
!= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) )
| ( $true
= ( ord_less_eq_a @ v1 @ v3 ) )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
!= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f4457,f623]) ).
thf(f623,plain,
! [X2: a,X0: tree_a,X1: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ X2 @ X0 @ X1 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f487]) ).
thf(f487,plain,
! [X0: tree_a,X1: tree_a,X2: a] :
( ( heapIm1140443833left_a @ ( t_a @ X2 @ X0 @ X1 ) )
= X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X8: tree_a,X9: tree_a,X6: a] :
( ( heapIm1140443833left_a @ ( t_a @ X6 @ X8 @ X9 ) )
= X8 ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_8_left_Osimps) ).
thf(f4457,plain,
( ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
!= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
!= $true )
| ( $true
= ( ord_less_eq_a @ v1 @ v3 ) ) ),
inference(forward_demodulation,[status(thm)],[f4456,f677]) ).
thf(f4456,plain,
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ r1 ) )
= $true )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
!= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f4455,f687]) ).
thf(f4455,plain,
( ( $true
= ( in_tree_a @ v @ ( t_a @ v3 @ l1 @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
!= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
!= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f643,f623]) ).
thf(f643,plain,
( ( ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
= $true )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
!= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f531]) ).
thf(f531,plain,
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
= $true )
| ( ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
= $true )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
!= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
!= $true ) ),
inference(flattening,[status(thm)],[f530]) ).
thf(f530,plain,
( ( ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
= $true )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
!= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
= $true )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f476]) ).
thf(f476,plain,
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
= $true )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
!= $true )
=> ( ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
= $true )
=> ( ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f387]) ).
thf(f387,plain,
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
= $true )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
!= $true )
=> ( ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
= $true )
=> ( ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f386]) ).
thf(f386,plain,
( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
=> ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
=> ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
=> ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
=> ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_7__C5__1_Ohyps_C_I1_J) ).
thf(f4454,plain,
~ spl56_3,
inference(avatar_split_clause,[status(thm)],[f668,f833]) ).
thf(f668,plain,
v != v3,
inference(cnf_transformation,[status(thm)],[f520]) ).
thf(f520,plain,
( ( v != v1 )
& ( v != v2 )
& ( v != v3 ) ),
inference(ennf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ( ( v = v3 )
| ( v = v1 )
| ( v = v2 ) ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_0_False) ).
thf(f4271,plain,
~ spl56_13,
inference(avatar_contradiction_clause,[status(thm)],[f4270]) ).
thf(f4270,plain,
( $false
| ~ spl56_13 ),
inference(trivial_inequality_removal,[status(thm)],[f4269]) ).
thf(f4269,plain,
( ( v1 != v1 )
| ~ spl56_13 ),
inference(superposition,[status(thm)],[f670,f3918]) ).
thf(f3918,plain,
( ( v = v1 )
| ~ spl56_13 ),
inference(avatar_component_clause,[status(thm)],[f3916]) ).
thf(f3916,definition,
( spl56_13
<=> ( v = v1 ) ),
introduced(definition,[new_symbols(naming,[spl56_13])],[avatar_definition]) ).
thf(f670,plain,
v != v1,
inference(cnf_transformation,[status(thm)],[f520]) ).
thf(f3919,plain,
( spl56_11
| spl56_12
| spl56_13 ),
inference(avatar_split_clause,[status(thm)],[f3906,f3916,f3912,f3908]) ).
thf(f3906,plain,
( ( v = v1 )
| ( $true
= ( ord_less_eq_a @ v1 @ v3 ) )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3905]) ).
thf(f3905,plain,
( ( $true
= ( ord_less_eq_a @ v1 @ v3 ) )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
= $true )
| ( $true != $true )
| ( v = v1 ) ),
inference(forward_demodulation,[status(thm)],[f3886,f686]) ).
thf(f3886,plain,
( ( v = v1 )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
= $true )
| ( $true
= ( ord_less_eq_a @ v1 @ v3 ) )
| ( ( ord_less_eq_a @ v2 @ v1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3876]) ).
thf(f3876,plain,
( ( $true
= ( ord_less_eq_a @ v1 @ v3 ) )
| ( $true != $true )
| ( v = v1 )
| ( ( ord_less_eq_a @ v2 @ v1 )
!= $true )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ l1 @ r1 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f1282,f608]) ).
thf(f1282,plain,
! [X2: tree_a,X3: a,X0: a,X1: tree_a] :
( ( $true
!= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( t_a @ X0 @ X1 @ X2 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
| ( $true
= ( ord_less_eq_a @ X0 @ X3 ) )
| ( $true
= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ X1 @ X2 ) ) ) )
| ( v = X0 )
| ( $true
!= ( ord_less_eq_a @ v2 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f1281,f677]) ).
thf(f1281,plain,
! [X2: tree_a,X3: a,X0: a,X1: tree_a] :
( ( $true
= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ X1 @ X2 ) ) ) )
| ( $true
= ( ord_less_eq_a @ X0 @ X3 ) )
| ( v = X0 )
| ( $true
!= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( t_a @ X0 @ X1 @ X2 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
| ( $true
!= ( ord_less_eq_a @ v2 @ ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1280,f687]) ).
thf(f1280,plain,
! [X2: tree_a,X3: a,X0: a,X1: tree_a] :
( ( $true
= ( ord_less_eq_a @ X0 @ X3 ) )
| ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ X1 @ ( heapIm1257206334ight_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) ) )
= $true )
| ( v = X0 )
| ( $true
!= ( ord_less_eq_a @ v2 @ ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) )
| ( $true
!= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( t_a @ X0 @ X1 @ X2 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1279,f623]) ).
thf(f1279,plain,
! [X2: tree_a,X3: a,X0: a,X1: tree_a] :
( ( v = X0 )
| ( $true
= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( heapIm1140443833left_a @ ( t_a @ X0 @ X1 @ X2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) ) ) )
| ( $true
!= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( t_a @ X0 @ X1 @ X2 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
| ( $true
!= ( ord_less_eq_a @ v2 @ ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) )
| ( $true
= ( ord_less_eq_a @ X0 @ X3 ) ) ),
inference(forward_demodulation,[status(thm)],[f1278,f677]) ).
thf(f1278,plain,
! [X2: tree_a,X3: a,X0: a,X1: tree_a] :
( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) @ X3 ) )
| ( $true
!= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( t_a @ X0 @ X1 @ X2 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
| ( $true
= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( heapIm1140443833left_a @ ( t_a @ X0 @ X1 @ X2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) ) ) )
| ( $true
!= ( ord_less_eq_a @ v2 @ ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) )
| ( v = X0 ) ),
inference(forward_demodulation,[status(thm)],[f1277,f677]) ).
thf(f1277,plain,
! [X2: tree_a,X3: a,X0: a,X1: tree_a] :
( ( $true
!= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( t_a @ X0 @ X1 @ X2 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
| ( v = X0 )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) )
| ( $true
= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( heapIm1140443833left_a @ ( t_a @ X0 @ X1 @ X2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) ) ) )
| ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) @ X3 ) ) ),
inference(forward_demodulation,[status(thm)],[f1260,f677]) ).
thf(f1260,plain,
! [X2: tree_a,X3: a,X0: a,X1: tree_a] :
( ( v
= ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) )
| ( $true
= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( heapIm1140443833left_a @ ( t_a @ X0 @ X1 @ X2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) ) ) )
| ( $true
!= ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ X3 @ ( t_a @ X0 @ X1 @ X2 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
| ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) @ X3 ) )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ X0 @ X1 @ X2 ) ) ) ) ),
inference(superposition,[status(thm)],[f776,f696]) ).
thf(f696,plain,
! [X2: tree_a,X3: a,X0: tree_a,X1: tree_a,X6: a,X4: tree_a,X5: a] :
( ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ X6 )
= $true )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f512]) ).
thf(f512,plain,
! [X0: tree_a,X1: tree_a,X2: tree_a,X3: a,X4: tree_a,X5: a,X6: a] :
( ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) )
| ( ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X6 ) )
| ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( t_a @ X5 @ X2 @ X4 ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) )
= ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) )
& ( ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X6 ) ) ) ) )
& ( ( ( ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ X6 )
= $true ) )
& ( ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
| ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ X6 )
!= $true ) ) )
| ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f491]) ).
thf(f491,plain,
! [X0: tree_a,X1: tree_a,X2: tree_a,X3: a,X4: tree_a,X5: a,X6: a] :
( ( ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) )
=> ( ( ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X6 ) )
=> ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( t_a @ X5 @ X2 @ X4 ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) )
= ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) )
& ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X6 ) )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) ) )
& ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) )
=> ( ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ X6 )
!= $true )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) )
& ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ X6 )
= $true )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f209]) ).
thf(f209,plain,
! [X0: tree_a,X1: tree_a,X2: tree_a,X3: a,X4: tree_a,X5: a,X6: a] :
( ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) )
=> ( ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ X6 )
= $true )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) )
& ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ X6 )
!= $true )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) ) )
& ( ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) )
=> ( ( ( $true
= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X6 ) )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) )
& ( ( $true
!= ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X6 ) )
=> ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( t_a @ X5 @ X2 @ X4 ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) )
= ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f208]) ).
thf(f208,plain,
! [X0: tree_a,X1: tree_a,X2: tree_a,X3: a,X4: tree_a,X5: a,X6: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ X6 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ X6 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X5 @ X2 @ X4 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X5 @ X2 @ X4 ) ) ) ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( val_a @ ( t_a @ X5 @ X2 @ X4 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X6 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) )
= ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ X6 )
=> ( ( t_a @ ( val_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( t_a @ X5 @ X2 @ X4 ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X3 @ X0 @ X1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) )
= ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X5 @ X2 @ X4 ) @ ( t_a @ X3 @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,axiom,
! [X27: tree_a,X28: tree_a,X24: tree_a,X26: a,X25: tree_a,X23: a,X6: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ X6 )
=> ( ( t_a @ X6 @ ( t_a @ X23 @ X24 @ X25 ) @ ( t_a @ X26 @ X27 @ X28 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X23 @ X24 @ X25 ) @ ( t_a @ X26 @ X27 @ X28 ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ X6 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X23 @ X24 @ X25 ) @ ( t_a @ X26 @ X27 @ X28 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X23 @ X24 @ X25 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X23 @ X24 @ X25 ) ) ) ) @ ( t_a @ X26 @ X27 @ X28 ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ ( val_a @ ( t_a @ X23 @ X24 @ X25 ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ X6 )
=> ( ( t_a @ X6 @ ( t_a @ X23 @ X24 @ X25 ) @ ( t_a @ X26 @ X27 @ X28 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X23 @ X24 @ X25 ) @ ( t_a @ X26 @ X27 @ X28 ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ X6 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( t_a @ X23 @ X24 @ X25 ) @ ( t_a @ X26 @ X27 @ X28 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ ( t_a @ X23 @ X24 @ X25 ) @ ( heapIm1091024090Down_a @ ( t_a @ X6 @ ( heapIm1140443833left_a @ ( t_a @ X26 @ X27 @ X28 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X26 @ X27 @ X28 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_16_siftDown_Osimps_I5_J) ).
thf(f776,plain,
! [X0: a,X1: tree_a] :
( ( $true
!= ( in_tree_a @ v @ ( t_a @ X0 @ X1 @ ( t_a @ v2 @ l2 @ r2 ) ) ) )
| ( v = X0 )
| ( $true
= ( in_tree_a @ v @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f765]) ).
thf(f765,plain,
! [X0: a,X1: tree_a] :
( ( $true != $true )
| ( v = X0 )
| ( $true
!= ( in_tree_a @ v @ ( t_a @ X0 @ X1 @ ( t_a @ v2 @ l2 @ r2 ) ) ) )
| ( $true
= ( in_tree_a @ v @ X1 ) ) ),
inference(superposition,[status(thm)],[f732,f659]) ).
thf(f732,plain,
( $true
!= ( in_tree_a @ v @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f718]) ).
thf(f718,plain,
( ( $true
!= ( in_tree_a @ v @ ( t_a @ v2 @ l2 @ r2 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f602,f657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP067^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n029.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
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:25:29 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
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : ITP067^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.45 % Domain : Interactive Theorem Proving
% 0.20/0.45 % Problem : Sledgehammer HeapImperative problem prob_172__5340680_1
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Des21]
% 0.20/0.45 % Names : HeapImperative/prob_172__5340680_1 [Des21]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0
% 0.20/0.45 % Syntax : Number of formulae : 216 ( 63 unt; 47 typ; 0 def)
% 0.20/0.45 % Number of atoms : 532 ( 157 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 12 ( 3 avg)
% 0.20/0.45 % Number of connectives : 2064 ( 75 ~; 8 |; 42 &;1668 @)
% 0.20/0.45 % ( 0 <=>; 271 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 19 ( 7 avg)
% 0.20/0.45 % Number of types : 5 ( 4 usr)
% 0.20/0.45 % Number of type conns : 224 ( 224 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 46 ( 43 usr; 14 con; 0-3 aty)
% 0.20/0.45 % Number of variables : 553 ( 40 ^; 506 !; 7 ?; 553 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:00.885
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % Could-be-implicit typings (4)
% 0.20/0.45 thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
% 0.20/0.45 multiset_a: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Heap__OTree_Itf__a_J,type,
% 0.20/0.45 tree_a: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 set_a: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_tf__a,type,
% 0.20/0.45 a: $tType ).
% 0.20/0.45
% 0.20/0.45 % Explicit typings (43)
% 0.20/0.45 thf(sy_c_Groups_Ominus__class_Ominus_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.20/0.45 minus_1649712171iset_a: multiset_a > multiset_a > multiset_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 minus_minus_set_a: set_a > set_a > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.20/0.45 plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.20/0.45 zero_zero_multiset_a: multiset_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oleft_001tf__a,type,
% 0.20/0.45 heapIm1140443833left_a: tree_a > tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oright_001tf__a,type,
% 0.20/0.45 heapIm1257206334ight_a: tree_a > tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_OsiftDown_001tf__a,type,
% 0.20/0.45 heapIm1091024090Down_a: tree_a > tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Heap_OTree_OE_001tf__a,type,
% 0.20/0.45 e_a: tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Heap_OTree_OT_001tf__a,type,
% 0.20/0.45 t_a: a > tree_a > tree_a > tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Heap_OTree_Opred__Tree_001tf__a,type,
% 0.20/0.45 pred_Tree_a: ( a > $o ) > tree_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Heap_OTree_Oset__Tree_001tf__a,type,
% 0.20/0.45 set_Tree_a: tree_a > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Heap_Oin__tree_001tf__a,type,
% 0.20/0.45 in_tree_a: a > tree_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Heap_Ois__heap_001tf__a,type,
% 0.20/0.45 is_heap_a: tree_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Heap_Omultiset_001tf__a,type,
% 0.20/0.45 multiset_a2: tree_a > multiset_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Heap_Oval_001tf__a,type,
% 0.20/0.45 val_a: tree_a > a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001tf__a,type,
% 0.20/0.45 lattic146396397_Max_a: set_a > a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Multiset_Oadd__mset_001tf__a,type,
% 0.20/0.45 add_mset_a: a > multiset_a > multiset_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Multiset_Oset__mset_001tf__a,type,
% 0.20/0.45 set_mset_a: multiset_a > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 0.20/0.45 bot_bot_a_o: a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 bot_bot_set_a: set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mtf__a_J_J,type,
% 0.20/0.45 ord_less_eq_o_o_a: ( $o > $o > a ) > ( $o > $o > a ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mtf__a_J,type,
% 0.20/0.45 ord_less_eq_o_a: ( $o > a ) > ( $o > a ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Heap__OTree_Itf__a_J_M_Eo_J,type,
% 0.20/0.45 ord_less_eq_Tree_a_o: ( tree_a > $o ) > ( tree_a > $o ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J,type,
% 0.20/0.45 ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.20/0.45 ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__a,type,
% 0.20/0.45 ord_less_eq_a: a > a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mtf__a_J,type,
% 0.20/0.45 order_Greatest_o_a: ( ( $o > a ) > $o ) > $o > a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oorder__class_OGreatest_001tf__a,type,
% 0.20/0.45 order_Greatest_a: ( a > $o ) > a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Set_OBall_001tf__a,type,
% 0.20/0.45 ball_a: set_a > ( a > $o ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.20/0.45 collect_a: ( a > $o ) > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.20/0.45 insert_a: a > set_a > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Set_Ois__singleton_001tf__a,type,
% 0.20/0.45 is_singleton_a: set_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_member_001tf__a,type,
% 0.20/0.45 member_a: a > set_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_l1____,type,
% 0.20/0.45 l1: tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_l2____,type,
% 0.20/0.45 l2: tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_r1____,type,
% 0.20/0.45 r1: tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_r2____,type,
% 0.20/0.45 r2: tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_t,type,
% 0.20/0.45 t: tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_v,type,
% 0.20/0.45 v: a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_v1____,type,
% 0.20/0.45 v1: a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_v2____,type,
% 0.20/0.45 v2: a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_v_H____,type,
% 0.20/0.45 v3: a ).
% 0.20/0.45
% 0.20/0.45 % Relevant facts (168)
% 0.20/0.45 thf(fact_0_False,axiom,
% 0.20/0.45 ~ ( ( v = v3 )
% 0.20/0.45 | ( v = v1 )
% 0.20/0.45 | ( v = v2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % False
% 0.20/0.45 thf(fact_1__092_060open_062in__tree_Av_A_IsiftDown_At_J_092_060close_062,axiom,
% 0.20/0.45 in_tree_a @ v @ ( heapIm1091024090Down_a @ t ) ).
% 0.20/0.45
% 0.20/0.45 % \<open>in_tree v (siftDown t)\<close>
% 0.20/0.45 thf(fact_2_True,axiom,
% 0.20/0.45 ord_less_eq_a @ v2 @ v1 ).
% 0.20/0.45
% 0.20/0.45 % True
% 0.20/0.45 thf(fact_3__C5__1_Oprems_C,axiom,
% 0.20/0.45 in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % "5_1.prems"
% 0.20/0.45 thf(fact_4_Tree_Oinject,axiom,
% 0.20/0.45 ! [X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.20/0.45 ( ( ( t_a @ X21 @ X22 @ X23 )
% 0.20/0.45 = ( t_a @ Y21 @ Y22 @ Y23 ) )
% 0.20/0.45 = ( ( X21 = Y21 )
% 0.20/0.45 & ( X22 = Y22 )
% 0.20/0.45 & ( X23 = Y23 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.inject
% 0.20/0.45 thf(fact_5_in__tree_Osimps_I2_J,axiom,
% 0.20/0.45 ! [V: a,V2: a,L: tree_a,R: tree_a] :
% 0.20/0.45 ( ( in_tree_a @ V @ ( t_a @ V2 @ L @ R ) )
% 0.20/0.45 = ( ( V = V2 )
% 0.20/0.45 | ( in_tree_a @ V @ L )
% 0.20/0.45 | ( in_tree_a @ V @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % in_tree.simps(2)
% 0.20/0.45 thf(fact_6__C5__1_Ohyps_C_I2_J,axiom,
% 0.20/0.45 ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
% 0.20/0.45 => ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ v3 )
% 0.20/0.45 => ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
% 0.20/0.45 => ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % "5_1.hyps"(2)
% 0.20/0.45 thf(fact_7__C5__1_Ohyps_C_I1_J,axiom,
% 0.20/0.45 ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
% 0.20/0.45 => ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
% 0.20/0.45 => ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
% 0.20/0.45 => ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % "5_1.hyps"(1)
% 0.20/0.45 thf(fact_8_left_Osimps,axiom,
% 0.20/0.45 ! [V: a,L: tree_a,R: tree_a] :
% 0.20/0.45 ( ( heapIm1140443833left_a @ ( t_a @ V @ L @ R ) )
% 0.20/0.45 = L ) ).
% 0.20/0.45
% 0.20/0.45 % left.simps
% 0.20/0.45 thf(fact_9_right_Osimps,axiom,
% 0.20/0.45 ! [V: a,L: tree_a,R: tree_a] :
% 0.20/0.45 ( ( heapIm1257206334ight_a @ ( t_a @ V @ L @ R ) )
% 0.20/0.45 = R ) ).
% 0.20/0.45
% 0.20/0.45 % right.simps
% 0.20/0.45 thf(fact_10_siftDown_Ocases,axiom,
% 0.20/0.45 ! [X: tree_a] :
% 0.20/0.45 ( ( X != e_a )
% 0.20/0.45 => ( ! [V3: a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V3 @ e_a @ e_a ) )
% 0.20/0.45 => ( ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V3 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.20/0.45 => ( ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V3 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.20/0.45 => ~ ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V3 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.cases
% 0.20/0.45 thf(fact_11_Tree_Opred__inject_I2_J,axiom,
% 0.20/0.45 ! [P: a > $o,A: a,Aa: tree_a,Ab: tree_a] :
% 0.20/0.45 ( ( pred_Tree_a @ P @ ( t_a @ A @ Aa @ Ab ) )
% 0.20/0.45 = ( ( P @ A )
% 0.20/0.45 & ( pred_Tree_a @ P @ Aa )
% 0.20/0.45 & ( pred_Tree_a @ P @ Ab ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.pred_inject(2)
% 0.20/0.45 thf(fact_12_in__tree_Osimps_I1_J,axiom,
% 0.20/0.45 ! [V: a] :
% 0.20/0.45 ~ ( in_tree_a @ V @ e_a ) ).
% 0.20/0.45
% 0.20/0.45 % in_tree.simps(1)
% 0.20/0.45 thf(fact_13_Tree_Oset__intros_I3_J,axiom,
% 0.20/0.45 ! [Ya: a,X23: tree_a,X21: a,X22: tree_a] :
% 0.20/0.45 ( ( member_a @ Ya @ ( set_Tree_a @ X23 ) )
% 0.20/0.45 => ( member_a @ Ya @ ( set_Tree_a @ ( t_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.set_intros(3)
% 0.20/0.45 thf(fact_14_Tree_Opred__inject_I1_J,axiom,
% 0.20/0.45 ! [P: a > $o] : ( pred_Tree_a @ P @ e_a ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.pred_inject(1)
% 0.20/0.45 thf(fact_15_siftDown_Osimps_I6_J,axiom,
% 0.20/0.45 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a,V: a] :
% 0.20/0.45 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( 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 ) ) ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(6)
% 0.20/0.45 thf(fact_16_siftDown_Osimps_I5_J,axiom,
% 0.20/0.45 ! [Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 0.20/0.45 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( 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 ) ) ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(5)
% 0.20/0.45 thf(fact_17_siftDown_Osimps_I4_J,axiom,
% 0.20/0.45 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 0.20/0.45 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( 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 ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(4)
% 0.20/0.45 thf(fact_18_siftDown_Osimps_I3_J,axiom,
% 0.20/0.45 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 0.20/0.45 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.20/0.45 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.20/0.45 = ( 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 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(3)
% 0.20/0.45 thf(fact_19_siftDown_Osimps_I1_J,axiom,
% 0.20/0.45 ( ( heapIm1091024090Down_a @ e_a )
% 0.20/0.45 = e_a ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(1)
% 0.20/0.45 thf(fact_20_Tree_Opred__cong,axiom,
% 0.20/0.45 ! [X: tree_a,Ya: tree_a,P: a > $o,Pa: a > $o] :
% 0.20/0.45 ( ( X = Ya )
% 0.20/0.45 => ( ! [Z: a] :
% 0.20/0.45 ( ( member_a @ Z @ ( set_Tree_a @ Ya ) )
% 0.20/0.45 => ( ( P @ Z )
% 0.20/0.45 = ( Pa @ Z ) ) )
% 0.20/0.45 => ( ( pred_Tree_a @ P @ X )
% 0.20/0.45 = ( pred_Tree_a @ Pa @ Ya ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.pred_cong
% 0.20/0.45 thf(fact_21_Tree_Opred__mono__strong,axiom,
% 0.20/0.45 ! [P: a > $o,X: tree_a,Pa: a > $o] :
% 0.20/0.45 ( ( pred_Tree_a @ P @ X )
% 0.20/0.45 => ( ! [Z: a] :
% 0.20/0.45 ( ( member_a @ Z @ ( set_Tree_a @ X ) )
% 0.20/0.45 => ( ( P @ Z )
% 0.20/0.45 => ( Pa @ Z ) ) )
% 0.20/0.45 => ( pred_Tree_a @ Pa @ X ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.pred_mono_strong
% 0.20/0.45 thf(fact_22_siftDown__in__tree,axiom,
% 0.20/0.45 ! [T: tree_a] :
% 0.20/0.45 ( ( T != e_a )
% 0.20/0.45 => ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ T ) ) @ T ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown_in_tree
% 0.20/0.45 thf(fact_23_siftDown__Node,axiom,
% 0.20/0.45 ! [T: tree_a,V: a,L: tree_a,R: tree_a] :
% 0.20/0.45 ( ( T
% 0.20/0.45 = ( t_a @ V @ L @ R ) )
% 0.20/0.45 => ? [L2: tree_a,V4: a,R2: tree_a] :
% 0.20/0.45 ( ( ( heapIm1091024090Down_a @ T )
% 0.20/0.45 = ( t_a @ V4 @ L2 @ R2 ) )
% 0.20/0.45 & ( ord_less_eq_a @ V @ V4 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown_Node
% 0.20/0.45 thf(fact_24_is__heap_Ocases,axiom,
% 0.20/0.45 ! [X: tree_a] :
% 0.20/0.45 ( ( X != e_a )
% 0.20/0.45 => ( ! [V3: a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V3 @ e_a @ e_a ) )
% 0.20/0.45 => ( ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V3 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.20/0.45 => ( ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V3 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.20/0.45 => ~ ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V3 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % is_heap.cases
% 0.20/0.45 thf(fact_25_Tree_Oexhaust,axiom,
% 0.20/0.45 ! [Y: tree_a] :
% 0.20/0.45 ( ( Y != e_a )
% 0.20/0.45 => ~ ! [X212: a,X222: tree_a,X232: tree_a] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( t_a @ X212 @ X222 @ X232 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.exhaust
% 0.20/0.45 thf(fact_26_Tree_Oinduct,axiom,
% 0.20/0.45 ! [P: tree_a > $o,Tree: tree_a] :
% 0.20/0.45 ( ( P @ e_a )
% 0.20/0.45 => ( ! [X1: a,X2: tree_a,X3: tree_a] :
% 0.20/0.45 ( ( P @ X2 )
% 0.20/0.45 => ( ( P @ X3 )
% 0.20/0.45 => ( P @ ( t_a @ X1 @ X2 @ X3 ) ) ) )
% 0.20/0.45 => ( P @ Tree ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.induct
% 0.20/0.45 thf(fact_27_Tree_Odistinct_I1_J,axiom,
% 0.20/0.45 ! [X21: a,X22: tree_a,X23: tree_a] :
% 0.20/0.45 ( e_a
% 0.20/0.45 != ( t_a @ X21 @ X22 @ X23 ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.distinct(1)
% 0.20/0.45 thf(fact_28_siftDown_Osimps_I2_J,axiom,
% 0.20/0.45 ! [V: a] :
% 0.20/0.45 ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ e_a ) )
% 0.20/0.45 = ( t_a @ V @ e_a @ e_a ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(2)
% 0.20/0.45 thf(fact_29_val_Osimps,axiom,
% 0.20/0.45 ! [V: a,Uu: tree_a,Uv: tree_a] :
% 0.20/0.45 ( ( val_a @ ( t_a @ V @ Uu @ Uv ) )
% 0.20/0.45 = V ) ).
% 0.20/0.45
% 0.20/0.45 % val.simps
% 0.20/0.45 thf(fact_30_Tree_Oset__cases,axiom,
% 0.20/0.45 ! [E: a,A: tree_a] :
% 0.20/0.45 ( ( member_a @ E @ ( set_Tree_a @ A ) )
% 0.20/0.45 => ( ! [Z2: tree_a,Z3: tree_a] :
% 0.20/0.46 ( A
% 0.20/0.46 != ( t_a @ E @ Z2 @ Z3 ) )
% 0.20/0.46 => ( ! [Z1: a,Z2: tree_a] :
% 0.20/0.46 ( ? [Z3: tree_a] :
% 0.20/0.46 ( A
% 0.20/0.46 = ( t_a @ Z1 @ Z2 @ Z3 ) )
% 0.20/0.46 => ~ ( member_a @ E @ ( set_Tree_a @ Z2 ) ) )
% 0.20/0.46 => ~ ! [Z1: a,Z2: tree_a,Z3: tree_a] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( t_a @ Z1 @ Z2 @ Z3 ) )
% 0.20/0.46 => ~ ( member_a @ E @ ( set_Tree_a @ Z3 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Tree.set_cases
% 0.20/0.46 thf(fact_31_Tree_Oset__intros_I1_J,axiom,
% 0.20/0.46 ! [X21: a,X22: tree_a,X23: tree_a] : ( member_a @ X21 @ ( set_Tree_a @ ( t_a @ X21 @ X22 @ X23 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Tree.set_intros(1)
% 0.20/0.46 thf(fact_32_Tree_Oset__intros_I2_J,axiom,
% 0.20/0.46 ! [Y: a,X22: tree_a,X21: a,X23: tree_a] :
% 0.20/0.46 ( ( member_a @ Y @ ( set_Tree_a @ X22 ) )
% 0.20/0.46 => ( member_a @ Y @ ( set_Tree_a @ ( t_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Tree.set_intros(2)
% 0.20/0.46 thf(fact_33_order__refl,axiom,
% 0.20/0.46 ! [X: $o > a] : ( ord_less_eq_o_a @ X @ X ) ).
% 0.20/0.46
% 0.20/0.46 % order_refl
% 0.20/0.46 thf(fact_34_order__refl,axiom,
% 0.20/0.46 ! [X: a] : ( ord_less_eq_a @ X @ X ) ).
% 0.20/0.46
% 0.20/0.46 % order_refl
% 0.20/0.46 thf(fact_35_is__heap_Osimps_I4_J,axiom,
% 0.20/0.46 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.20/0.46 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.20/0.46 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.46 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_heap.simps(4)
% 0.20/0.46 thf(fact_36_is__heap_Osimps_I3_J,axiom,
% 0.20/0.46 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.20/0.46 ( ( is_heap_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.46 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.46 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_heap.simps(3)
% 0.20/0.46 thf(fact_37_is__heap__max,axiom,
% 0.20/0.46 ! [V: a,T: tree_a] :
% 0.20/0.46 ( ( in_tree_a @ V @ T )
% 0.20/0.46 => ( ( is_heap_a @ T )
% 0.20/0.46 => ( ord_less_eq_a @ V @ ( val_a @ T ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_heap_max
% 0.20/0.46 thf(fact_38_is__heap_Osimps_I6_J,axiom,
% 0.20/0.46 ! [V: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.20/0.46 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.46 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.46 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.20/0.46 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.20/0.46 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_heap.simps(6)
% 0.20/0.46 thf(fact_39_is__heap_Osimps_I5_J,axiom,
% 0.20/0.46 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 0.20/0.46 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.46 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 0.20/0.46 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) )
% 0.20/0.46 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 0.20/0.46 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_heap.simps(5)
% 0.20/0.46 thf(fact_40_le__funD,axiom,
% 0.20/0.46 ! [F: $o > a,G: $o > a,X: $o] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ F @ G )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_funD
% 0.20/0.46 thf(fact_41_le__funE,axiom,
% 0.20/0.46 ! [F: $o > a,G: $o > a,X: $o] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ F @ G )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_funE
% 0.20/0.46 thf(fact_42_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A: a,P: a > $o] :
% 0.20/0.46 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.20/0.46 = ( P @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_43_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A2: set_a] :
% 0.20/0.46 ( ( collect_a
% 0.20/0.46 @ ^ [X4: a] : ( member_a @ X4 @ A2 ) )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_44_le__funI,axiom,
% 0.20/0.46 ! [F: $o > a,G: $o > a] :
% 0.20/0.46 ( ! [X5: $o] : ( ord_less_eq_a @ ( F @ X5 ) @ ( G @ X5 ) )
% 0.20/0.46 => ( ord_less_eq_o_a @ F @ G ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_funI
% 0.20/0.46 thf(fact_45_le__fun__def,axiom,
% 0.20/0.46 ( ord_less_eq_o_a
% 0.20/0.46 = ( ^ [F2: $o > a,G2: $o > a] :
% 0.20/0.46 ! [X4: $o] : ( ord_less_eq_a @ ( F2 @ X4 ) @ ( G2 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_fun_def
% 0.20/0.46 thf(fact_46_Tree_Opred__mono,axiom,
% 0.20/0.46 ! [P: a > $o,Pa: a > $o] :
% 0.20/0.46 ( ( ord_less_eq_a_o @ P @ Pa )
% 0.20/0.46 => ( ord_less_eq_Tree_a_o @ ( pred_Tree_a @ P ) @ ( pred_Tree_a @ Pa ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Tree.pred_mono
% 0.20/0.46 thf(fact_47_is__heap_Osimps_I1_J,axiom,
% 0.20/0.46 is_heap_a @ e_a ).
% 0.20/0.46
% 0.20/0.46 % is_heap.simps(1)
% 0.20/0.46 thf(fact_48_is__heap_Osimps_I2_J,axiom,
% 0.20/0.46 ! [V: a] : ( is_heap_a @ ( t_a @ V @ e_a @ e_a ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_heap.simps(2)
% 0.20/0.46 thf(fact_49_dual__order_Oantisym,axiom,
% 0.20/0.46 ! [B: $o > a,A: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ B @ A )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ A @ B )
% 0.20/0.46 => ( A = B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.antisym
% 0.20/0.46 thf(fact_50_dual__order_Oantisym,axiom,
% 0.20/0.46 ! [B: a,A: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ B @ A )
% 0.20/0.46 => ( ( ord_less_eq_a @ A @ B )
% 0.20/0.46 => ( A = B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.antisym
% 0.20/0.46 thf(fact_51_dual__order_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: $o > a,Z4: $o > a] : ( Y2 = Z4 ) )
% 0.20/0.46 = ( ^ [A3: $o > a,B2: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ B2 @ A3 )
% 0.20/0.46 & ( ord_less_eq_o_a @ A3 @ B2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.eq_iff
% 0.20/0.46 thf(fact_52_dual__order_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: a,Z4: a] : ( Y2 = Z4 ) )
% 0.20/0.46 = ( ^ [A3: a,B2: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ B2 @ A3 )
% 0.20/0.46 & ( ord_less_eq_a @ A3 @ B2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.eq_iff
% 0.20/0.46 thf(fact_53_dual__order_Otrans,axiom,
% 0.20/0.46 ! [B: $o > a,A: $o > a,C: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ B @ A )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ C @ B )
% 0.20/0.46 => ( ord_less_eq_o_a @ C @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.trans
% 0.20/0.46 thf(fact_54_dual__order_Otrans,axiom,
% 0.20/0.46 ! [B: a,A: a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ B @ A )
% 0.20/0.46 => ( ( ord_less_eq_a @ C @ B )
% 0.20/0.46 => ( ord_less_eq_a @ C @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.trans
% 0.20/0.46 thf(fact_55_linorder__wlog,axiom,
% 0.20/0.46 ! [P: a > a > $o,A: a,B: a] :
% 0.20/0.46 ( ! [A4: a,B3: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A4 @ B3 )
% 0.20/0.46 => ( P @ A4 @ B3 ) )
% 0.20/0.46 => ( ! [A4: a,B3: a] :
% 0.20/0.46 ( ( P @ B3 @ A4 )
% 0.20/0.46 => ( P @ A4 @ B3 ) )
% 0.20/0.46 => ( P @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % linorder_wlog
% 0.20/0.46 thf(fact_56_dual__order_Orefl,axiom,
% 0.20/0.46 ! [A: $o > a] : ( ord_less_eq_o_a @ A @ A ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.refl
% 0.20/0.46 thf(fact_57_dual__order_Orefl,axiom,
% 0.20/0.46 ! [A: a] : ( ord_less_eq_a @ A @ A ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.refl
% 0.20/0.46 thf(fact_58_order__trans,axiom,
% 0.20/0.46 ! [X: $o > a,Y: $o > a,Z5: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X @ Y )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ Y @ Z5 )
% 0.20/0.46 => ( ord_less_eq_o_a @ X @ Z5 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_trans
% 0.20/0.46 thf(fact_59_order__trans,axiom,
% 0.20/0.46 ! [X: a,Y: a,Z5: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.46 => ( ( ord_less_eq_a @ Y @ Z5 )
% 0.20/0.46 => ( ord_less_eq_a @ X @ Z5 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_trans
% 0.20/0.46 thf(fact_60_order__class_Oorder_Oantisym,axiom,
% 0.20/0.46 ! [A: $o > a,B: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ B @ A )
% 0.20/0.46 => ( A = B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.antisym
% 0.20/0.46 thf(fact_61_order__class_Oorder_Oantisym,axiom,
% 0.20/0.46 ! [A: a,B: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.46 => ( ( ord_less_eq_a @ B @ A )
% 0.20/0.46 => ( A = B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.antisym
% 0.20/0.46 thf(fact_62_ord__le__eq__trans,axiom,
% 0.20/0.46 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.20/0.46 => ( ( B = C )
% 0.20/0.46 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_trans
% 0.20/0.46 thf(fact_63_ord__le__eq__trans,axiom,
% 0.20/0.46 ! [A: a,B: a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.46 => ( ( B = C )
% 0.20/0.46 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_trans
% 0.20/0.46 thf(fact_64_ord__eq__le__trans,axiom,
% 0.20/0.46 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.20/0.46 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_trans
% 0.20/0.46 thf(fact_65_ord__eq__le__trans,axiom,
% 0.20/0.46 ! [A: a,B: a,C: a] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.46 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_trans
% 0.20/0.46 thf(fact_66_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: $o > a,Z4: $o > a] : ( Y2 = Z4 ) )
% 0.20/0.46 = ( ^ [A3: $o > a,B2: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A3 @ B2 )
% 0.20/0.46 & ( ord_less_eq_o_a @ B2 @ A3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.eq_iff
% 0.20/0.46 thf(fact_67_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: a,Z4: a] : ( Y2 = Z4 ) )
% 0.20/0.46 = ( ^ [A3: a,B2: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A3 @ B2 )
% 0.20/0.46 & ( ord_less_eq_a @ B2 @ A3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.eq_iff
% 0.20/0.46 thf(fact_68_antisym__conv,axiom,
% 0.20/0.46 ! [Y: $o > a,X: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ Y @ X )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ X @ Y )
% 0.20/0.46 = ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv
% 0.20/0.46 thf(fact_69_antisym__conv,axiom,
% 0.20/0.46 ! [Y: a,X: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ Y @ X )
% 0.20/0.46 => ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.46 = ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv
% 0.20/0.46 thf(fact_70_le__cases3,axiom,
% 0.20/0.46 ! [X: a,Y: a,Z5: a] :
% 0.20/0.46 ( ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.46 => ~ ( ord_less_eq_a @ Y @ Z5 ) )
% 0.20/0.46 => ( ( ( ord_less_eq_a @ Y @ X )
% 0.20/0.46 => ~ ( ord_less_eq_a @ X @ Z5 ) )
% 0.20/0.46 => ( ( ( ord_less_eq_a @ X @ Z5 )
% 0.20/0.46 => ~ ( ord_less_eq_a @ Z5 @ Y ) )
% 0.20/0.46 => ( ( ( ord_less_eq_a @ Z5 @ Y )
% 0.20/0.46 => ~ ( ord_less_eq_a @ Y @ X ) )
% 0.20/0.46 => ( ( ( ord_less_eq_a @ Y @ Z5 )
% 0.20/0.46 => ~ ( ord_less_eq_a @ Z5 @ X ) )
% 0.20/0.46 => ~ ( ( ord_less_eq_a @ Z5 @ X )
% 0.20/0.46 => ~ ( ord_less_eq_a @ X @ Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_cases3
% 0.20/0.46 thf(fact_71_order_Otrans,axiom,
% 0.20/0.46 ! [A: $o > a,B: $o > a,C: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.20/0.46 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.trans
% 0.20/0.46 thf(fact_72_order_Otrans,axiom,
% 0.20/0.46 ! [A: a,B: a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.46 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.trans
% 0.20/0.46 thf(fact_73_le__cases,axiom,
% 0.20/0.46 ! [X: a,Y: a] :
% 0.20/0.46 ( ~ ( ord_less_eq_a @ X @ Y )
% 0.20/0.46 => ( ord_less_eq_a @ Y @ X ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_cases
% 0.20/0.46 thf(fact_74_eq__refl,axiom,
% 0.20/0.46 ! [X: $o > a,Y: $o > a] :
% 0.20/0.46 ( ( X = Y )
% 0.20/0.46 => ( ord_less_eq_o_a @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_refl
% 0.20/0.46 thf(fact_75_eq__refl,axiom,
% 0.20/0.46 ! [X: a,Y: a] :
% 0.20/0.46 ( ( X = Y )
% 0.20/0.46 => ( ord_less_eq_a @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_refl
% 0.20/0.46 thf(fact_76_linear,axiom,
% 0.20/0.46 ! [X: a,Y: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.46 | ( ord_less_eq_a @ Y @ X ) ) ).
% 0.20/0.46
% 0.20/0.46 % linear
% 0.20/0.46 thf(fact_77_antisym,axiom,
% 0.20/0.46 ! [X: $o > a,Y: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X @ Y )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ Y @ X )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym
% 0.20/0.46 thf(fact_78_antisym,axiom,
% 0.20/0.46 ! [X: a,Y: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.46 => ( ( ord_less_eq_a @ Y @ X )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym
% 0.20/0.46 thf(fact_79_eq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: $o > a,Z4: $o > a] : ( Y2 = Z4 ) )
% 0.20/0.46 = ( ^ [X4: $o > a,Y3: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X4 @ Y3 )
% 0.20/0.46 & ( ord_less_eq_o_a @ Y3 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_iff
% 0.20/0.46 thf(fact_80_eq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: a,Z4: a] : ( Y2 = Z4 ) )
% 0.20/0.46 = ( ^ [X4: a,Y3: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X4 @ Y3 )
% 0.20/0.46 & ( ord_less_eq_a @ Y3 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_iff
% 0.20/0.46 thf(fact_81_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.46 => ( ( ( F @ B )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: a,Y4: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_82_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.20/0.46 => ( ( ( F @ B )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: $o > a,Y4: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_83_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.20/0.46 => ( ( ( F @ B )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: $o > a,Y4: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_84_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A: a,B: a,F: a > a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.46 => ( ( ( F @ B )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: a,Y4: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_85_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( F @ B ) )
% 0.20/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.46 => ( ! [X5: a,Y4: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_86_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( F @ B ) )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.20/0.46 => ( ! [X5: $o > a,Y4: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_87_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( F @ B ) )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.20/0.46 => ( ! [X5: $o > a,Y4: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_88_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A: a,F: a > a,B: a,C: a] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( F @ B ) )
% 0.20/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.46 => ( ! [X5: a,Y4: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_89_order__subst2,axiom,
% 0.20/0.46 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 0.20/0.46 => ( ! [X5: a,Y4: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_90_order__subst2,axiom,
% 0.20/0.46 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.20/0.46 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 0.20/0.46 => ( ! [X5: $o > a,Y4: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_91_order__subst2,axiom,
% 0.20/0.46 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A @ B )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 0.20/0.46 => ( ! [X5: $o > a,Y4: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_92_order__subst2,axiom,
% 0.20/0.46 ! [A: a,B: a,F: a > a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.46 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 0.20/0.46 => ( ! [X5: a,Y4: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_93_order__subst1,axiom,
% 0.20/0.46 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.20/0.46 => ( ! [X5: $o > a,Y4: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_94_order__subst1,axiom,
% 0.20/0.46 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 0.20/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.46 => ( ! [X5: a,Y4: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_95_order__subst1,axiom,
% 0.20/0.46 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 0.20/0.46 => ( ( ord_less_eq_o_a @ B @ C )
% 0.20/0.46 => ( ! [X5: $o > a,Y4: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_96_order__subst1,axiom,
% 0.20/0.46 ! [A: a,F: a > a,B: a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 0.20/0.46 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.46 => ( ! [X5: a,Y4: a] :
% 0.20/0.46 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_97_Greatest__equality,axiom,
% 0.20/0.46 ! [P: ( $o > a ) > $o,X: $o > a] :
% 0.20/0.46 ( ( P @ X )
% 0.20/0.46 => ( ! [Y4: $o > a] :
% 0.20/0.46 ( ( P @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ Y4 @ X ) )
% 0.20/0.46 => ( ( order_Greatest_o_a @ P )
% 0.20/0.46 = X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Greatest_equality
% 0.20/0.46 thf(fact_98_Greatest__equality,axiom,
% 0.20/0.46 ! [P: a > $o,X: a] :
% 0.20/0.46 ( ( P @ X )
% 0.20/0.46 => ( ! [Y4: a] :
% 0.20/0.46 ( ( P @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ Y4 @ X ) )
% 0.20/0.46 => ( ( order_Greatest_a @ P )
% 0.20/0.46 = X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Greatest_equality
% 0.20/0.46 thf(fact_99_GreatestI2__order,axiom,
% 0.20/0.46 ! [P: ( $o > a ) > $o,X: $o > a,Q: ( $o > a ) > $o] :
% 0.20/0.46 ( ( P @ X )
% 0.20/0.46 => ( ! [Y4: $o > a] :
% 0.20/0.46 ( ( P @ Y4 )
% 0.20/0.46 => ( ord_less_eq_o_a @ Y4 @ X ) )
% 0.20/0.46 => ( ! [X5: $o > a] :
% 0.20/0.46 ( ( P @ X5 )
% 0.20/0.46 => ( ! [Y5: $o > a] :
% 0.20/0.46 ( ( P @ Y5 )
% 0.20/0.46 => ( ord_less_eq_o_a @ Y5 @ X5 ) )
% 0.20/0.46 => ( Q @ X5 ) ) )
% 0.20/0.46 => ( Q @ ( order_Greatest_o_a @ P ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % GreatestI2_order
% 0.20/0.46 thf(fact_100_GreatestI2__order,axiom,
% 0.20/0.46 ! [P: a > $o,X: a,Q: a > $o] :
% 0.20/0.46 ( ( P @ X )
% 0.20/0.46 => ( ! [Y4: a] :
% 0.20/0.46 ( ( P @ Y4 )
% 0.20/0.46 => ( ord_less_eq_a @ Y4 @ X ) )
% 0.20/0.46 => ( ! [X5: a] :
% 0.20/0.46 ( ( P @ X5 )
% 0.20/0.46 => ( ! [Y5: a] :
% 0.20/0.46 ( ( P @ Y5 )
% 0.20/0.46 => ( ord_less_eq_a @ Y5 @ X5 ) )
% 0.20/0.46 => ( Q @ X5 ) ) )
% 0.20/0.46 => ( Q @ ( order_Greatest_a @ P ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % GreatestI2_order
% 0.20/0.46 thf(fact_101_le__rel__bool__arg__iff,axiom,
% 0.20/0.46 ( ord_less_eq_o_o_a
% 0.20/0.46 = ( ^ [X6: $o > $o > a,Y6: $o > $o > a] :
% 0.20/0.46 ( ( ord_less_eq_o_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 0.20/0.46 & ( ord_less_eq_o_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_rel_bool_arg_iff
% 0.20/0.46 thf(fact_102_le__rel__bool__arg__iff,axiom,
% 0.20/0.46 ( ord_less_eq_o_a
% 0.20/0.46 = ( ^ [X6: $o > a,Y6: $o > a] :
% 0.20/0.46 ( ( ord_less_eq_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 0.20/0.46 & ( ord_less_eq_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_rel_bool_arg_iff
% 0.20/0.46 thf(fact_103_verit__la__disequality,axiom,
% 0.20/0.46 ! [A: a,B: a] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 | ~ ( ord_less_eq_a @ A @ B )
% 0.20/0.46 | ~ ( ord_less_eq_a @ B @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % verit_la_disequality
% 0.20/0.46 thf(fact_104_Tree_Osimps_I14_J,axiom,
% 0.20/0.46 ( ( set_Tree_a @ e_a )
% 0.20/0.46 = bot_bot_set_a ) ).
% 0.20/0.46
% 0.20/0.46 % Tree.simps(14)
% 0.20/0.46 thf(fact_105_Tree_Opred__set,axiom,
% 0.20/0.46 ( pred_Tree_a
% 0.20/0.46 = ( ^ [P2: a > $o,X4: tree_a] :
% 0.20/0.46 ! [Y3: a] :
% 0.20/0.46 ( ( member_a @ Y3 @ ( set_Tree_a @ X4 ) )
% 0.20/0.46 => ( P2 @ Y3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Tree.pred_set
% 0.20/0.46 thf(fact_106_empty__iff,axiom,
% 0.20/0.46 ! [C: a] :
% 0.20/0.46 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 0.20/0.46
% 0.20/0.46 % empty_iff
% 0.20/0.46 thf(fact_107_all__not__in__conv,axiom,
% 0.20/0.46 ! [A2: set_a] :
% 0.20/0.46 ( ( ! [X4: a] :
% 0.20/0.46 ~ ( member_a @ X4 @ A2 ) )
% 0.20/0.46 = ( A2 = bot_bot_set_a ) ) ).
% 0.20/0.46
% 0.20/0.46 % all_not_in_conv
% 0.20/0.46 thf(fact_108_subsetI,axiom,
% 0.20/0.46 ! [A2: set_a,B4: set_a] :
% 0.20/0.46 ( ! [X5: a] :
% 0.20/0.46 ( ( member_a @ X5 @ A2 )
% 0.20/0.46 => ( member_a @ X5 @ B4 ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetI
% 0.20/0.46 thf(fact_109_in__mono,axiom,
% 0.20/0.46 ! [A2: set_a,B4: set_a,X: a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.20/0.46 => ( ( member_a @ X @ A2 )
% 0.20/0.46 => ( member_a @ X @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_mono
% 0.20/0.46 thf(fact_110_subsetD,axiom,
% 0.20/0.46 ! [A2: set_a,B4: set_a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 0.20/0.46 => ( ( member_a @ C @ A2 )
% 0.20/0.46 => ( member_a @ C @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetD
% 0.20/0.46 thf(fact_111_subset__eq,axiom,
% 0.20/0.46 ( ord_less_eq_set_a
% 0.20/0.46 = ( ^ [A5: set_a,B5: set_a] :
% 0.20/0.46 ! [X4: a] :
% 0.20/0.46 ( ( member_a @ X4 @ A5 )
% 0.20/0.46 => ( member_a @ X4 @ B5 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_eq
% 0.20/0.46 thf(fact_112_subset__iff,axiom,
% 0.20/0.46 ( ord_less_eq_set_a
% 0.20/0.46 = ( ^ [A5: set_a,B5: set_a] :
% 0.20/0.46 ! [T2: a] :
% 0.20/0.46 ( ( member_a @ T2 @ A5 )
% 0.20/0.46 => ( member_a @ T2 @ B5 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_iff
% 0.20/0.46 thf(fact_113_ex__in__conv,axiom,
% 0.20/0.46 ! [A2: set_a] :
% 0.20/0.46 ( ( ? [X4: a] : ( member_a @ X4 @ A2 ) )
% 0.20/0.46 = ( A2 != bot_bot_set_a ) ) ).
% 0.20/0.46
% 0.20/0.46 % ex_in_conv
% 0.20/0.46 thf(fact_114_equals0I,axiom,
% 0.20/0.46 ! [A2: set_a] :
% 0.20/0.46 ( ! [Y4: a] :
% 0.20/0.46 ~ ( member_a @ Y4 @ A2 )
% 0.20/0.46 => ( A2 = bot_bot_set_a ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0I
% 0.20/0.46 thf(fact_115_equals0D,axiom,
% 0.20/0.46 ! [A2: set_a,A: a] :
% 0.20/0.46 ( ( A2 = bot_bot_set_a )
% 0.20/0.46 => ~ ( member_a @ A @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0D
% 0.20/0.46 thf(fact_116_emptyE,axiom,
% 0.20/0.46 ! [A: a] :
% 0.20/0.46 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 0.20/0.46
% 0.20/0.46 % emptyE
% 0.20/0.46 thf(fact_117_Ball__def,axiom,
% 0.20/0.46 ( ball_a
% 0.20/0.46 = ( ^ [A5: set_a,P2: a > $o] :
% 0.20/0.46 ! [X4: a] :
% 0.20/0.46 ( ( member_a @ X4 @ A5 )
% 0.20/0.46 => ( P2 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Ball_def
% 0.20/0.46 thf(fact_118_subset__emptyI,axiom,
% 0.20/0.46 ! [A2: set_a] :
% 0.20/0.46 ( ! [X5: a] :
% 0.20/0.46 ~ ( member_a @ X5 @ A2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ bot_bot_set_a ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_emptyI
% 0.20/0.46 thf(fact_119_ball__reg,axiom,
% 0.20/0.46 ! [R3: set_a,P: a > $o,Q: a > $o] :
% 0.20/0.46 ( ! [X5: a] :
% 0.20/0.46 ( ( member_a @ X5 @ R3 )
% 0.20/0.46 => ( ( P @ X5 )
% 0.20/0.46 => ( Q @ X5 ) ) )
% 0.20/0.46 => ( ! [X5: a] :
% 0.20/0.46 ( ( member_a @ X5 @ R3 )
% 0.20/0.46 => ( P @ X5 ) )
% 0.20/0.46 => ! [X7: a] :
% 0.20/0.46 ( ( member_a @ X7 @ R3 )
% 0.20/0.46 => ( Q @ X7 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ball_reg
% 0.20/0.46 thf(fact_120_bot__empty__eq,axiom,
% 0.20/0.46 ( bot_bot_a_o
% 0.20/0.46 = ( ^ [X4: a] : ( member_a @ X4 @ bot_bot_set_a ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_empty_eq
% 0.20/0.46 thf(fact_121_heap__top__geq,axiom,
% 0.20/0.46 ! [A: a,T: tree_a] :
% 0.20/0.46 ( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ T ) ) )
% 0.20/0.46 => ( ( is_heap_a @ T )
% 0.20/0.46 => ( ord_less_eq_a @ A @ ( val_a @ T ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % heap_top_geq
% 0.20/0.46 thf(fact_122_heap__top__max,axiom,
% 0.20/0.46 ! [T: tree_a] :
% 0.20/0.46 ( ( T != e_a )
% 0.20/0.46 => ( ( is_heap_a @ T )
% 0.20/0.46 => ( ( val_a @ T )
% 0.20/0.46 = ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ T ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % heap_top_max
% 0.20/0.46 thf(fact_123_multiset_Osimps_I1_J,axiom,
% 0.20/0.46 ( ( multiset_a2 @ e_a )
% 0.20/0.46 = zero_zero_multiset_a ) ).
% 0.20/0.46
% 0.20/0.46 % multiset.simps(1)
% 0.20/0.46 thf(fact_124_is__singletonI_H,axiom,
% 0.20/0.46 ! [A2: set_a] :
% 0.20/0.46 ( ( A2 != bot_bot_set_a )
% 0.20/0.46 => ( ! [X5: a,Y4: a] :
% 0.20/0.46 ( ( member_a @ X5 @ A2 )
% 0.20/0.46 => ( ( member_a @ Y4 @ A2 )
% 0.20/0.46 => ( X5 = Y4 ) ) )
% 0.20/0.46 => ( is_singleton_a @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonI'
% 0.20/0.46 thf(fact_125_Diff__iff,axiom,
% 0.20/0.46 ! [C: a,A2: set_a,B4: set_a] :
% 0.20/0.46 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) )
% 0.20/0.46 = ( ( member_a @ C @ A2 )
% 0.20/0.46 & ~ ( member_a @ C @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Diff_iff
% 0.20/0.46 thf(fact_126_DiffI,axiom,
% 0.20/0.46 ! [C: a,A2: set_a,B4: set_a] :
% 0.20/0.46 ( ( member_a @ C @ A2 )
% 0.20/0.46 => ( ~ ( member_a @ C @ B4 )
% 0.20/0.46 => ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % DiffI
% 0.20/0.46 thf(fact_127_DiffD2,axiom,
% 0.20/0.46 ! [C: a,A2: set_a,B4: set_a] :
% 0.20/0.46 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) )
% 0.20/0.46 => ~ ( member_a @ C @ B4 ) ) ).
% 0.20/0.46
% 0.20/0.46 % DiffD2
% 0.20/0.46 thf(fact_128_DiffD1,axiom,
% 0.20/0.46 ! [C: a,A2: set_a,B4: set_a] :
% 0.20/0.46 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) )
% 0.20/0.46 => ( member_a @ C @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % DiffD1
% 0.20/0.46 thf(fact_129_DiffE,axiom,
% 0.20/0.46 ! [C: a,A2: set_a,B4: set_a] :
% 0.20/0.46 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) )
% 0.20/0.46 => ~ ( ( member_a @ C @ A2 )
% 0.20/0.46 => ( member_a @ C @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % DiffE
% 0.20/0.46 thf(fact_130_set__mset__eq__empty__iff,axiom,
% 0.20/0.46 ! [M: multiset_a] :
% 0.20/0.46 ( ( ( set_mset_a @ M )
% 0.20/0.46 = bot_bot_set_a )
% 0.20/0.46 = ( M = zero_zero_multiset_a ) ) ).
% 0.20/0.46
% 0.20/0.46 % set_mset_eq_empty_iff
% 0.20/0.46 thf(fact_131_set__mset__empty,axiom,
% 0.20/0.46 ( ( set_mset_a @ zero_zero_multiset_a )
% 0.20/0.46 = bot_bot_set_a ) ).
% 0.20/0.46
% 0.20/0.46 % set_mset_empty
% 0.20/0.46 thf(fact_132_multiset__induct__max,axiom,
% 0.20/0.46 ! [P: multiset_a > $o,M: multiset_a] :
% 0.20/0.46 ( ( P @ zero_zero_multiset_a )
% 0.20/0.46 => ( ! [X5: a,M2: multiset_a] :
% 0.20/0.46 ( ( P @ M2 )
% 0.20/0.46 => ( ! [Xa: a] :
% 0.20/0.46 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 0.20/0.46 => ( ord_less_eq_a @ Xa @ X5 ) )
% 0.20/0.46 => ( P @ ( add_mset_a @ X5 @ M2 ) ) ) )
% 0.20/0.46 => ( P @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % multiset_induct_max
% 0.20/0.46 thf(fact_133_multiset__induct__min,axiom,
% 0.20/0.46 ! [P: multiset_a > $o,M: multiset_a] :
% 0.20/0.46 ( ( P @ zero_zero_multiset_a )
% 0.20/0.46 => ( ! [X5: a,M2: multiset_a] :
% 0.20/0.46 ( ( P @ M2 )
% 0.20/0.46 => ( ! [Xa: a] :
% 0.20/0.46 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 0.20/0.46 => ( ord_less_eq_a @ X5 @ Xa ) )
% 0.20/0.46 => ( P @ ( add_mset_a @ X5 @ M2 ) ) ) )
% 0.20/0.46 => ( P @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % multiset_induct_min
% 0.20/0.46 thf(fact_134_at__most__one__mset__mset__diff,axiom,
% 0.20/0.46 ! [A: a,M: multiset_a] :
% 0.20/0.46 ( ~ ( member_a @ A @ ( set_mset_a @ ( minus_1649712171iset_a @ M @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) )
% 0.20/0.46 => ( ( set_mset_a @ ( minus_1649712171iset_a @ M @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
% 0.20/0.46 = ( minus_minus_set_a @ ( set_mset_a @ M ) @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % at_most_one_mset_mset_diff
% 0.20/0.46 thf(fact_135_multiset_Osimps_I2_J,axiom,
% 0.20/0.46 ! [V: a,L: tree_a,R: tree_a] :
% 0.20/0.46 ( ( multiset_a2 @ ( t_a @ V @ L @ R ) )
% 0.20/0.46 = ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ L ) @ ( add_mset_a @ V @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ R ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % multiset.simps(2)
% 0.20/0.46 thf(fact_136_insert__iff,axiom,
% 0.20/0.46 ! [A: a,B: a,A2: set_a] :
% 0.20/0.46 ( ( member_a @ A @ ( insert_a @ B @ A2 ) )
% 0.20/0.46 = ( ( A = B )
% 0.20/0.46 | ( member_a @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_iff
% 0.20/0.46 thf(fact_137_insertCI,axiom,
% 0.20/0.46 ! [A: a,B4: set_a,B: a] :
% 0.20/0.46 ( ( ~ ( member_a @ A @ B4 )
% 0.20/0.46 => ( A = B ) )
% 0.20/0.46 => ( member_a @ A @ ( insert_a @ B @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertCI
% 0.20/0.46 thf(fact_138_singletonI,axiom,
% 0.20/0.46 ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonI
% 0.20/0.46 thf(fact_139_insert__subset,axiom,
% 0.20/0.46 ! [X: a,A2: set_a,B4: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ ( insert_a @ X @ A2 ) @ B4 )
% 0.20/0.46 = ( ( member_a @ X @ B4 )
% 0.20/0.46 & ( ord_less_eq_set_a @ A2 @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_subset
% 0.20/0.46 thf(fact_140_insert__Diff1,axiom,
% 0.20/0.46 ! [X: a,B4: set_a,A2: set_a] :
% 0.20/0.46 ( ( member_a @ X @ B4 )
% 0.20/0.46 => ( ( minus_minus_set_a @ ( insert_a @ X @ A2 ) @ B4 )
% 0.20/0.46 = ( minus_minus_set_a @ A2 @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_Diff1
% 0.20/0.46 thf(fact_141_Diff__insert0,axiom,
% 0.20/0.46 ! [X: a,A2: set_a,B4: set_a] :
% 0.20/0.46 ( ~ ( member_a @ X @ A2 )
% 0.20/0.46 => ( ( minus_minus_set_a @ A2 @ ( insert_a @ X @ B4 ) )
% 0.20/0.46 = ( minus_minus_set_a @ A2 @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Diff_insert0
% 0.20/0.46 thf(fact_142_insert__Diff__if,axiom,
% 0.20/0.46 ! [X: a,B4: set_a,A2: set_a] :
% 0.20/0.46 ( ( ( member_a @ X @ B4 )
% 0.20/0.46 => ( ( minus_minus_set_a @ ( insert_a @ X @ A2 ) @ B4 )
% 0.20/0.46 = ( minus_minus_set_a @ A2 @ B4 ) ) )
% 0.20/0.46 & ( ~ ( member_a @ X @ B4 )
% 0.20/0.46 => ( ( minus_minus_set_a @ ( insert_a @ X @ A2 ) @ B4 )
% 0.20/0.46 = ( insert_a @ X @ ( minus_minus_set_a @ A2 @ B4 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_Diff_if
% 0.20/0.46 thf(fact_143_verit__sum__simplify,axiom,
% 0.20/0.46 ! [A: multiset_a] :
% 0.20/0.46 ( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % verit_sum_simplify
% 0.20/0.46 thf(fact_144_add__right__mono,axiom,
% 0.20/0.46 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.20/0.46 ( ( ord_le1199012836iset_a @ A @ B )
% 0.20/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_right_mono
% 0.20/0.46 thf(fact_145_add__left__mono,axiom,
% 0.20/0.46 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 0.20/0.46 ( ( ord_le1199012836iset_a @ A @ B )
% 0.20/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_left_mono
% 0.20/0.46 thf(fact_146_add__mono,axiom,
% 0.20/0.46 ! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
% 0.20/0.46 ( ( ord_le1199012836iset_a @ A @ B )
% 0.20/0.46 => ( ( ord_le1199012836iset_a @ C @ D )
% 0.20/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_mono
% 0.20/0.46 thf(fact_147_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.20/0.46 ! [I: multiset_a,J: multiset_a,K: multiset_a,L: multiset_a] :
% 0.20/0.46 ( ( ( ord_le1199012836iset_a @ I @ J )
% 0.20/0.46 & ( ord_le1199012836iset_a @ K @ L ) )
% 0.20/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_mono_thms_linordered_semiring(1)
% 0.20/0.46 thf(fact_148_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.20/0.46 ! [I: multiset_a,J: multiset_a,K: multiset_a,L: multiset_a] :
% 0.20/0.46 ( ( ( I = J )
% 0.20/0.46 & ( ord_le1199012836iset_a @ K @ L ) )
% 0.20/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_mono_thms_linordered_semiring(2)
% 0.20/0.46 thf(fact_149_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.20/0.46 ! [I: multiset_a,J: multiset_a,K: multiset_a,L: multiset_a] :
% 0.20/0.46 ( ( ( ord_le1199012836iset_a @ I @ J )
% 0.20/0.46 & ( K = L ) )
% 0.20/0.46 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_mono_thms_linordered_semiring(3)
% 0.20/0.46 thf(fact_150_mk__disjoint__insert,axiom,
% 0.20/0.46 ! [A: a,A2: set_a] :
% 0.20/0.46 ( ( member_a @ A @ A2 )
% 0.20/0.46 => ? [B6: set_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert_a @ A @ B6 ) )
% 0.20/0.46 & ~ ( member_a @ A @ B6 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % mk_disjoint_insert
% 0.20/0.46 thf(fact_151_insert__eq__iff,axiom,
% 0.20/0.46 ! [A: a,A2: set_a,B: a,B4: set_a] :
% 0.20/0.46 ( ~ ( member_a @ A @ A2 )
% 0.20/0.46 => ( ~ ( member_a @ B @ B4 )
% 0.20/0.46 => ( ( ( insert_a @ A @ A2 )
% 0.20/0.46 = ( insert_a @ B @ B4 ) )
% 0.20/0.46 = ( ( ( A = B )
% 0.20/0.46 => ( A2 = B4 ) )
% 0.20/0.46 & ( ( A != B )
% 0.20/0.46 => ? [C2: set_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert_a @ B @ C2 ) )
% 0.20/0.46 & ~ ( member_a @ B @ C2 )
% 0.20/0.46 & ( B4
% 0.20/0.46 = ( insert_a @ A @ C2 ) )
% 0.20/0.46 & ~ ( member_a @ A @ C2 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_eq_iff
% 0.20/0.46 thf(fact_152_insert__absorb,axiom,
% 0.20/0.46 ! [A: a,A2: set_a] :
% 0.20/0.46 ( ( member_a @ A @ A2 )
% 0.20/0.46 => ( ( insert_a @ A @ A2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_absorb
% 0.20/0.46 thf(fact_153_insert__ident,axiom,
% 0.20/0.46 ! [X: a,A2: set_a,B4: set_a] :
% 0.20/0.46 ( ~ ( member_a @ X @ A2 )
% 0.20/0.46 => ( ~ ( member_a @ X @ B4 )
% 0.20/0.46 => ( ( ( insert_a @ X @ A2 )
% 0.20/0.46 = ( insert_a @ X @ B4 ) )
% 0.20/0.46 = ( A2 = B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_ident
% 0.20/0.46 thf(fact_154_Set_Oset__insert,axiom,
% 0.20/0.46 ! [X: a,A2: set_a] :
% 0.20/0.46 ( ( member_a @ X @ A2 )
% 0.20/0.46 => ~ ! [B6: set_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert_a @ X @ B6 ) )
% 0.20/0.46 => ( member_a @ X @ B6 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Set.set_insert
% 0.20/0.46 thf(fact_155_insertI2,axiom,
% 0.20/0.46 ! [A: a,B4: set_a,B: a] :
% 0.20/0.46 ( ( member_a @ A @ B4 )
% 0.20/0.46 => ( member_a @ A @ ( insert_a @ B @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI2
% 0.20/0.46 thf(fact_156_insertI1,axiom,
% 0.20/0.46 ! [A: a,B4: set_a] : ( member_a @ A @ ( insert_a @ A @ B4 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI1
% 0.20/0.46 thf(fact_157_insertE,axiom,
% 0.20/0.46 ! [A: a,B: a,A2: set_a] :
% 0.20/0.46 ( ( member_a @ A @ ( insert_a @ B @ A2 ) )
% 0.20/0.46 => ( ( A != B )
% 0.20/0.46 => ( member_a @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertE
% 0.20/0.46 thf(fact_158_singletonD,axiom,
% 0.20/0.46 ! [B: a,A: a] :
% 0.20/0.46 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 0.20/0.46 => ( B = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonD
% 0.20/0.46 thf(fact_159_singleton__iff,axiom,
% 0.20/0.46 ! [B: a,A: a] :
% 0.20/0.46 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 0.20/0.46 = ( B = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_iff
% 0.20/0.46 thf(fact_160_insert__subsetI,axiom,
% 0.20/0.46 ! [X: a,A2: set_a,X8: set_a] :
% 0.20/0.46 ( ( member_a @ X @ A2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ X8 @ A2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( insert_a @ X @ X8 ) @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_subsetI
% 0.20/0.46 thf(fact_161_subset__insert,axiom,
% 0.20/0.46 ! [X: a,A2: set_a,B4: set_a] :
% 0.20/0.46 ( ~ ( member_a @ X @ A2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ A2 @ ( insert_a @ X @ B4 ) )
% 0.20/0.46 = ( ord_less_eq_set_a @ A2 @ B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_insert
% 0.20/0.46 thf(fact_162_Diff__insert__absorb,axiom,
% 0.20/0.46 ! [X: a,A2: set_a] :
% 0.20/0.46 ( ~ ( member_a @ X @ A2 )
% 0.20/0.46 => ( ( minus_minus_set_a @ ( insert_a @ X @ A2 ) @ ( insert_a @ X @ bot_bot_set_a ) )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Diff_insert_absorb
% 0.20/0.46 thf(fact_163_insert__Diff,axiom,
% 0.20/0.46 ! [A: a,A2: set_a] :
% 0.20/0.46 ( ( member_a @ A @ A2 )
% 0.20/0.46 => ( ( insert_a @ A @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_Diff
% 0.20/0.46 thf(fact_164_subset__Diff__insert,axiom,
% 0.20/0.46 ! [A2: set_a,B4: set_a,X: a,C3: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ ( minus_minus_set_a @ B4 @ ( insert_a @ X @ C3 ) ) )
% 0.20/0.46 = ( ( ord_less_eq_set_a @ A2 @ ( minus_minus_set_a @ B4 @ C3 ) )
% 0.20/0.46 & ~ ( member_a @ X @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_Diff_insert
% 0.20/0.46 thf(fact_165_subset__insert__iff,axiom,
% 0.20/0.46 ! [A2: set_a,X: a,B4: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ ( insert_a @ X @ B4 ) )
% 0.20/0.46 = ( ( ( member_a @ X @ A2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( minus_minus_set_a @ A2 @ ( insert_a @ X @ bot_bot_set_a ) ) @ B4 ) )
% 0.20/0.46 & ( ~ ( member_a @ X @ A2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_insert_iff
% 0.20/0.46 thf(fact_166_set__mset__single,axiom,
% 0.20/0.46 ! [B: a] :
% 0.20/0.46 ( ( set_mset_a @ ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 0.20/0.46 = ( insert_a @ B @ bot_bot_set_a ) ) ).
% 0.20/0.46
% 0.20/0.46 % set_mset_single
% 0.20/0.46 thf(fact_167_Max__singleton,axiom,
% 0.20/0.46 ! [X: a] :
% 0.20/0.46 ( ( lattic146396397_Max_a @ ( insert_a @ X @ bot_bot_set_a ) )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % Max_singleton
% 0.20/0.46
% 0.20/0.46 % Conjectures (1)
% 0.20/0.46 thf(conj_0,conjecture,
% 0.20/0.46 in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 2.11/1.46 ---- Embedded in THF ---
% 2.11/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.11/1.46 %%% Generated on Tue Feb 24 08:25:30 EST 2026
% 2.11/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.11/1.46 %%% Logic specification used:
% 2.11/1.46 %%% thf(spec, logic, $$dhol).
% 2.11/1.46
% 2.11/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2DTF5848.p
% See solution above
% 2.11/1.46 ------------------------
% 2.11/1.48 ---- Cleaned THF ---
% 2.11/1.48 thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
% 2.11/1.48 multiset_a: $tType ).
% 2.11/1.48
% 2.11/1.48 thf(ty_n_t__Heap__OTree_Itf__a_J,type,
% 2.11/1.48 tree_a: $tType ).
% 2.11/1.48
% 2.11/1.48 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.11/1.48 set_a: $tType ).
% 2.11/1.48
% 2.11/1.48 thf(ty_n_tf__a,type,
% 2.11/1.48 a: $tType ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Groups_Ominus__class_Ominus_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.11/1.48 minus_1649712171iset_a: multiset_a > multiset_a > multiset_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
% 2.11/1.48 minus_minus_set_a: set_a > set_a > set_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.11/1.48 plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.11/1.48 zero_zero_multiset_a: multiset_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oleft_001tf__a,type,
% 2.11/1.48 heapIm1140443833left_a: tree_a > tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_Oright_001tf__a,type,
% 2.11/1.48 heapIm1257206334ight_a: tree_a > tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_HeapImperative__Mirabelle__ksbqzsoydx_OsiftDown_001tf__a,type,
% 2.11/1.48 heapIm1091024090Down_a: tree_a > tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Heap_OTree_OE_001tf__a,type,
% 2.11/1.48 e_a: tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Heap_OTree_OT_001tf__a,type,
% 2.11/1.48 t_a: a > tree_a > tree_a > tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Heap_OTree_Opred__Tree_001tf__a,type,
% 2.11/1.48 pred_Tree_a: ( a > $o ) > tree_a > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Heap_OTree_Oset__Tree_001tf__a,type,
% 2.11/1.48 set_Tree_a: tree_a > set_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Heap_Oin__tree_001tf__a,type,
% 2.11/1.48 in_tree_a: a > tree_a > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Heap_Ois__heap_001tf__a,type,
% 2.11/1.48 is_heap_a: tree_a > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Heap_Omultiset_001tf__a,type,
% 2.11/1.48 multiset_a2: tree_a > multiset_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Heap_Oval_001tf__a,type,
% 2.11/1.48 val_a: tree_a > a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001tf__a,type,
% 2.11/1.48 lattic146396397_Max_a: set_a > a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Multiset_Oadd__mset_001tf__a,type,
% 2.11/1.48 add_mset_a: a > multiset_a > multiset_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Multiset_Oset__mset_001tf__a,type,
% 2.11/1.48 set_mset_a: multiset_a > set_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 2.11/1.48 bot_bot_a_o: a > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 2.11/1.48 bot_bot_set_a: set_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mtf__a_J_J,type,
% 2.11/1.48 ord_less_eq_o_o_a: ( $o > $o > a ) > ( $o > $o > a ) > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mtf__a_J,type,
% 2.11/1.48 ord_less_eq_o_a: ( $o > a ) > ( $o > a ) > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Heap__OTree_Itf__a_J_M_Eo_J,type,
% 2.11/1.48 ord_less_eq_Tree_a_o: ( tree_a > $o ) > ( tree_a > $o ) > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J,type,
% 2.11/1.48 ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Multiset__Omultiset_Itf__a_J,type,
% 2.11/1.48 ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 2.11/1.48 ord_less_eq_set_a: set_a > set_a > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__a,type,
% 2.11/1.48 ord_less_eq_a: a > a > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mtf__a_J,type,
% 2.11/1.48 order_Greatest_o_a: ( ( $o > a ) > $o ) > $o > a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Orderings_Oorder__class_OGreatest_001tf__a,type,
% 2.11/1.48 order_Greatest_a: ( a > $o ) > a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Set_OBall_001tf__a,type,
% 2.11/1.48 ball_a: set_a > ( a > $o ) > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.11/1.48 collect_a: ( a > $o ) > set_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Set_Oinsert_001tf__a,type,
% 2.11/1.48 insert_a: a > set_a > set_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_Set_Ois__singleton_001tf__a,type,
% 2.11/1.48 is_singleton_a: set_a > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_c_member_001tf__a,type,
% 2.11/1.48 member_a: a > set_a > $o ).
% 2.11/1.48
% 2.11/1.48 thf(sy_v_l1____,type,
% 2.11/1.48 l1: tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_v_l2____,type,
% 2.11/1.48 l2: tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_v_r1____,type,
% 2.11/1.48 r1: tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_v_r2____,type,
% 2.11/1.48 r2: tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_v_t,type,
% 2.11/1.48 t: tree_a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_v_v,type,
% 2.11/1.48 v: a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_v_v1____,type,
% 2.11/1.48 v1: a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_v_v2____,type,
% 2.11/1.48 v2: a ).
% 2.11/1.48
% 2.11/1.48 thf(sy_v_v_H____,type,
% 2.11/1.48 v3: a ).
% 2.11/1.48
% 2.11/1.48 thf(fact_0_False,axiom,
% 2.11/1.48 ~ ( ( v = v3 )
% 2.11/1.48 | ( v = v1 )
% 2.11/1.48 | ( v = v2 ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_1__092_060open_062in__tree_Av_A_IsiftDown_At_J_092_060close_062,axiom,
% 2.11/1.48 in_tree_a @ v @ ( heapIm1091024090Down_a @ t ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_2_True,axiom,
% 2.11/1.48 ord_less_eq_a @ v2 @ v1 ).
% 2.11/1.48
% 2.11/1.48 thf(fact_3__C5__1_Oprems_C,axiom,
% 2.11/1.48 in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_4_Tree_Oinject,axiom,
% 2.11/1.48 ! [X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 2.11/1.48 ( ( ( t_a @ X21 @ X22 @ X23 )
% 2.11/1.48 = ( t_a @ Y21 @ Y22 @ Y23 ) )
% 2.11/1.48 = ( ( X21 = Y21 )
% 2.11/1.48 & ( X22 = Y22 )
% 2.11/1.48 & ( X23 = Y23 ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_5_in__tree_Osimps_I2_J,axiom,
% 2.11/1.48 ! [V: a,V2: a,L: tree_a,R: tree_a] :
% 2.11/1.48 ( ( in_tree_a @ V @ ( t_a @ V2 @ L @ R ) )
% 2.11/1.48 = ( ( V = V2 )
% 2.11/1.48 | ( in_tree_a @ V @ L )
% 2.11/1.48 | ( in_tree_a @ V @ R ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_6__C5__1_Ohyps_C_I2_J,axiom,
% 2.11/1.48 ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
% 2.11/1.48 => ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ v3 )
% 2.11/1.48 => ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
% 2.11/1.48 => ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_7__C5__1_Ohyps_C_I1_J,axiom,
% 2.11/1.48 ( ( ord_less_eq_a @ ( val_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) )
% 2.11/1.48 => ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ v3 )
% 2.11/1.48 => ( ( in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
% 2.11/1.48 => ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_8_left_Osimps,axiom,
% 2.11/1.48 ! [V: a,L: tree_a,R: tree_a] :
% 2.11/1.48 ( ( heapIm1140443833left_a @ ( t_a @ V @ L @ R ) )
% 2.11/1.48 = L ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_9_right_Osimps,axiom,
% 2.11/1.48 ! [V: a,L: tree_a,R: tree_a] :
% 2.11/1.48 ( ( heapIm1257206334ight_a @ ( t_a @ V @ L @ R ) )
% 2.11/1.48 = R ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_10_siftDown_Ocases,axiom,
% 2.11/1.48 ! [X: tree_a] :
% 2.11/1.48 ( ( X != e_a )
% 2.11/1.48 => ( ! [V3: a] :
% 2.11/1.48 ( X
% 2.11/1.48 != ( t_a @ V3 @ e_a @ e_a ) )
% 2.11/1.48 => ( ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.11/1.48 ( X
% 2.11/1.48 != ( t_a @ V3 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 2.11/1.48 => ( ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.11/1.48 ( X
% 2.11/1.48 != ( t_a @ V3 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 2.11/1.48 => ~ ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 2.11/1.48 ( X
% 2.11/1.48 != ( t_a @ V3 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_11_Tree_Opred__inject_I2_J,axiom,
% 2.11/1.48 ! [P: a > $o,A: a,Aa: tree_a,Ab: tree_a] :
% 2.11/1.48 ( ( pred_Tree_a @ P @ ( t_a @ A @ Aa @ Ab ) )
% 2.11/1.48 = ( ( P @ A )
% 2.11/1.48 & ( pred_Tree_a @ P @ Aa )
% 2.11/1.48 & ( pred_Tree_a @ P @ Ab ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_12_in__tree_Osimps_I1_J,axiom,
% 2.11/1.48 ! [V: a] :
% 2.11/1.48 ~ ( in_tree_a @ V @ e_a ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_13_Tree_Oset__intros_I3_J,axiom,
% 2.11/1.48 ! [Ya: a,X23: tree_a,X21: a,X22: tree_a] :
% 2.11/1.48 ( ( member_a @ Ya @ ( set_Tree_a @ X23 ) )
% 2.11/1.48 => ( member_a @ Ya @ ( set_Tree_a @ ( t_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_14_Tree_Opred__inject_I1_J,axiom,
% 2.11/1.48 ! [P: a > $o] : ( pred_Tree_a @ P @ e_a ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_15_siftDown_Osimps_I6_J,axiom,
% 2.11/1.48 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a,V: a] :
% 2.11/1.48 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.11/1.48 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.11/1.48 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 = ( 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 ) ) ) ) ) )
% 2.11/1.48 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.11/1.48 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 = ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.11/1.48 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 = ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_16_siftDown_Osimps_I5_J,axiom,
% 2.11/1.48 ! [Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 2.11/1.48 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.11/1.48 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 2.11/1.48 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.11/1.48 = ( 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 ) ) ) ) ) )
% 2.11/1.48 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.11/1.48 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 2.11/1.48 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.11/1.48 = ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_17_siftDown_Osimps_I4_J,axiom,
% 2.11/1.48 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 2.11/1.48 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 = ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.11/1.48 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 = ( 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 ) ) ) ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_18_siftDown_Osimps_I3_J,axiom,
% 2.11/1.48 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
% 2.11/1.48 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.11/1.48 = ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) ) )
% 2.11/1.48 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 => ( ( heapIm1091024090Down_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.11/1.48 = ( 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 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_19_siftDown_Osimps_I1_J,axiom,
% 2.11/1.48 ( ( heapIm1091024090Down_a @ e_a )
% 2.11/1.48 = e_a ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_20_Tree_Opred__cong,axiom,
% 2.11/1.48 ! [X: tree_a,Ya: tree_a,P: a > $o,Pa: a > $o] :
% 2.11/1.48 ( ( X = Ya )
% 2.11/1.48 => ( ! [Z: a] :
% 2.11/1.48 ( ( member_a @ Z @ ( set_Tree_a @ Ya ) )
% 2.11/1.48 => ( ( P @ Z )
% 2.11/1.48 = ( Pa @ Z ) ) )
% 2.11/1.48 => ( ( pred_Tree_a @ P @ X )
% 2.11/1.48 = ( pred_Tree_a @ Pa @ Ya ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_21_Tree_Opred__mono__strong,axiom,
% 2.11/1.48 ! [P: a > $o,X: tree_a,Pa: a > $o] :
% 2.11/1.48 ( ( pred_Tree_a @ P @ X )
% 2.11/1.48 => ( ! [Z: a] :
% 2.11/1.48 ( ( member_a @ Z @ ( set_Tree_a @ X ) )
% 2.11/1.48 => ( ( P @ Z )
% 2.11/1.48 => ( Pa @ Z ) ) )
% 2.11/1.48 => ( pred_Tree_a @ Pa @ X ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_22_siftDown__in__tree,axiom,
% 2.11/1.48 ! [T: tree_a] :
% 2.11/1.48 ( ( T != e_a )
% 2.11/1.48 => ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ T ) ) @ T ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_23_siftDown__Node,axiom,
% 2.11/1.48 ! [T: tree_a,V: a,L: tree_a,R: tree_a] :
% 2.11/1.48 ( ( T
% 2.11/1.48 = ( t_a @ V @ L @ R ) )
% 2.11/1.48 => ? [L2: tree_a,V4: a,R2: tree_a] :
% 2.11/1.48 ( ( ( heapIm1091024090Down_a @ T )
% 2.11/1.48 = ( t_a @ V4 @ L2 @ R2 ) )
% 2.11/1.48 & ( ord_less_eq_a @ V @ V4 ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_24_is__heap_Ocases,axiom,
% 2.11/1.48 ! [X: tree_a] :
% 2.11/1.48 ( ( X != e_a )
% 2.11/1.48 => ( ! [V3: a] :
% 2.11/1.48 ( X
% 2.11/1.48 != ( t_a @ V3 @ e_a @ e_a ) )
% 2.11/1.48 => ( ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.11/1.48 ( X
% 2.11/1.48 != ( t_a @ V3 @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 2.11/1.48 => ( ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.11/1.48 ( X
% 2.11/1.48 != ( t_a @ V3 @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 2.11/1.48 => ~ ! [V3: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 2.11/1.48 ( X
% 2.11/1.48 != ( t_a @ V3 @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_25_Tree_Oexhaust,axiom,
% 2.11/1.48 ! [Y: tree_a] :
% 2.11/1.48 ( ( Y != e_a )
% 2.11/1.48 => ~ ! [X212: a,X222: tree_a,X232: tree_a] :
% 2.11/1.48 ( Y
% 2.11/1.48 != ( t_a @ X212 @ X222 @ X232 ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_26_Tree_Oinduct,axiom,
% 2.11/1.48 ! [P: tree_a > $o,Tree: tree_a] :
% 2.11/1.48 ( ( P @ e_a )
% 2.11/1.48 => ( ! [X1: a,X2: tree_a,X3: tree_a] :
% 2.11/1.48 ( ( P @ X2 )
% 2.11/1.48 => ( ( P @ X3 )
% 2.11/1.48 => ( P @ ( t_a @ X1 @ X2 @ X3 ) ) ) )
% 2.11/1.48 => ( P @ Tree ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_27_Tree_Odistinct_I1_J,axiom,
% 2.11/1.48 ! [X21: a,X22: tree_a,X23: tree_a] :
% 2.11/1.48 ( e_a
% 2.11/1.48 != ( t_a @ X21 @ X22 @ X23 ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_28_siftDown_Osimps_I2_J,axiom,
% 2.11/1.48 ! [V: a] :
% 2.11/1.48 ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ e_a ) )
% 2.11/1.48 = ( t_a @ V @ e_a @ e_a ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_29_val_Osimps,axiom,
% 2.11/1.48 ! [V: a,Uu: tree_a,Uv: tree_a] :
% 2.11/1.48 ( ( val_a @ ( t_a @ V @ Uu @ Uv ) )
% 2.11/1.48 = V ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_30_Tree_Oset__cases,axiom,
% 2.11/1.48 ! [E: a,A: tree_a] :
% 2.11/1.48 ( ( member_a @ E @ ( set_Tree_a @ A ) )
% 2.11/1.48 => ( ! [Z2: tree_a,Z3: tree_a] :
% 2.11/1.48 ( A
% 2.11/1.48 != ( t_a @ E @ Z2 @ Z3 ) )
% 2.11/1.48 => ( ! [Z1: a,Z2: tree_a] :
% 2.11/1.48 ( ? [Z3: tree_a] :
% 2.11/1.48 ( A
% 2.11/1.48 = ( t_a @ Z1 @ Z2 @ Z3 ) )
% 2.11/1.48 => ~ ( member_a @ E @ ( set_Tree_a @ Z2 ) ) )
% 2.11/1.48 => ~ ! [Z1: a,Z2: tree_a,Z3: tree_a] :
% 2.11/1.48 ( ( A
% 2.11/1.48 = ( t_a @ Z1 @ Z2 @ Z3 ) )
% 2.11/1.48 => ~ ( member_a @ E @ ( set_Tree_a @ Z3 ) ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_31_Tree_Oset__intros_I1_J,axiom,
% 2.11/1.48 ! [X21: a,X22: tree_a,X23: tree_a] : ( member_a @ X21 @ ( set_Tree_a @ ( t_a @ X21 @ X22 @ X23 ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_32_Tree_Oset__intros_I2_J,axiom,
% 2.11/1.48 ! [Y: a,X22: tree_a,X21: a,X23: tree_a] :
% 2.11/1.48 ( ( member_a @ Y @ ( set_Tree_a @ X22 ) )
% 2.11/1.48 => ( member_a @ Y @ ( set_Tree_a @ ( t_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_33_order__refl,axiom,
% 2.11/1.48 ! [X: $o > a] : ( ord_less_eq_o_a @ X @ X ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_34_order__refl,axiom,
% 2.11/1.48 ! [X: a] : ( ord_less_eq_a @ X @ X ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_35_is__heap_Osimps_I4_J,axiom,
% 2.11/1.48 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.11/1.48 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.11/1.48 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_36_is__heap_Osimps_I3_J,axiom,
% 2.11/1.48 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.11/1.48 ( ( is_heap_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_37_is__heap__max,axiom,
% 2.11/1.48 ! [V: a,T: tree_a] :
% 2.11/1.48 ( ( in_tree_a @ V @ T )
% 2.11/1.48 => ( ( is_heap_a @ T )
% 2.11/1.48 => ( ord_less_eq_a @ V @ ( val_a @ T ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_38_is__heap_Osimps_I6_J,axiom,
% 2.11/1.48 ! [V: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.11/1.48 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.11/1.48 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 2.11/1.48 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.11/1.48 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_39_is__heap_Osimps_I5_J,axiom,
% 2.11/1.48 ! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 2.11/1.48 ( ( is_heap_a @ ( t_a @ V @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.11/1.48 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V )
% 2.11/1.48 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) )
% 2.11/1.48 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
% 2.11/1.48 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_40_le__funD,axiom,
% 2.11/1.48 ! [F: $o > a,G: $o > a,X: $o] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ F @ G )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_41_le__funE,axiom,
% 2.11/1.48 ! [F: $o > a,G: $o > a,X: $o] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ F @ G )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_42_mem__Collect__eq,axiom,
% 2.11/1.48 ! [A: a,P: a > $o] :
% 2.11/1.48 ( ( member_a @ A @ ( collect_a @ P ) )
% 2.11/1.48 = ( P @ A ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_43_Collect__mem__eq,axiom,
% 2.11/1.48 ! [A2: set_a] :
% 2.11/1.48 ( ( collect_a
% 2.11/1.48 @ ^ [X4: a] : ( member_a @ X4 @ A2 ) )
% 2.11/1.48 = A2 ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_44_le__funI,axiom,
% 2.11/1.48 ! [F: $o > a,G: $o > a] :
% 2.11/1.48 ( ! [X5: $o] : ( ord_less_eq_a @ ( F @ X5 ) @ ( G @ X5 ) )
% 2.11/1.48 => ( ord_less_eq_o_a @ F @ G ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_45_le__fun__def,axiom,
% 2.11/1.48 ( ord_less_eq_o_a
% 2.11/1.48 = ( ^ [F2: $o > a,G2: $o > a] :
% 2.11/1.48 ! [X4: $o] : ( ord_less_eq_a @ ( F2 @ X4 ) @ ( G2 @ X4 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_46_Tree_Opred__mono,axiom,
% 2.11/1.48 ! [P: a > $o,Pa: a > $o] :
% 2.11/1.48 ( ( ord_less_eq_a_o @ P @ Pa )
% 2.11/1.48 => ( ord_less_eq_Tree_a_o @ ( pred_Tree_a @ P ) @ ( pred_Tree_a @ Pa ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_47_is__heap_Osimps_I1_J,axiom,
% 2.11/1.48 is_heap_a @ e_a ).
% 2.11/1.48
% 2.11/1.48 thf(fact_48_is__heap_Osimps_I2_J,axiom,
% 2.11/1.48 ! [V: a] : ( is_heap_a @ ( t_a @ V @ e_a @ e_a ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_49_dual__order_Oantisym,axiom,
% 2.11/1.48 ! [B: $o > a,A: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ B @ A )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ A @ B )
% 2.11/1.48 => ( A = B ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_50_dual__order_Oantisym,axiom,
% 2.11/1.48 ! [B: a,A: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ B @ A )
% 2.11/1.48 => ( ( ord_less_eq_a @ A @ B )
% 2.11/1.48 => ( A = B ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_51_dual__order_Oeq__iff,axiom,
% 2.11/1.48 ( ( ^ [Y2: $o > a,Z4: $o > a] : ( Y2 = Z4 ) )
% 2.11/1.48 = ( ^ [A3: $o > a,B2: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ B2 @ A3 )
% 2.11/1.48 & ( ord_less_eq_o_a @ A3 @ B2 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_52_dual__order_Oeq__iff,axiom,
% 2.11/1.48 ( ( ^ [Y2: a,Z4: a] : ( Y2 = Z4 ) )
% 2.11/1.48 = ( ^ [A3: a,B2: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ B2 @ A3 )
% 2.11/1.48 & ( ord_less_eq_a @ A3 @ B2 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_53_dual__order_Otrans,axiom,
% 2.11/1.48 ! [B: $o > a,A: $o > a,C: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ B @ A )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ C @ B )
% 2.11/1.48 => ( ord_less_eq_o_a @ C @ A ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_54_dual__order_Otrans,axiom,
% 2.11/1.48 ! [B: a,A: a,C: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ B @ A )
% 2.11/1.48 => ( ( ord_less_eq_a @ C @ B )
% 2.11/1.48 => ( ord_less_eq_a @ C @ A ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_55_linorder__wlog,axiom,
% 2.11/1.48 ! [P: a > a > $o,A: a,B: a] :
% 2.11/1.48 ( ! [A4: a,B3: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A4 @ B3 )
% 2.11/1.48 => ( P @ A4 @ B3 ) )
% 2.11/1.48 => ( ! [A4: a,B3: a] :
% 2.11/1.48 ( ( P @ B3 @ A4 )
% 2.11/1.48 => ( P @ A4 @ B3 ) )
% 2.11/1.48 => ( P @ A @ B ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_56_dual__order_Orefl,axiom,
% 2.11/1.48 ! [A: $o > a] : ( ord_less_eq_o_a @ A @ A ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_57_dual__order_Orefl,axiom,
% 2.11/1.48 ! [A: a] : ( ord_less_eq_a @ A @ A ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_58_order__trans,axiom,
% 2.11/1.48 ! [X: $o > a,Y: $o > a,Z5: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X @ Y )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ Y @ Z5 )
% 2.11/1.48 => ( ord_less_eq_o_a @ X @ Z5 ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_59_order__trans,axiom,
% 2.11/1.48 ! [X: a,Y: a,Z5: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X @ Y )
% 2.11/1.48 => ( ( ord_less_eq_a @ Y @ Z5 )
% 2.11/1.48 => ( ord_less_eq_a @ X @ Z5 ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_60_order__class_Oorder_Oantisym,axiom,
% 2.11/1.48 ! [A: $o > a,B: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A @ B )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ B @ A )
% 2.11/1.48 => ( A = B ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_61_order__class_Oorder_Oantisym,axiom,
% 2.11/1.48 ! [A: a,B: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A @ B )
% 2.11/1.48 => ( ( ord_less_eq_a @ B @ A )
% 2.11/1.48 => ( A = B ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_62_ord__le__eq__trans,axiom,
% 2.11/1.48 ! [A: $o > a,B: $o > a,C: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A @ B )
% 2.11/1.48 => ( ( B = C )
% 2.11/1.48 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_63_ord__le__eq__trans,axiom,
% 2.11/1.48 ! [A: a,B: a,C: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A @ B )
% 2.11/1.48 => ( ( B = C )
% 2.11/1.48 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_64_ord__eq__le__trans,axiom,
% 2.11/1.48 ! [A: $o > a,B: $o > a,C: $o > a] :
% 2.11/1.48 ( ( A = B )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ B @ C )
% 2.11/1.48 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_65_ord__eq__le__trans,axiom,
% 2.11/1.48 ! [A: a,B: a,C: a] :
% 2.11/1.48 ( ( A = B )
% 2.11/1.48 => ( ( ord_less_eq_a @ B @ C )
% 2.11/1.48 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_66_order__class_Oorder_Oeq__iff,axiom,
% 2.11/1.48 ( ( ^ [Y2: $o > a,Z4: $o > a] : ( Y2 = Z4 ) )
% 2.11/1.48 = ( ^ [A3: $o > a,B2: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A3 @ B2 )
% 2.11/1.48 & ( ord_less_eq_o_a @ B2 @ A3 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_67_order__class_Oorder_Oeq__iff,axiom,
% 2.11/1.48 ( ( ^ [Y2: a,Z4: a] : ( Y2 = Z4 ) )
% 2.11/1.48 = ( ^ [A3: a,B2: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A3 @ B2 )
% 2.11/1.48 & ( ord_less_eq_a @ B2 @ A3 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_68_antisym__conv,axiom,
% 2.11/1.48 ! [Y: $o > a,X: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ Y @ X )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ X @ Y )
% 2.11/1.48 = ( X = Y ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_69_antisym__conv,axiom,
% 2.11/1.48 ! [Y: a,X: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ Y @ X )
% 2.11/1.48 => ( ( ord_less_eq_a @ X @ Y )
% 2.11/1.48 = ( X = Y ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_70_le__cases3,axiom,
% 2.11/1.48 ! [X: a,Y: a,Z5: a] :
% 2.11/1.48 ( ( ( ord_less_eq_a @ X @ Y )
% 2.11/1.48 => ~ ( ord_less_eq_a @ Y @ Z5 ) )
% 2.11/1.48 => ( ( ( ord_less_eq_a @ Y @ X )
% 2.11/1.48 => ~ ( ord_less_eq_a @ X @ Z5 ) )
% 2.11/1.48 => ( ( ( ord_less_eq_a @ X @ Z5 )
% 2.11/1.48 => ~ ( ord_less_eq_a @ Z5 @ Y ) )
% 2.11/1.48 => ( ( ( ord_less_eq_a @ Z5 @ Y )
% 2.11/1.48 => ~ ( ord_less_eq_a @ Y @ X ) )
% 2.11/1.48 => ( ( ( ord_less_eq_a @ Y @ Z5 )
% 2.11/1.48 => ~ ( ord_less_eq_a @ Z5 @ X ) )
% 2.11/1.48 => ~ ( ( ord_less_eq_a @ Z5 @ X )
% 2.11/1.48 => ~ ( ord_less_eq_a @ X @ Y ) ) ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_71_order_Otrans,axiom,
% 2.11/1.48 ! [A: $o > a,B: $o > a,C: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A @ B )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ B @ C )
% 2.11/1.48 => ( ord_less_eq_o_a @ A @ C ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_72_order_Otrans,axiom,
% 2.11/1.48 ! [A: a,B: a,C: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A @ B )
% 2.11/1.48 => ( ( ord_less_eq_a @ B @ C )
% 2.11/1.48 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_73_le__cases,axiom,
% 2.11/1.48 ! [X: a,Y: a] :
% 2.11/1.48 ( ~ ( ord_less_eq_a @ X @ Y )
% 2.11/1.48 => ( ord_less_eq_a @ Y @ X ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_74_eq__refl,axiom,
% 2.11/1.48 ! [X: $o > a,Y: $o > a] :
% 2.11/1.48 ( ( X = Y )
% 2.11/1.48 => ( ord_less_eq_o_a @ X @ Y ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_75_eq__refl,axiom,
% 2.11/1.48 ! [X: a,Y: a] :
% 2.11/1.48 ( ( X = Y )
% 2.11/1.48 => ( ord_less_eq_a @ X @ Y ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_76_linear,axiom,
% 2.11/1.48 ! [X: a,Y: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X @ Y )
% 2.11/1.48 | ( ord_less_eq_a @ Y @ X ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_77_antisym,axiom,
% 2.11/1.48 ! [X: $o > a,Y: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X @ Y )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ Y @ X )
% 2.11/1.48 => ( X = Y ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_78_antisym,axiom,
% 2.11/1.48 ! [X: a,Y: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X @ Y )
% 2.11/1.48 => ( ( ord_less_eq_a @ Y @ X )
% 2.11/1.48 => ( X = Y ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_79_eq__iff,axiom,
% 2.11/1.48 ( ( ^ [Y2: $o > a,Z4: $o > a] : ( Y2 = Z4 ) )
% 2.11/1.48 = ( ^ [X4: $o > a,Y3: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X4 @ Y3 )
% 2.11/1.48 & ( ord_less_eq_o_a @ Y3 @ X4 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_80_eq__iff,axiom,
% 2.11/1.48 ( ( ^ [Y2: a,Z4: a] : ( Y2 = Z4 ) )
% 2.11/1.48 = ( ^ [X4: a,Y3: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X4 @ Y3 )
% 2.11/1.48 & ( ord_less_eq_a @ Y3 @ X4 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_81_ord__le__eq__subst,axiom,
% 2.11/1.48 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A @ B )
% 2.11/1.48 => ( ( ( F @ B )
% 2.11/1.48 = C )
% 2.11/1.48 => ( ! [X5: a,Y4: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_82_ord__le__eq__subst,axiom,
% 2.11/1.48 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A @ B )
% 2.11/1.48 => ( ( ( F @ B )
% 2.11/1.48 = C )
% 2.11/1.48 => ( ! [X5: $o > a,Y4: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_83_ord__le__eq__subst,axiom,
% 2.11/1.48 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A @ B )
% 2.11/1.48 => ( ( ( F @ B )
% 2.11/1.48 = C )
% 2.11/1.48 => ( ! [X5: $o > a,Y4: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_84_ord__le__eq__subst,axiom,
% 2.11/1.48 ! [A: a,B: a,F: a > a,C: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A @ B )
% 2.11/1.48 => ( ( ( F @ B )
% 2.11/1.48 = C )
% 2.11/1.48 => ( ! [X5: a,Y4: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_85_ord__eq__le__subst,axiom,
% 2.11/1.48 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 2.11/1.48 ( ( A
% 2.11/1.48 = ( F @ B ) )
% 2.11/1.48 => ( ( ord_less_eq_a @ B @ C )
% 2.11/1.48 => ( ! [X5: a,Y4: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_86_ord__eq__le__subst,axiom,
% 2.11/1.48 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 2.11/1.48 ( ( A
% 2.11/1.48 = ( F @ B ) )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ B @ C )
% 2.11/1.48 => ( ! [X5: $o > a,Y4: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_87_ord__eq__le__subst,axiom,
% 2.11/1.48 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 2.11/1.48 ( ( A
% 2.11/1.48 = ( F @ B ) )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ B @ C )
% 2.11/1.48 => ( ! [X5: $o > a,Y4: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_88_ord__eq__le__subst,axiom,
% 2.11/1.48 ! [A: a,F: a > a,B: a,C: a] :
% 2.11/1.48 ( ( A
% 2.11/1.48 = ( F @ B ) )
% 2.11/1.48 => ( ( ord_less_eq_a @ B @ C )
% 2.11/1.48 => ( ! [X5: a,Y4: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_89_order__subst2,axiom,
% 2.11/1.48 ! [A: a,B: a,F: a > $o > a,C: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A @ B )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 2.11/1.48 => ( ! [X5: a,Y4: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_90_order__subst2,axiom,
% 2.11/1.48 ! [A: $o > a,B: $o > a,F: ( $o > a ) > a,C: a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A @ B )
% 2.11/1.48 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 2.11/1.48 => ( ! [X5: $o > a,Y4: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_91_order__subst2,axiom,
% 2.11/1.48 ! [A: $o > a,B: $o > a,F: ( $o > a ) > $o > a,C: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A @ B )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ ( F @ B ) @ C )
% 2.11/1.48 => ( ! [X5: $o > a,Y4: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_92_order__subst2,axiom,
% 2.11/1.48 ! [A: a,B: a,F: a > a,C: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A @ B )
% 2.11/1.48 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 2.11/1.48 => ( ! [X5: a,Y4: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_93_order__subst1,axiom,
% 2.11/1.48 ! [A: a,F: ( $o > a ) > a,B: $o > a,C: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ B @ C )
% 2.11/1.48 => ( ! [X5: $o > a,Y4: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_94_order__subst1,axiom,
% 2.11/1.48 ! [A: $o > a,F: a > $o > a,B: a,C: a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 2.11/1.48 => ( ( ord_less_eq_a @ B @ C )
% 2.11/1.48 => ( ! [X5: a,Y4: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_95_order__subst1,axiom,
% 2.11/1.48 ! [A: $o > a,F: ( $o > a ) > $o > a,B: $o > a,C: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ A @ ( F @ B ) )
% 2.11/1.48 => ( ( ord_less_eq_o_a @ B @ C )
% 2.11/1.48 => ( ! [X5: $o > a,Y4: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_o_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_96_order__subst1,axiom,
% 2.11/1.48 ! [A: a,F: a > a,B: a,C: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 2.11/1.48 => ( ( ord_less_eq_a @ B @ C )
% 2.11/1.48 => ( ! [X5: a,Y4: a] :
% 2.11/1.48 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.11/1.48 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_97_Greatest__equality,axiom,
% 2.11/1.48 ! [P: ( $o > a ) > $o,X: $o > a] :
% 2.11/1.48 ( ( P @ X )
% 2.11/1.48 => ( ! [Y4: $o > a] :
% 2.11/1.48 ( ( P @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ Y4 @ X ) )
% 2.11/1.48 => ( ( order_Greatest_o_a @ P )
% 2.11/1.48 = X ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_98_Greatest__equality,axiom,
% 2.11/1.48 ! [P: a > $o,X: a] :
% 2.11/1.48 ( ( P @ X )
% 2.11/1.48 => ( ! [Y4: a] :
% 2.11/1.48 ( ( P @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ Y4 @ X ) )
% 2.11/1.48 => ( ( order_Greatest_a @ P )
% 2.11/1.48 = X ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_99_GreatestI2__order,axiom,
% 2.11/1.48 ! [P: ( $o > a ) > $o,X: $o > a,Q: ( $o > a ) > $o] :
% 2.11/1.48 ( ( P @ X )
% 2.11/1.48 => ( ! [Y4: $o > a] :
% 2.11/1.48 ( ( P @ Y4 )
% 2.11/1.48 => ( ord_less_eq_o_a @ Y4 @ X ) )
% 2.11/1.48 => ( ! [X5: $o > a] :
% 2.11/1.48 ( ( P @ X5 )
% 2.11/1.48 => ( ! [Y5: $o > a] :
% 2.11/1.48 ( ( P @ Y5 )
% 2.11/1.48 => ( ord_less_eq_o_a @ Y5 @ X5 ) )
% 2.11/1.48 => ( Q @ X5 ) ) )
% 2.11/1.48 => ( Q @ ( order_Greatest_o_a @ P ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_100_GreatestI2__order,axiom,
% 2.11/1.48 ! [P: a > $o,X: a,Q: a > $o] :
% 2.11/1.48 ( ( P @ X )
% 2.11/1.48 => ( ! [Y4: a] :
% 2.11/1.48 ( ( P @ Y4 )
% 2.11/1.48 => ( ord_less_eq_a @ Y4 @ X ) )
% 2.11/1.48 => ( ! [X5: a] :
% 2.11/1.48 ( ( P @ X5 )
% 2.11/1.48 => ( ! [Y5: a] :
% 2.11/1.48 ( ( P @ Y5 )
% 2.11/1.48 => ( ord_less_eq_a @ Y5 @ X5 ) )
% 2.11/1.48 => ( Q @ X5 ) ) )
% 2.11/1.48 => ( Q @ ( order_Greatest_a @ P ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_101_le__rel__bool__arg__iff,axiom,
% 2.11/1.48 ( ord_less_eq_o_o_a
% 2.11/1.48 = ( ^ [X6: $o > $o > a,Y6: $o > $o > a] :
% 2.11/1.48 ( ( ord_less_eq_o_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 2.11/1.48 & ( ord_less_eq_o_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_102_le__rel__bool__arg__iff,axiom,
% 2.11/1.48 ( ord_less_eq_o_a
% 2.11/1.48 = ( ^ [X6: $o > a,Y6: $o > a] :
% 2.11/1.48 ( ( ord_less_eq_a @ ( X6 @ $false ) @ ( Y6 @ $false ) )
% 2.11/1.48 & ( ord_less_eq_a @ ( X6 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_103_verit__la__disequality,axiom,
% 2.11/1.48 ! [A: a,B: a] :
% 2.11/1.48 ( ( A = B )
% 2.11/1.48 | ~ ( ord_less_eq_a @ A @ B )
% 2.11/1.48 | ~ ( ord_less_eq_a @ B @ A ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_104_Tree_Osimps_I14_J,axiom,
% 2.11/1.48 ( ( set_Tree_a @ e_a )
% 2.11/1.48 = bot_bot_set_a ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_105_Tree_Opred__set,axiom,
% 2.11/1.48 ( pred_Tree_a
% 2.11/1.48 = ( ^ [P2: a > $o,X4: tree_a] :
% 2.11/1.48 ! [Y3: a] :
% 2.11/1.48 ( ( member_a @ Y3 @ ( set_Tree_a @ X4 ) )
% 2.11/1.48 => ( P2 @ Y3 ) ) ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_106_empty__iff,axiom,
% 2.11/1.48 ! [C: a] :
% 2.11/1.48 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_107_all__not__in__conv,axiom,
% 2.11/1.48 ! [A2: set_a] :
% 2.11/1.48 ( ( ! [X4: a] :
% 2.11/1.48 ~ ( member_a @ X4 @ A2 ) )
% 2.11/1.48 = ( A2 = bot_bot_set_a ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_108_subsetI,axiom,
% 2.11/1.48 ! [A2: set_a,B4: set_a] :
% 2.11/1.48 ( ! [X5: a] :
% 2.11/1.48 ( ( member_a @ X5 @ A2 )
% 2.11/1.48 => ( member_a @ X5 @ B4 ) )
% 2.11/1.48 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ).
% 2.11/1.48
% 2.11/1.48 thf(fact_109_in__mono,axiom,
% 2.11/1.48 ! [A2: set_a,B4: set_a,X: a] :
% 2.11/1.48 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.11/1.48 => ( ( member_a @ X @ A2 )
% 2.11/1.48 => ( member_a @ X @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_110_subsetD,axiom,
% 2.11/1.49 ! [A2: set_a,B4: set_a,C: a] :
% 2.11/1.49 ( ( ord_less_eq_set_a @ A2 @ B4 )
% 2.11/1.49 => ( ( member_a @ C @ A2 )
% 2.11/1.49 => ( member_a @ C @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_111_subset__eq,axiom,
% 2.11/1.49 ( ord_less_eq_set_a
% 2.11/1.49 = ( ^ [A5: set_a,B5: set_a] :
% 2.11/1.49 ! [X4: a] :
% 2.11/1.49 ( ( member_a @ X4 @ A5 )
% 2.11/1.49 => ( member_a @ X4 @ B5 ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_112_subset__iff,axiom,
% 2.11/1.49 ( ord_less_eq_set_a
% 2.11/1.49 = ( ^ [A5: set_a,B5: set_a] :
% 2.11/1.49 ! [T2: a] :
% 2.11/1.49 ( ( member_a @ T2 @ A5 )
% 2.11/1.49 => ( member_a @ T2 @ B5 ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_113_ex__in__conv,axiom,
% 2.11/1.49 ! [A2: set_a] :
% 2.11/1.49 ( ( ? [X4: a] : ( member_a @ X4 @ A2 ) )
% 2.11/1.49 = ( A2 != bot_bot_set_a ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_114_equals0I,axiom,
% 2.11/1.49 ! [A2: set_a] :
% 2.11/1.49 ( ! [Y4: a] :
% 2.11/1.49 ~ ( member_a @ Y4 @ A2 )
% 2.11/1.49 => ( A2 = bot_bot_set_a ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_115_equals0D,axiom,
% 2.11/1.49 ! [A2: set_a,A: a] :
% 2.11/1.49 ( ( A2 = bot_bot_set_a )
% 2.11/1.49 => ~ ( member_a @ A @ A2 ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_116_emptyE,axiom,
% 2.11/1.49 ! [A: a] :
% 2.11/1.49 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_117_Ball__def,axiom,
% 2.11/1.49 ( ball_a
% 2.11/1.49 = ( ^ [A5: set_a,P2: a > $o] :
% 2.11/1.49 ! [X4: a] :
% 2.11/1.49 ( ( member_a @ X4 @ A5 )
% 2.11/1.49 => ( P2 @ X4 ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_118_subset__emptyI,axiom,
% 2.11/1.49 ! [A2: set_a] :
% 2.11/1.49 ( ! [X5: a] :
% 2.11/1.49 ~ ( member_a @ X5 @ A2 )
% 2.11/1.49 => ( ord_less_eq_set_a @ A2 @ bot_bot_set_a ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_119_ball__reg,axiom,
% 2.11/1.49 ! [R3: set_a,P: a > $o,Q: a > $o] :
% 2.11/1.49 ( ! [X5: a] :
% 2.11/1.49 ( ( member_a @ X5 @ R3 )
% 2.11/1.49 => ( ( P @ X5 )
% 2.11/1.49 => ( Q @ X5 ) ) )
% 2.11/1.49 => ( ! [X5: a] :
% 2.11/1.49 ( ( member_a @ X5 @ R3 )
% 2.11/1.49 => ( P @ X5 ) )
% 2.11/1.49 => ! [X7: a] :
% 2.11/1.49 ( ( member_a @ X7 @ R3 )
% 2.11/1.49 => ( Q @ X7 ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_120_bot__empty__eq,axiom,
% 2.11/1.49 ( bot_bot_a_o
% 2.11/1.49 = ( ^ [X4: a] : ( member_a @ X4 @ bot_bot_set_a ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_121_heap__top__geq,axiom,
% 2.11/1.49 ! [A: a,T: tree_a] :
% 2.11/1.49 ( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ T ) ) )
% 2.11/1.49 => ( ( is_heap_a @ T )
% 2.11/1.49 => ( ord_less_eq_a @ A @ ( val_a @ T ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_122_heap__top__max,axiom,
% 2.11/1.49 ! [T: tree_a] :
% 2.11/1.49 ( ( T != e_a )
% 2.11/1.49 => ( ( is_heap_a @ T )
% 2.11/1.49 => ( ( val_a @ T )
% 2.11/1.49 = ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ T ) ) ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_123_multiset_Osimps_I1_J,axiom,
% 2.11/1.49 ( ( multiset_a2 @ e_a )
% 2.11/1.49 = zero_zero_multiset_a ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_124_is__singletonI_H,axiom,
% 2.11/1.49 ! [A2: set_a] :
% 2.11/1.49 ( ( A2 != bot_bot_set_a )
% 2.11/1.49 => ( ! [X5: a,Y4: a] :
% 2.11/1.49 ( ( member_a @ X5 @ A2 )
% 2.11/1.49 => ( ( member_a @ Y4 @ A2 )
% 2.11/1.49 => ( X5 = Y4 ) ) )
% 2.11/1.49 => ( is_singleton_a @ A2 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_125_Diff__iff,axiom,
% 2.11/1.49 ! [C: a,A2: set_a,B4: set_a] :
% 2.11/1.49 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) )
% 2.11/1.49 = ( ( member_a @ C @ A2 )
% 2.11/1.49 & ~ ( member_a @ C @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_126_DiffI,axiom,
% 2.11/1.49 ! [C: a,A2: set_a,B4: set_a] :
% 2.11/1.49 ( ( member_a @ C @ A2 )
% 2.11/1.49 => ( ~ ( member_a @ C @ B4 )
% 2.11/1.49 => ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_127_DiffD2,axiom,
% 2.11/1.49 ! [C: a,A2: set_a,B4: set_a] :
% 2.11/1.49 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) )
% 2.11/1.49 => ~ ( member_a @ C @ B4 ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_128_DiffD1,axiom,
% 2.11/1.49 ! [C: a,A2: set_a,B4: set_a] :
% 2.11/1.49 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) )
% 2.11/1.49 => ( member_a @ C @ A2 ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_129_DiffE,axiom,
% 2.11/1.49 ! [C: a,A2: set_a,B4: set_a] :
% 2.11/1.49 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B4 ) )
% 2.11/1.49 => ~ ( ( member_a @ C @ A2 )
% 2.11/1.49 => ( member_a @ C @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_130_set__mset__eq__empty__iff,axiom,
% 2.11/1.49 ! [M: multiset_a] :
% 2.11/1.49 ( ( ( set_mset_a @ M )
% 2.11/1.49 = bot_bot_set_a )
% 2.11/1.49 = ( M = zero_zero_multiset_a ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_131_set__mset__empty,axiom,
% 2.11/1.49 ( ( set_mset_a @ zero_zero_multiset_a )
% 2.11/1.49 = bot_bot_set_a ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_132_multiset__induct__max,axiom,
% 2.11/1.49 ! [P: multiset_a > $o,M: multiset_a] :
% 2.11/1.49 ( ( P @ zero_zero_multiset_a )
% 2.11/1.49 => ( ! [X5: a,M2: multiset_a] :
% 2.11/1.49 ( ( P @ M2 )
% 2.11/1.49 => ( ! [Xa: a] :
% 2.11/1.49 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 2.11/1.49 => ( ord_less_eq_a @ Xa @ X5 ) )
% 2.11/1.49 => ( P @ ( add_mset_a @ X5 @ M2 ) ) ) )
% 2.11/1.49 => ( P @ M ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_133_multiset__induct__min,axiom,
% 2.11/1.49 ! [P: multiset_a > $o,M: multiset_a] :
% 2.11/1.49 ( ( P @ zero_zero_multiset_a )
% 2.11/1.49 => ( ! [X5: a,M2: multiset_a] :
% 2.11/1.49 ( ( P @ M2 )
% 2.11/1.49 => ( ! [Xa: a] :
% 2.11/1.49 ( ( member_a @ Xa @ ( set_mset_a @ M2 ) )
% 2.11/1.49 => ( ord_less_eq_a @ X5 @ Xa ) )
% 2.11/1.49 => ( P @ ( add_mset_a @ X5 @ M2 ) ) ) )
% 2.11/1.49 => ( P @ M ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_134_at__most__one__mset__mset__diff,axiom,
% 2.11/1.49 ! [A: a,M: multiset_a] :
% 2.11/1.49 ( ~ ( member_a @ A @ ( set_mset_a @ ( minus_1649712171iset_a @ M @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) )
% 2.11/1.49 => ( ( set_mset_a @ ( minus_1649712171iset_a @ M @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
% 2.11/1.49 = ( minus_minus_set_a @ ( set_mset_a @ M ) @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_135_multiset_Osimps_I2_J,axiom,
% 2.11/1.49 ! [V: a,L: tree_a,R: tree_a] :
% 2.11/1.49 ( ( multiset_a2 @ ( t_a @ V @ L @ R ) )
% 2.11/1.49 = ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ L ) @ ( add_mset_a @ V @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ R ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_136_insert__iff,axiom,
% 2.11/1.49 ! [A: a,B: a,A2: set_a] :
% 2.11/1.49 ( ( member_a @ A @ ( insert_a @ B @ A2 ) )
% 2.11/1.49 = ( ( A = B )
% 2.11/1.49 | ( member_a @ A @ A2 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_137_insertCI,axiom,
% 2.11/1.49 ! [A: a,B4: set_a,B: a] :
% 2.11/1.49 ( ( ~ ( member_a @ A @ B4 )
% 2.11/1.49 => ( A = B ) )
% 2.11/1.49 => ( member_a @ A @ ( insert_a @ B @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_138_singletonI,axiom,
% 2.11/1.49 ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_139_insert__subset,axiom,
% 2.11/1.49 ! [X: a,A2: set_a,B4: set_a] :
% 2.11/1.49 ( ( ord_less_eq_set_a @ ( insert_a @ X @ A2 ) @ B4 )
% 2.11/1.49 = ( ( member_a @ X @ B4 )
% 2.11/1.49 & ( ord_less_eq_set_a @ A2 @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_140_insert__Diff1,axiom,
% 2.11/1.49 ! [X: a,B4: set_a,A2: set_a] :
% 2.11/1.49 ( ( member_a @ X @ B4 )
% 2.11/1.49 => ( ( minus_minus_set_a @ ( insert_a @ X @ A2 ) @ B4 )
% 2.11/1.49 = ( minus_minus_set_a @ A2 @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_141_Diff__insert0,axiom,
% 2.11/1.49 ! [X: a,A2: set_a,B4: set_a] :
% 2.11/1.49 ( ~ ( member_a @ X @ A2 )
% 2.11/1.49 => ( ( minus_minus_set_a @ A2 @ ( insert_a @ X @ B4 ) )
% 2.11/1.49 = ( minus_minus_set_a @ A2 @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_142_insert__Diff__if,axiom,
% 2.11/1.49 ! [X: a,B4: set_a,A2: set_a] :
% 2.11/1.49 ( ( ( member_a @ X @ B4 )
% 2.11/1.49 => ( ( minus_minus_set_a @ ( insert_a @ X @ A2 ) @ B4 )
% 2.11/1.49 = ( minus_minus_set_a @ A2 @ B4 ) ) )
% 2.11/1.49 & ( ~ ( member_a @ X @ B4 )
% 2.11/1.49 => ( ( minus_minus_set_a @ ( insert_a @ X @ A2 ) @ B4 )
% 2.11/1.49 = ( insert_a @ X @ ( minus_minus_set_a @ A2 @ B4 ) ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_143_verit__sum__simplify,axiom,
% 2.11/1.49 ! [A: multiset_a] :
% 2.11/1.49 ( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
% 2.11/1.49 = A ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_144_add__right__mono,axiom,
% 2.11/1.49 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 2.11/1.49 ( ( ord_le1199012836iset_a @ A @ B )
% 2.11/1.49 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_145_add__left__mono,axiom,
% 2.11/1.49 ! [A: multiset_a,B: multiset_a,C: multiset_a] :
% 2.11/1.49 ( ( ord_le1199012836iset_a @ A @ B )
% 2.11/1.49 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_146_add__mono,axiom,
% 2.11/1.49 ! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
% 2.11/1.49 ( ( ord_le1199012836iset_a @ A @ B )
% 2.11/1.49 => ( ( ord_le1199012836iset_a @ C @ D )
% 2.11/1.49 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_147_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.11/1.49 ! [I: multiset_a,J: multiset_a,K: multiset_a,L: multiset_a] :
% 2.11/1.49 ( ( ( ord_le1199012836iset_a @ I @ J )
% 2.11/1.49 & ( ord_le1199012836iset_a @ K @ L ) )
% 2.11/1.49 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_148_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.11/1.49 ! [I: multiset_a,J: multiset_a,K: multiset_a,L: multiset_a] :
% 2.11/1.49 ( ( ( I = J )
% 2.11/1.49 & ( ord_le1199012836iset_a @ K @ L ) )
% 2.11/1.49 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_149_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.11/1.49 ! [I: multiset_a,J: multiset_a,K: multiset_a,L: multiset_a] :
% 2.11/1.49 ( ( ( ord_le1199012836iset_a @ I @ J )
% 2.11/1.49 & ( K = L ) )
% 2.11/1.49 => ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ I @ K ) @ ( plus_plus_multiset_a @ J @ L ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_150_mk__disjoint__insert,axiom,
% 2.11/1.49 ! [A: a,A2: set_a] :
% 2.11/1.49 ( ( member_a @ A @ A2 )
% 2.11/1.49 => ? [B6: set_a] :
% 2.11/1.49 ( ( A2
% 2.11/1.49 = ( insert_a @ A @ B6 ) )
% 2.11/1.49 & ~ ( member_a @ A @ B6 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_151_insert__eq__iff,axiom,
% 2.11/1.49 ! [A: a,A2: set_a,B: a,B4: set_a] :
% 2.11/1.49 ( ~ ( member_a @ A @ A2 )
% 2.11/1.49 => ( ~ ( member_a @ B @ B4 )
% 2.11/1.49 => ( ( ( insert_a @ A @ A2 )
% 2.11/1.49 = ( insert_a @ B @ B4 ) )
% 2.11/1.49 = ( ( ( A = B )
% 2.11/1.49 => ( A2 = B4 ) )
% 2.11/1.49 & ( ( A != B )
% 2.11/1.49 => ? [C2: set_a] :
% 2.11/1.49 ( ( A2
% 2.11/1.49 = ( insert_a @ B @ C2 ) )
% 2.11/1.49 & ~ ( member_a @ B @ C2 )
% 2.11/1.49 & ( B4
% 2.11/1.49 = ( insert_a @ A @ C2 ) )
% 2.11/1.49 & ~ ( member_a @ A @ C2 ) ) ) ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_152_insert__absorb,axiom,
% 2.11/1.49 ! [A: a,A2: set_a] :
% 2.11/1.49 ( ( member_a @ A @ A2 )
% 2.11/1.49 => ( ( insert_a @ A @ A2 )
% 2.11/1.49 = A2 ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_153_insert__ident,axiom,
% 2.11/1.49 ! [X: a,A2: set_a,B4: set_a] :
% 2.11/1.49 ( ~ ( member_a @ X @ A2 )
% 2.11/1.49 => ( ~ ( member_a @ X @ B4 )
% 2.11/1.49 => ( ( ( insert_a @ X @ A2 )
% 2.11/1.49 = ( insert_a @ X @ B4 ) )
% 2.11/1.49 = ( A2 = B4 ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_154_Set_Oset__insert,axiom,
% 2.11/1.49 ! [X: a,A2: set_a] :
% 2.11/1.49 ( ( member_a @ X @ A2 )
% 2.11/1.49 => ~ ! [B6: set_a] :
% 2.11/1.49 ( ( A2
% 2.11/1.49 = ( insert_a @ X @ B6 ) )
% 2.11/1.49 => ( member_a @ X @ B6 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_155_insertI2,axiom,
% 2.11/1.49 ! [A: a,B4: set_a,B: a] :
% 2.11/1.49 ( ( member_a @ A @ B4 )
% 2.11/1.49 => ( member_a @ A @ ( insert_a @ B @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_156_insertI1,axiom,
% 2.11/1.49 ! [A: a,B4: set_a] : ( member_a @ A @ ( insert_a @ A @ B4 ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_157_insertE,axiom,
% 2.11/1.49 ! [A: a,B: a,A2: set_a] :
% 2.11/1.49 ( ( member_a @ A @ ( insert_a @ B @ A2 ) )
% 2.11/1.49 => ( ( A != B )
% 2.11/1.49 => ( member_a @ A @ A2 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_158_singletonD,axiom,
% 2.11/1.49 ! [B: a,A: a] :
% 2.11/1.49 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 2.11/1.49 => ( B = A ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_159_singleton__iff,axiom,
% 2.11/1.49 ! [B: a,A: a] :
% 2.11/1.49 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 2.11/1.49 = ( B = A ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_160_insert__subsetI,axiom,
% 2.11/1.49 ! [X: a,A2: set_a,X8: set_a] :
% 2.11/1.49 ( ( member_a @ X @ A2 )
% 2.11/1.49 => ( ( ord_less_eq_set_a @ X8 @ A2 )
% 2.11/1.49 => ( ord_less_eq_set_a @ ( insert_a @ X @ X8 ) @ A2 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_161_subset__insert,axiom,
% 2.11/1.49 ! [X: a,A2: set_a,B4: set_a] :
% 2.11/1.49 ( ~ ( member_a @ X @ A2 )
% 2.11/1.49 => ( ( ord_less_eq_set_a @ A2 @ ( insert_a @ X @ B4 ) )
% 2.11/1.49 = ( ord_less_eq_set_a @ A2 @ B4 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_162_Diff__insert__absorb,axiom,
% 2.11/1.49 ! [X: a,A2: set_a] :
% 2.11/1.49 ( ~ ( member_a @ X @ A2 )
% 2.11/1.49 => ( ( minus_minus_set_a @ ( insert_a @ X @ A2 ) @ ( insert_a @ X @ bot_bot_set_a ) )
% 2.11/1.49 = A2 ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_163_insert__Diff,axiom,
% 2.11/1.49 ! [A: a,A2: set_a] :
% 2.11/1.49 ( ( member_a @ A @ A2 )
% 2.11/1.49 => ( ( insert_a @ A @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 2.11/1.49 = A2 ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_164_subset__Diff__insert,axiom,
% 2.11/1.49 ! [A2: set_a,B4: set_a,X: a,C3: set_a] :
% 2.11/1.49 ( ( ord_less_eq_set_a @ A2 @ ( minus_minus_set_a @ B4 @ ( insert_a @ X @ C3 ) ) )
% 2.11/1.49 = ( ( ord_less_eq_set_a @ A2 @ ( minus_minus_set_a @ B4 @ C3 ) )
% 2.11/1.49 & ~ ( member_a @ X @ A2 ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_165_subset__insert__iff,axiom,
% 2.11/1.49 ! [A2: set_a,X: a,B4: set_a] :
% 2.11/1.49 ( ( ord_less_eq_set_a @ A2 @ ( insert_a @ X @ B4 ) )
% 2.11/1.49 = ( ( ( member_a @ X @ A2 )
% 2.11/1.49 => ( ord_less_eq_set_a @ ( minus_minus_set_a @ A2 @ ( insert_a @ X @ bot_bot_set_a ) ) @ B4 ) )
% 2.11/1.49 & ( ~ ( member_a @ X @ A2 )
% 2.11/1.49 => ( ord_less_eq_set_a @ A2 @ B4 ) ) ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_166_set__mset__single,axiom,
% 2.11/1.49 ! [B: a] :
% 2.11/1.49 ( ( set_mset_a @ ( add_mset_a @ B @ zero_zero_multiset_a ) )
% 2.11/1.49 = ( insert_a @ B @ bot_bot_set_a ) ) ).
% 2.11/1.49
% 2.11/1.49 thf(fact_167_Max__singleton,axiom,
% 2.11/1.49 ! [X: a] :
% 2.11/1.49 ( ( lattic146396397_Max_a @ ( insert_a @ X @ bot_bot_set_a ) )
% 2.11/1.49 = X ) ).
% 2.11/1.49
% 2.11/1.49 thf(conj_0,conjecture,
% 2.11/1.49 in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ).
% 2.11/1.49 ------------------------
% 2.28/1.51 % (6042)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_5848 for (2999ds/27Mi)
% 2.28/1.51 % (6041)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_5848 for (2999ds/4Mi)
% 2.28/1.51 % (6040)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/183Mi)
% 2.28/1.51 % (6041)Instruction limit reached!
% 2.28/1.51 % (6041)------------------------------
% 2.28/1.51 % (6041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.51 % (6041)Termination reason: Unknown
% 2.28/1.51 % (6041)Termination phase: shuffling
% 2.28/1.51
% 2.28/1.51 % (6041)Memory used [KB]: 1279
% 2.28/1.51 % (6041)Time elapsed: 0.003 s
% 2.28/1.51 % (6041)Instructions burned: 5 (million)
% 2.28/1.51 % (6041)------------------------------
% 2.28/1.51 % (6041)------------------------------
% 2.28/1.51 % (6046)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/18Mi)
% 2.28/1.52 % (6043)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/2Mi)
% 2.28/1.52 % (6044)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_5848 for (2999ds/2Mi)
% 2.28/1.52 % (6045)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_5848 for (2999ds/275Mi)
% 2.28/1.52 % (6042)Instruction limit reached!
% 2.28/1.52 % (6042)------------------------------
% 2.28/1.52 % (6042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.52 % (6042)Termination reason: Unknown
% 2.28/1.52 % (6042)Termination phase: Property scanning
% 2.28/1.52
% 2.28/1.52 % (6042)Memory used [KB]: 1535
% 2.28/1.52 % (6042)Time elapsed: 0.010 s
% 2.28/1.52 % (6042)Instructions burned: 28 (million)
% 2.28/1.52 % (6042)------------------------------
% 2.28/1.52 % (6042)------------------------------
% 2.28/1.52 % (6043)Instruction limit reached!
% 2.28/1.52 % (6043)------------------------------
% 2.28/1.52 % (6043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.52 % (6043)Termination reason: Unknown
% 2.28/1.52 % (6043)Termination phase: shuffling
% 2.28/1.52
% 2.28/1.52 % (6043)Memory used [KB]: 1151
% 2.28/1.52 % (6043)Time elapsed: 0.004 s
% 2.28/1.52 % (6043)Instructions burned: 3 (million)
% 2.28/1.52 % (6043)------------------------------
% 2.28/1.52 % (6043)------------------------------
% 2.28/1.52 % (6044)Instruction limit reached!
% 2.28/1.52 % (6044)------------------------------
% 2.28/1.52 % (6044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.52 % (6044)Termination reason: Unknown
% 2.28/1.52 % (6044)Termination phase: shuffling
% 2.28/1.52
% 2.28/1.52 % (6044)Memory used [KB]: 1279
% 2.28/1.52 % (6044)Time elapsed: 0.004 s
% 2.28/1.52 % (6044)Instructions burned: 3 (million)
% 2.28/1.52 % (6044)------------------------------
% 2.28/1.52 % (6044)------------------------------
% 2.28/1.52 % (6049)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/3Mi)
% 2.28/1.52 % (6049)Instruction limit reached!
% 2.28/1.52 % (6049)------------------------------
% 2.28/1.52 % (6049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.52 % (6049)Termination reason: Unknown
% 2.28/1.52 % (6049)Termination phase: shuffling
% 2.28/1.52
% 2.28/1.52 % (6049)Memory used [KB]: 1151
% 2.28/1.52 % (6049)Time elapsed: 0.002 s
% 2.28/1.52 % (6049)Instructions burned: 3 (million)
% 2.28/1.52 % (6049)------------------------------
% 2.28/1.52 % (6049)------------------------------
% 2.28/1.52 % (6046)Instruction limit reached!
% 2.28/1.52 % (6046)------------------------------
% 2.28/1.52 % (6046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.52 % (6046)Termination reason: Unknown
% 2.28/1.52 % (6046)Termination phase: shuffling
% 2.28/1.52
% 2.28/1.52 % (6046)Memory used [KB]: 1407
% 2.28/1.52 % (6046)Time elapsed: 0.013 s
% 2.28/1.52 % (6046)Instructions burned: 18 (million)
% 2.28/1.52 % (6046)------------------------------
% 2.28/1.52 % (6046)------------------------------
% 2.28/1.53 % (6050)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_5848 for (2999ds/37Mi)
% 2.28/1.53 % (6053)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_5848 for (2999ds/1041Mi)
% 2.28/1.54 % (6051)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_5848 for (2999ds/15Mi)
% 2.28/1.54 % (6052)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_5848 for (2999ds/3Mi)
% 2.28/1.54 % (6050)Instruction limit reached!
% 2.28/1.54 % (6050)------------------------------
% 2.28/1.54 % (6050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.54 % (6050)Termination reason: Unknown
% 2.28/1.54 % (6050)Termination phase: Property scanning
% 2.28/1.54
% 2.28/1.54 % (6050)Memory used [KB]: 1918
% 2.28/1.54 % (6050)Time elapsed: 0.011 s
% 2.28/1.54 % (6050)Instructions burned: 38 (million)
% 2.28/1.54 % (6050)------------------------------
% 2.28/1.54 % (6050)------------------------------
% 2.28/1.54 % (6052)Instruction limit reached!
% 2.28/1.54 % (6052)------------------------------
% 2.28/1.54 % (6052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.54 % (6052)Termination reason: Unknown
% 2.28/1.54 % (6052)Termination phase: shuffling
% 2.28/1.54
% 2.28/1.54 % (6052)Memory used [KB]: 1279
% 2.28/1.54 % (6052)Time elapsed: 0.004 s
% 2.28/1.54 % (6052)Instructions burned: 3 (million)
% 2.28/1.54 % (6052)------------------------------
% 2.28/1.54 % (6052)------------------------------
% 2.28/1.54 % (6058)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/7Mi)
% 2.28/1.54 % (6058)Instruction limit reached!
% 2.28/1.54 % (6058)------------------------------
% 2.28/1.54 % (6058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.54 % (6058)Termination reason: Unknown
% 2.28/1.54 % (6058)Termination phase: shuffling
% 2.28/1.54
% 2.28/1.54 % (6058)Memory used [KB]: 1279
% 2.28/1.54 % (6058)Time elapsed: 0.005 s
% 2.28/1.54 % (6058)Instructions burned: 9 (million)
% 2.28/1.54 % (6058)------------------------------
% 2.28/1.54 % (6058)------------------------------
% 2.28/1.55 % (6051)Instruction limit reached!
% 2.28/1.55 % (6051)------------------------------
% 2.28/1.55 % (6051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.55 % (6051)Termination reason: Unknown
% 2.28/1.55 % (6051)Termination phase: shuffling
% 2.28/1.55
% 2.28/1.55 % (6051)Memory used [KB]: 1407
% 2.28/1.55 % (6051)Time elapsed: 0.011 s
% 2.28/1.55 % (6051)Instructions burned: 15 (million)
% 2.28/1.55 % (6051)------------------------------
% 2.28/1.55 % (6051)------------------------------
% 2.28/1.55 % (6070)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/16Mi)
% 2.28/1.55 % (6070)Instruction limit reached!
% 2.28/1.55 % (6070)------------------------------
% 2.28/1.55 % (6070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.55 % (6070)Termination reason: Unknown
% 2.28/1.55 % (6070)Termination phase: shuffling
% 2.28/1.55
% 2.28/1.55 % (6070)Memory used [KB]: 1407
% 2.28/1.55 % (6070)Time elapsed: 0.006 s
% 2.28/1.55 % (6070)Instructions burned: 17 (million)
% 2.28/1.55 % (6070)------------------------------
% 2.28/1.55 % (6070)------------------------------
% 2.28/1.55 % (6074)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_5848 for (2999ds/3Mi)
% 2.28/1.55 % (6045)Refutation not found, incomplete strategy
% 2.28/1.55 % (6045)------------------------------
% 2.28/1.55 % (6045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.55 % (6045)Termination reason: Refutation not found, incomplete strategy
% 2.28/1.55
% 2.28/1.55
% 2.28/1.55 % (6045)Memory used [KB]: 6396
% 2.28/1.55 % (6045)Time elapsed: 0.037 s
% 2.28/1.55 % (6045)Instructions burned: 64 (million)
% 2.28/1.55 % (6045)------------------------------
% 2.28/1.55 % (6045)------------------------------
% 2.28/1.55 % (6074)Instruction limit reached!
% 2.28/1.55 % (6074)------------------------------
% 2.28/1.55 % (6074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.55 % (6074)Termination reason: Unknown
% 2.28/1.55 % (6074)Termination phase: shuffling
% 2.28/1.55
% 2.28/1.55 % (6074)Memory used [KB]: 1279
% 2.28/1.55 % (6074)Time elapsed: 0.002 s
% 2.28/1.55 % (6074)Instructions burned: 4 (million)
% 2.28/1.55 % (6074)------------------------------
% 2.28/1.55 % (6074)------------------------------
% 2.28/1.56 % (6071)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_5848 for (2999ds/3Mi)
% 2.28/1.56 % (6071)Instruction limit reached!
% 2.28/1.56 % (6071)------------------------------
% 2.28/1.56 % (6071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.56 % (6071)Termination reason: Unknown
% 2.28/1.56 % (6071)Termination phase: shuffling
% 2.28/1.56
% 2.28/1.56 % (6071)Memory used [KB]: 1279
% 2.28/1.56 % (6071)Time elapsed: 0.004 s
% 2.28/1.56 % (6071)Instructions burned: 4 (million)
% 2.28/1.56 % (6071)------------------------------
% 2.28/1.56 % (6071)------------------------------
% 2.28/1.56 % (6081)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/3Mi)
% 2.28/1.56 % (6081)Instruction limit reached!
% 2.28/1.56 % (6081)------------------------------
% 2.28/1.56 % (6081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.56 % (6081)Termination reason: Unknown
% 2.28/1.56 % (6081)Termination phase: shuffling
% 2.28/1.56
% 2.28/1.56 % (6081)Memory used [KB]: 1279
% 2.28/1.56 % (6081)Time elapsed: 0.002 s
% 2.28/1.56 % (6081)Instructions burned: 4 (million)
% 2.28/1.56 % (6081)------------------------------
% 2.28/1.56 % (6081)------------------------------
% 2.28/1.56 % (6076)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/7Mi)
% 2.28/1.56 % (6085)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/18Mi)
% 2.28/1.57 % (6076)Instruction limit reached!
% 2.28/1.57 % (6076)------------------------------
% 2.28/1.57 % (6076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.57 % (6076)Termination reason: Unknown
% 2.28/1.57 % (6076)Termination phase: shuffling
% 2.28/1.57
% 2.28/1.57 % (6076)Memory used [KB]: 1279
% 2.28/1.57 % (6076)Time elapsed: 0.006 s
% 2.28/1.57 % (6076)Instructions burned: 7 (million)
% 2.28/1.57 % (6076)------------------------------
% 2.28/1.57 % (6076)------------------------------
% 2.28/1.57 % (6040)Instruction limit reached!
% 2.28/1.57 % (6040)------------------------------
% 2.28/1.57 % (6040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.57 % (6040)Termination reason: Unknown
% 2.28/1.57 % (6040)Termination phase: Saturation
% 2.28/1.57
% 2.28/1.57 % (6040)Memory used [KB]: 6908
% 2.28/1.57 % (6040)Time elapsed: 0.059 s
% 2.28/1.57 % (6040)Instructions burned: 184 (million)
% 2.28/1.57 % (6040)------------------------------
% 2.28/1.57 % (6040)------------------------------
% 2.28/1.57 % (6085)Instruction limit reached!
% 2.28/1.57 % (6085)------------------------------
% 2.28/1.57 % (6085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.57 % (6085)Termination reason: Unknown
% 2.28/1.57 % (6085)Termination phase: shuffling
% 2.28/1.57
% 2.28/1.57 % (6085)Memory used [KB]: 1407
% 2.28/1.57 % (6085)Time elapsed: 0.007 s
% 2.28/1.57 % (6085)Instructions burned: 19 (million)
% 2.28/1.57 % (6085)------------------------------
% 2.28/1.57 % (6085)------------------------------
% 2.28/1.57 % (6084)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/4Mi)
% 2.28/1.57 % (6087)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/6Mi)
% 2.28/1.57 % (6087)Instruction limit reached!
% 2.28/1.57 % (6087)------------------------------
% 2.28/1.57 % (6087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.57 % (6087)Termination reason: Unknown
% 2.28/1.57 % (6087)Termination phase: shuffling
% 2.28/1.57
% 2.28/1.57 % (6087)Memory used [KB]: 1279
% 2.28/1.57 % (6087)Time elapsed: 0.003 s
% 2.28/1.57 % (6087)Instructions burned: 6 (million)
% 2.28/1.57 % (6087)------------------------------
% 2.28/1.57 % (6087)------------------------------
% 2.28/1.57 % (6084)Instruction limit reached!
% 2.28/1.57 % (6084)------------------------------
% 2.28/1.57 % (6084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.57 % (6084)Termination reason: Unknown
% 2.28/1.57 % (6084)Termination phase: shuffling
% 2.28/1.57
% 2.28/1.57 % (6084)Memory used [KB]: 1279
% 2.28/1.57 % (6084)Time elapsed: 0.005 s
% 2.28/1.57 % (6084)Instructions burned: 5 (million)
% 2.28/1.57 % (6084)------------------------------
% 2.28/1.57 % (6084)------------------------------
% 2.28/1.58 % (6086)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/710Mi)
% 2.28/1.58 % (6089)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_5848 for (2999ds/21Mi)
% 2.28/1.58 % (6090)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/5Mi)
% 2.28/1.58 % (6090)Instruction limit reached!
% 2.28/1.58 % (6090)------------------------------
% 2.28/1.58 % (6090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.58 % (6090)Termination reason: Unknown
% 2.28/1.58 % (6090)Termination phase: shuffling
% 2.28/1.58
% 2.28/1.58 % (6090)Memory used [KB]: 1279
% 2.28/1.58 % (6090)Time elapsed: 0.003 s
% 2.28/1.58 % (6090)Instructions burned: 7 (million)
% 2.28/1.58 % (6090)------------------------------
% 2.28/1.58 % (6090)------------------------------
% 2.28/1.58 % (6095)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_5848 for (2999ds/6Mi)
% 2.28/1.58 % (6088)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_5848 for (2999ds/902Mi)
% 2.28/1.58 % (6095)Instruction limit reached!
% 2.28/1.58 % (6095)------------------------------
% 2.28/1.58 % (6095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.58 % (6095)Termination reason: Unknown
% 2.28/1.58 % (6095)Termination phase: shuffling
% 2.28/1.58
% 2.28/1.58 % (6095)Memory used [KB]: 1279
% 2.28/1.58 % (6095)Time elapsed: 0.003 s
% 2.28/1.58 % (6095)Instructions burned: 7 (million)
% 2.28/1.58 % (6095)------------------------------
% 2.28/1.58 % (6095)------------------------------
% 2.28/1.58 % (6089)Instruction limit reached!
% 2.28/1.58 % (6089)------------------------------
% 2.28/1.58 % (6089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.58 % (6089)Termination reason: Unknown
% 2.28/1.58 % (6089)Termination phase: Property scanning
% 2.28/1.58
% 2.28/1.58 % (6089)Memory used [KB]: 1535
% 2.28/1.58 % (6089)Time elapsed: 0.008 s
% 2.28/1.58 % (6089)Instructions burned: 21 (million)
% 2.28/1.58 % (6089)------------------------------
% 2.28/1.58 % (6089)------------------------------
% 2.28/1.59 % (6104)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_5848 for (2999ds/779Mi)
% 2.28/1.59 % (6097)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/377Mi)
% 2.28/1.59 % (6107)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_5848 for (2999ds/19Mi)
% 2.28/1.60 % (6109)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/879Mi)
% 2.28/1.60 % (6107)Instruction limit reached!
% 2.28/1.60 % (6107)------------------------------
% 2.28/1.60 % (6107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.60 % (6107)Termination reason: Unknown
% 2.28/1.60 % (6107)Termination phase: shuffling
% 2.28/1.60
% 2.28/1.60 % (6107)Memory used [KB]: 1535
% 2.28/1.60 % (6107)Time elapsed: 0.007 s
% 2.28/1.60 % (6107)Instructions burned: 21 (million)
% 2.28/1.60 % (6107)------------------------------
% 2.28/1.60 % (6107)------------------------------
% 2.28/1.61 % (6113)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5848 for (2999ds/17Mi)
% 2.28/1.61 % (6113)Instruction limit reached!
% 2.28/1.61 % (6113)------------------------------
% 2.28/1.61 % (6113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.61 % (6113)Termination reason: Unknown
% 2.28/1.61 % (6113)Termination phase: shuffling
% 2.28/1.61
% 2.28/1.61 % (6113)Memory used [KB]: 1535
% 2.28/1.61 % (6113)Time elapsed: 0.007 s
% 2.28/1.61 % (6113)Instructions burned: 19 (million)
% 2.28/1.61 % (6113)------------------------------
% 2.28/1.61 % (6113)------------------------------
% 2.28/1.62 % (6088)Refutation not found, incomplete strategy
% 2.28/1.62 % (6088)------------------------------
% 2.28/1.62 % (6088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.62 % (6088)Termination reason: Refutation not found, incomplete strategy
% 2.28/1.62
% 2.28/1.62
% 2.28/1.62 % (6088)Memory used [KB]: 6652
% 2.28/1.62 % (6088)Time elapsed: 0.033 s
% 2.28/1.62 % (6088)Instructions burned: 93 (million)
% 2.28/1.62 % (6088)------------------------------
% 2.28/1.62 % (6088)------------------------------
% 2.28/1.62 % (6122)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5848 for (2998ds/3Mi)
% 2.28/1.63 % (6122)Instruction limit reached!
% 2.28/1.63 % (6122)------------------------------
% 2.28/1.63 % (6122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.63 % (6122)Termination reason: Unknown
% 2.28/1.63 % (6122)Termination phase: shuffling
% 2.28/1.63
% 2.28/1.63 % (6122)Memory used [KB]: 1279
% 2.28/1.63 % (6122)Time elapsed: 0.002 s
% 2.28/1.63 % (6122)Instructions burned: 3 (million)
% 2.28/1.63 % (6122)------------------------------
% 2.28/1.63 % (6122)------------------------------
% 2.28/1.63 % (6124)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5848 for (2998ds/30Mi)
% 2.28/1.63 % (6128)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5848 for (2998ds/127Mi)
% 2.28/1.63 % (6124)Instruction limit reached!
% 2.28/1.63 % (6124)------------------------------
% 2.28/1.63 % (6124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.63 % (6124)Termination reason: Unknown
% 2.28/1.63 % (6124)Termination phase: Property scanning
% 2.28/1.63
% 2.28/1.63 % (6124)Memory used [KB]: 1535
% 2.28/1.63 % (6124)Time elapsed: 0.010 s
% 2.28/1.63 % (6124)Instructions burned: 31 (million)
% 2.28/1.63 % (6124)------------------------------
% 2.28/1.63 % (6124)------------------------------
% 2.28/1.64 % (6130)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_5848 for (2998ds/100Mi)
% 2.28/1.67 % (6130)Instruction limit reached!
% 2.28/1.67 % (6130)------------------------------
% 2.28/1.67 % (6130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.67 % (6130)Termination reason: Unknown
% 2.28/1.67 % (6130)Termination phase: Property scanning
% 2.28/1.67
% 2.28/1.67 % (6130)Memory used [KB]: 1918
% 2.28/1.67 % (6130)Time elapsed: 0.027 s
% 2.28/1.67 % (6130)Instructions burned: 100 (million)
% 2.28/1.67 % (6130)------------------------------
% 2.28/1.67 % (6130)------------------------------
% 2.28/1.67 % (6128)Instruction limit reached!
% 2.28/1.67 % (6128)------------------------------
% 2.28/1.67 % (6128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.67 % (6128)Termination reason: Unknown
% 2.28/1.67 % (6128)Termination phase: Saturation
% 2.28/1.67
% 2.28/1.67 % (6128)Memory used [KB]: 6780
% 2.28/1.67 % (6128)Time elapsed: 0.038 s
% 2.28/1.67 % (6128)Instructions burned: 128 (million)
% 2.28/1.67 % (6128)------------------------------
% 2.28/1.67 % (6128)------------------------------
% 2.28/1.68 % (6144)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_5848 for (2998ds/3Mi)
% 2.28/1.68 % (6144)Instruction limit reached!
% 2.28/1.68 % (6144)------------------------------
% 2.28/1.68 % (6144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.68 % (6144)Termination reason: Unknown
% 2.28/1.68 % (6144)Termination phase: shuffling
% 2.28/1.68
% 2.28/1.68 % (6144)Memory used [KB]: 1151
% 2.28/1.68 % (6144)Time elapsed: 0.002 s
% 2.28/1.68 % (6144)Instructions burned: 3 (million)
% 2.28/1.68 % (6144)------------------------------
% 2.28/1.68 % (6144)------------------------------
% 2.28/1.68 % (6145)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_5848 for (2998ds/20Mi)
% 2.28/1.69 % (6145)Instruction limit reached!
% 2.28/1.69 % (6145)------------------------------
% 2.28/1.69 % (6145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.69 % (6145)Termination reason: Unknown
% 2.28/1.69 % (6145)Termination phase: Property scanning
% 2.28/1.69
% 2.28/1.69 % (6145)Memory used [KB]: 1535
% 2.28/1.69 % (6145)Time elapsed: 0.008 s
% 2.28/1.69 % (6145)Instructions burned: 22 (million)
% 2.28/1.69 % (6145)------------------------------
% 2.28/1.69 % (6145)------------------------------
% 2.28/1.69 % (6150)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_5848 for (2997ds/86Mi)
% 2.28/1.70 % (6153)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_5848 for (2997ds/107Mi)
% 2.28/1.71 % (6150)Instruction limit reached!
% 2.28/1.71 % (6150)------------------------------
% 2.28/1.71 % (6150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.71 % (6150)Termination reason: Unknown
% 2.28/1.71 % (6150)Termination phase: Saturation
% 2.28/1.71
% 2.28/1.71 % (6150)Memory used [KB]: 6396
% 2.28/1.71 % (6150)Time elapsed: 0.025 s
% 2.28/1.71 % (6150)Instructions burned: 88 (million)
% 2.28/1.71 % (6150)------------------------------
% 2.28/1.71 % (6150)------------------------------
% 2.28/1.72 % (6164)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_5848 for (2997ds/39Mi)
% 2.28/1.73 % (6153)Instruction limit reached!
% 2.28/1.73 % (6153)------------------------------
% 2.28/1.73 % (6153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.73 % (6153)Termination reason: Unknown
% 2.28/1.73 % (6153)Termination phase: Saturation
% 2.28/1.73
% 2.28/1.73 % (6153)Memory used [KB]: 6524
% 2.28/1.73 % (6153)Time elapsed: 0.032 s
% 2.28/1.73 % (6153)Instructions burned: 107 (million)
% 2.28/1.73 % (6153)------------------------------
% 2.28/1.73 % (6153)------------------------------
% 2.28/1.73 % (6164)Instruction limit reached!
% 2.28/1.73 % (6164)------------------------------
% 2.28/1.73 % (6164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.73 % (6164)Termination reason: Unknown
% 2.28/1.73 % (6164)Termination phase: Property scanning
% 2.28/1.73
% 2.28/1.73 % (6164)Memory used [KB]: 1918
% 2.28/1.73 % (6164)Time elapsed: 0.012 s
% 2.28/1.73 % (6164)Instructions burned: 42 (million)
% 2.28/1.73 % (6164)------------------------------
% 2.28/1.73 % (6164)------------------------------
% 2.28/1.74 % (6097)Instruction limit reached!
% 2.28/1.74 % (6097)------------------------------
% 2.28/1.74 % (6097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.74 % (6097)Termination reason: Unknown
% 2.28/1.74 % (6097)Termination phase: Saturation
% 2.28/1.74
% 2.28/1.74 % (6097)Memory used [KB]: 7803
% 2.28/1.74 % (6097)Time elapsed: 0.169 s
% 2.28/1.74 % (6097)Instructions burned: 379 (million)
% 2.28/1.74 % (6097)------------------------------
% 2.28/1.74 % (6097)------------------------------
% 2.28/1.74 % (6168)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_5848 for (2997ds/448Mi)
% 2.28/1.74 % (6170)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_5848 for (2997ds/46Mi)
% 2.28/1.75 % (6171)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_5848 for (2997ds/98Mi)
% 2.28/1.76 % (6170)Instruction limit reached!
% 2.28/1.76 % (6170)------------------------------
% 2.28/1.76 % (6170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.76 % (6170)Termination reason: Unknown
% 2.28/1.76 % (6170)Termination phase: Property scanning
% 2.28/1.76
% 2.28/1.76 % (6170)Memory used [KB]: 1791
% 2.28/1.76 % (6170)Time elapsed: 0.015 s
% 2.28/1.76 % (6170)Instructions burned: 47 (million)
% 2.28/1.76 % (6170)------------------------------
% 2.28/1.76 % (6170)------------------------------
% 2.28/1.77 % (6177)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_5848 for (2997ds/507Mi)
% 2.28/1.78 % (6171)Instruction limit reached!
% 2.28/1.78 % (6171)------------------------------
% 2.28/1.78 % (6171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.78 % (6171)Termination reason: Unknown
% 2.28/1.78 % (6171)Termination phase: Property scanning
% 2.28/1.78
% 2.28/1.78 % (6171)Memory used [KB]: 1918
% 2.28/1.78 % (6171)Time elapsed: 0.028 s
% 2.28/1.78 % (6171)Instructions burned: 99 (million)
% 2.28/1.78 % (6171)------------------------------
% 2.28/1.78 % (6171)------------------------------
% 2.28/1.79 % (6181)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_5848 for (2997ds/149Mi)
% 2.28/1.80 % (6177)Refutation not found, incomplete strategy
% 2.28/1.80 % (6177)------------------------------
% 2.28/1.80 % (6177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.80 % (6177)Termination reason: Refutation not found, incomplete strategy
% 2.28/1.80
% 2.28/1.80
% 2.28/1.80 % (6177)Memory used [KB]: 6908
% 2.28/1.80 % (6177)Time elapsed: 0.033 s
% 2.28/1.80 % (6177)Instructions burned: 112 (million)
% 2.28/1.80 % (6177)------------------------------
% 2.28/1.80 % (6177)------------------------------
% 2.28/1.80 % (6086)Instruction limit reached!
% 2.28/1.80 % (6086)------------------------------
% 2.28/1.80 % (6086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.80 % (6086)Termination reason: Unknown
% 2.28/1.80 % (6086)Termination phase: Saturation
% 2.28/1.80
% 2.28/1.80 % (6086)Memory used [KB]: 7419
% 2.28/1.80 % (6086)Time elapsed: 0.230 s
% 2.28/1.80 % (6086)Instructions burned: 710 (million)
% 2.28/1.80 % (6086)------------------------------
% 2.28/1.80 % (6086)------------------------------
% 2.28/1.81 % (6188)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_5848 for (2996ds/39Mi)
% 2.28/1.81 % (6189)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_5848 for (2996ds/6Mi)
% 2.28/1.82 % (6189)Instruction limit reached!
% 2.28/1.82 % (6189)------------------------------
% 2.28/1.82 % (6189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.82 % (6189)Termination reason: Unknown
% 2.28/1.82 % (6189)Termination phase: shuffling
% 2.28/1.82
% 2.28/1.82 % (6189)Memory used [KB]: 1279
% 2.28/1.82 % (6189)Time elapsed: 0.004 s
% 2.28/1.82 % (6189)Instructions burned: 7 (million)
% 2.28/1.82 % (6189)------------------------------
% 2.28/1.82 % (6189)------------------------------
% 2.28/1.82 % (6188)Instruction limit reached!
% 2.28/1.82 % (6188)------------------------------
% 2.28/1.82 % (6188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.82 % (6188)Termination reason: Unknown
% 2.28/1.82 % (6188)Termination phase: Clausification
% 2.28/1.82
% 2.28/1.82 % (6188)Memory used [KB]: 1791
% 2.28/1.82 % (6188)Time elapsed: 0.013 s
% 2.28/1.82 % (6188)Instructions burned: 41 (million)
% 2.28/1.82 % (6188)------------------------------
% 2.28/1.82 % (6188)------------------------------
% 2.28/1.82 % (6104)Instruction limit reached!
% 2.28/1.82 % (6104)------------------------------
% 2.28/1.82 % (6104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.82 % (6104)Termination reason: Unknown
% 2.28/1.82 % (6104)Termination phase: Saturation
% 2.28/1.82
% 2.28/1.82 % (6104)Memory used [KB]: 8571
% 2.28/1.82 % (6104)Time elapsed: 0.254 s
% 2.28/1.82 % (6104)Instructions burned: 781 (million)
% 2.28/1.82 % (6104)------------------------------
% 2.28/1.82 % (6104)------------------------------
% 2.28/1.83 % (6193)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_5848 for (2996ds/1087Mi)
% 2.28/1.83 % (6196)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_5848 for (2996ds/44Mi)
% 2.28/1.83 % (6181)Instruction limit reached!
% 2.28/1.83 % (6181)------------------------------
% 2.28/1.83 % (6181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.83 % (6181)Termination reason: Unknown
% 2.28/1.83 % (6181)Termination phase: Saturation
% 2.28/1.83
% 2.28/1.83 % (6181)Memory used [KB]: 6908
% 2.28/1.83 % (6181)Time elapsed: 0.049 s
% 2.28/1.83 % (6181)Instructions burned: 149 (million)
% 2.28/1.83 % (6181)------------------------------
% 2.28/1.83 % (6181)------------------------------
% 2.28/1.84 % (6195)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_5848 for (2996ds/47Mi)
% 2.28/1.84 % (6202)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_5848 for (2996ds/432Mi)
% 2.28/1.84 % (6196)Instruction limit reached!
% 2.28/1.84 % (6196)------------------------------
% 2.28/1.84 % (6196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.84 % (6196)Termination reason: Unknown
% 2.28/1.84 % (6196)Termination phase: Property scanning
% 2.28/1.84
% 2.28/1.84 % (6196)Memory used [KB]: 1918
% 2.28/1.84 % (6196)Time elapsed: 0.013 s
% 2.28/1.84 % (6196)Instructions burned: 45 (million)
% 2.28/1.84 % (6196)------------------------------
% 2.28/1.84 % (6196)------------------------------
% 2.28/1.85 % (6210)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_5848 for (2996ds/62Mi)
% 2.28/1.86 % (6053)Instruction limit reached!
% 2.28/1.86 % (6053)------------------------------
% 2.28/1.86 % (6053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.86 % (6053)Termination reason: Unknown
% 2.28/1.86 % (6053)Termination phase: Saturation
% 2.28/1.86
% 2.28/1.86 % (6053)Memory used [KB]: 9594
% 2.28/1.86 % (6053)Time elapsed: 0.327 s
% 2.28/1.86 % (6053)Instructions burned: 1041 (million)
% 2.28/1.86 % (6053)------------------------------
% 2.28/1.86 % (6053)------------------------------
% 2.28/1.86 % (6195)Instruction limit reached!
% 2.28/1.86 % (6195)------------------------------
% 2.28/1.86 % (6195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.86 % (6195)Termination reason: Unknown
% 2.28/1.86 % (6195)Termination phase: Property scanning
% 2.28/1.86
% 2.28/1.86 % (6195)Memory used [KB]: 1791
% 2.28/1.86 % (6195)Time elapsed: 0.028 s
% 2.28/1.86 % (6195)Instructions burned: 48 (million)
% 2.28/1.86 % (6195)------------------------------
% 2.28/1.86 % (6195)------------------------------
% 2.28/1.87 % (6219)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_5848 for (2996ds/31Mi)
% 2.28/1.87 % (6168)Instruction limit reached!
% 2.28/1.87 % (6168)------------------------------
% 2.28/1.87 % (6168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.87 % (6168)Termination reason: Unknown
% 2.28/1.87 % (6168)Termination phase: Saturation
% 2.28/1.87
% 2.28/1.87 % (6168)Memory used [KB]: 7675
% 2.28/1.87 % (6168)Time elapsed: 0.132 s
% 2.28/1.87 % (6168)Instructions burned: 449 (million)
% 2.28/1.87 % (6168)------------------------------
% 2.28/1.87 % (6168)------------------------------
% 2.28/1.87 % (6210)Instruction limit reached!
% 2.28/1.87 % (6210)------------------------------
% 2.28/1.87 % (6210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.87 % (6210)Termination reason: Unknown
% 2.28/1.87 % (6210)Termination phase: Property scanning
% 2.28/1.87
% 2.28/1.87 % (6210)Memory used [KB]: 1918
% 2.28/1.87 % (6210)Time elapsed: 0.018 s
% 2.28/1.87 % (6210)Instructions burned: 65 (million)
% 2.28/1.87 % (6210)------------------------------
% 2.28/1.87 % (6210)------------------------------
% 2.28/1.87 % (6109)Refutation not found, non-redundant clauses discarded% (6109)------------------------------
% 2.28/1.87 % (6109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.87 % (6109)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.28/1.87
% 2.28/1.87 % (6109)Memory used [KB]: 7931
% 2.28/1.87 % (6109)Time elapsed: 0.300 s
% 2.28/1.87 % (6109)Instructions burned: 827 (million)
% 2.28/1.87 % (6109)------------------------------
% 2.28/1.87 % (6109)------------------------------
% 2.28/1.88 % (6219)Instruction limit reached!
% 2.28/1.88 % (6219)------------------------------
% 2.28/1.88 % (6219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.88 % (6219)Termination reason: Unknown
% 2.28/1.88 % (6219)Termination phase: shuffling
% 2.28/1.88
% 2.28/1.88 % (6219)Memory used [KB]: 1535
% 2.28/1.88 % (6219)Time elapsed: 0.011 s
% 2.28/1.88 % (6219)Instructions burned: 33 (million)
% 2.28/1.88 % (6219)------------------------------
% 2.28/1.88 % (6219)------------------------------
% 2.28/1.88 % (6229)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_5848 for (2996ds/453Mi)
% 2.28/1.88 % (6230)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_5848 for (2996ds/71Mi)
% 2.28/1.88 % (6233)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_5848 for (2996ds/83Mi)
% 2.28/1.88 % (6225)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_5848 for (2996ds/96Mi)
% 2.28/1.89 % (6236)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_5848 for (2996ds/11Mi)
% 2.28/1.89 % (6236)Instruction limit reached!
% 2.28/1.89 % (6236)------------------------------
% 2.28/1.89 % (6236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.89 % (6236)Termination reason: Unknown
% 2.28/1.89 % (6236)Termination phase: shuffling
% 2.28/1.89
% 2.28/1.89 % (6236)Memory used [KB]: 1407
% 2.28/1.89 % (6236)Time elapsed: 0.004 s
% 2.28/1.89 % (6236)Instructions burned: 11 (million)
% 2.28/1.89 % (6236)------------------------------
% 2.28/1.89 % (6236)------------------------------
% 2.28/1.90 % (6240)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_5848 for (2996ds/41Mi)
% 2.28/1.90 % (6230)Instruction limit reached!
% 2.28/1.90 % (6230)------------------------------
% 2.28/1.90 % (6230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.90 % (6230)Termination reason: Unknown
% 2.28/1.90 % (6230)Termination phase: Property scanning
% 2.28/1.90
% 2.28/1.90 % (6230)Memory used [KB]: 1918
% 2.28/1.90 % (6230)Time elapsed: 0.021 s
% 2.28/1.90 % (6230)Instructions burned: 72 (million)
% 2.28/1.90 % (6230)------------------------------
% 2.28/1.90 % (6230)------------------------------
% 2.28/1.91 % (6233)Instruction limit reached!
% 2.28/1.91 % (6233)------------------------------
% 2.28/1.91 % (6233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.91 % (6233)Termination reason: Unknown
% 2.28/1.91 % (6233)Termination phase: Saturation
% 2.28/1.91
% 2.28/1.91 % (6233)Memory used [KB]: 6396
% 2.28/1.91 % (6233)Time elapsed: 0.026 s
% 2.28/1.91 % (6233)Instructions burned: 85 (million)
% 2.28/1.91 % (6233)------------------------------
% 2.28/1.91 % (6233)------------------------------
% 2.28/1.91 % (6240)Instruction limit reached!
% 2.28/1.91 % (6240)------------------------------
% 2.28/1.91 % (6240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.91 % (6240)Termination reason: Unknown
% 2.28/1.91 % (6240)Termination phase: Property scanning
% 2.28/1.91
% 2.28/1.91 % (6240)Memory used [KB]: 1918
% 2.28/1.91 % (6240)Time elapsed: 0.012 s
% 2.28/1.91 % (6240)Instructions burned: 42 (million)
% 2.28/1.91 % (6240)------------------------------
% 2.28/1.91 % (6240)------------------------------
% 2.28/1.91 % (6244)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5848 for (2995ds/6Mi)
% 2.28/1.91 % (6244)Instruction limit reached!
% 2.28/1.91 % (6244)------------------------------
% 2.28/1.91 % (6244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.91 % (6244)Termination reason: Unknown
% 2.28/1.91 % (6244)Termination phase: shuffling
% 2.28/1.91
% 2.28/1.91 % (6244)Memory used [KB]: 1279
% 2.28/1.91 % (6244)Time elapsed: 0.004 s
% 2.28/1.91 % (6244)Instructions burned: 8 (million)
% 2.28/1.91 % (6244)------------------------------
% 2.28/1.91 % (6244)------------------------------
% 2.28/1.92 % (6245)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_5848 for (2995ds/150Mi)
% 2.28/1.92 % (6246)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_5848 for (2995ds/343Mi)
% 2.28/1.92 % (6247)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_5848 for (2995ds/109Mi)
% 2.28/1.93 % (6225)Instruction limit reached!
% 2.28/1.93 % (6225)------------------------------
% 2.28/1.93 % (6225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.93 % (6225)Termination reason: Unknown
% 2.28/1.93 % (6225)Termination phase: Saturation
% 2.28/1.93
% 2.28/1.93 % (6225)Memory used [KB]: 6396
% 2.28/1.93 % (6225)Time elapsed: 0.048 s
% 2.28/1.93 % (6225)Instructions burned: 96 (million)
% 2.28/1.93 % (6225)------------------------------
% 2.28/1.93 % (6225)------------------------------
% 2.28/1.94 % (6248)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_5848 for (2995ds/253Mi)
% 2.28/1.95 % (6247)Instruction limit reached!
% 2.28/1.95 % (6247)------------------------------
% 2.28/1.95 % (6247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.95 % (6247)Termination reason: Unknown
% 2.28/1.95 % (6247)Termination phase: Saturation
% 2.28/1.95
% 2.28/1.95 % (6247)Memory used [KB]: 6524
% 2.28/1.95 % (6247)Time elapsed: 0.032 s
% 2.28/1.95 % (6247)Instructions burned: 111 (million)
% 2.28/1.95 % (6247)------------------------------
% 2.28/1.95 % (6247)------------------------------
% 2.28/1.96 % (6245)Instruction limit reached!
% 2.28/1.96 % (6245)------------------------------
% 2.28/1.96 % (6245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.96 % (6245)Termination reason: Unknown
% 2.28/1.96 % (6245)Termination phase: Saturation
% 2.28/1.96
% 2.28/1.96 % (6245)Memory used [KB]: 6908
% 2.28/1.96 % (6245)Time elapsed: 0.045 s
% 2.28/1.96 % (6245)Instructions burned: 151 (million)
% 2.28/1.96 % (6245)------------------------------
% 2.28/1.96 % (6245)------------------------------
% 2.28/1.96 % (6249)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_5848 for (2995ds/140Mi)
% 2.28/1.97 % (6250)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_5848 for (2995ds/614Mi)
% 2.28/1.98 % (6202)Instruction limit reached!
% 2.28/1.98 % (6202)------------------------------
% 2.28/1.98 % (6202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.98 % (6202)Termination reason: Unknown
% 2.28/1.98 % (6202)Termination phase: Saturation
% 2.28/1.98
% 2.28/1.98 % (6202)Memory used [KB]: 4093
% 2.28/1.98 % (6202)Time elapsed: 0.140 s
% 2.28/1.98 % (6202)Instructions burned: 432 (million)
% 2.28/1.98 % (6202)------------------------------
% 2.28/1.98 % (6202)------------------------------
% 2.28/1.99 % (6251)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_5848 for (2995ds/202Mi)
% 2.28/2.00 % (6249)Instruction limit reached!
% 2.28/2.00 % (6249)------------------------------
% 2.28/2.00 % (6249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/2.00 % (6249)Termination reason: Unknown
% 2.28/2.00 % (6249)Termination phase: Saturation
% 2.28/2.00
% 2.28/2.00 % (6249)Memory used [KB]: 6524
% 2.28/2.00 % (6249)Time elapsed: 0.043 s
% 2.28/2.00 % (6249)Instructions burned: 141 (million)
% 2.28/2.00 % (6249)------------------------------
% 2.28/2.00 % (6249)------------------------------
% 2.28/2.01 % (6251)Refutation not found, incomplete strategy
% 2.28/2.01 % (6251)------------------------------
% 2.28/2.01 % (6251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/2.01 % (6251)Termination reason: Refutation not found, incomplete strategy
% 2.28/2.01
% 2.28/2.01
% 2.28/2.01 % (6251)Memory used [KB]: 6140
% 2.28/2.01 % (6251)Time elapsed: 0.039 s
% 2.28/2.01 % (6251)Instructions burned: 45 (million)
% 2.28/2.01 % (6251)------------------------------
% 2.28/2.01 % (6251)------------------------------
% 2.28/2.01 % (6229)Instruction limit reached!
% 2.28/2.01 % (6229)------------------------------
% 2.28/2.01 % (6229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/2.01 % (6229)Termination reason: Unknown
% 2.28/2.01 % (6229)Termination phase: Saturation
% 2.28/2.01
% 2.28/2.01 % (6229)Memory used [KB]: 7419
% 2.28/2.01 % (6229)Time elapsed: 0.134 s
% 2.28/2.01 % (6229)Instructions burned: 454 (million)
% 2.28/2.01 % (6229)------------------------------
% 2.28/2.01 % (6229)------------------------------
% 5.82/2.01 % (6252)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_5848 for (2994ds/339Mi)
% 5.82/2.02 % (6253)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_5848 for (2994ds/283Mi)
% 5.82/2.02 % (6254)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_5848 for (2994ds/134Mi)
% 5.82/2.02 % (6248)Instruction limit reached!
% 5.82/2.02 % (6248)------------------------------
% 5.82/2.02 % (6248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.02 % (6248)Termination reason: Unknown
% 5.82/2.02 % (6248)Termination phase: Saturation
% 5.82/2.02
% 5.82/2.02 % (6248)Memory used [KB]: 6780
% 5.82/2.02 % (6248)Time elapsed: 0.085 s
% 5.82/2.02 % (6248)Instructions burned: 255 (million)
% 5.82/2.02 % (6248)------------------------------
% 5.82/2.02 % (6248)------------------------------
% 5.82/2.03 % (6246)Instruction limit reached!
% 5.82/2.03 % (6246)------------------------------
% 5.82/2.03 % (6246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.03 % (6246)Termination reason: Unknown
% 5.82/2.03 % (6246)Termination phase: Saturation
% 5.82/2.03
% 5.82/2.03 % (6246)Memory used [KB]: 7036
% 5.82/2.03 % (6246)Time elapsed: 0.108 s
% 5.82/2.03 % (6246)Instructions burned: 345 (million)
% 5.82/2.03 % (6246)------------------------------
% 5.82/2.03 % (6246)------------------------------
% 5.82/2.03 % (6255)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_5848 for (2994ds/298Mi)
% 5.82/2.03 % (6256)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_5848 for (2994ds/192Mi)
% 5.82/2.06 % (6254)Instruction limit reached!
% 5.82/2.06 % (6254)------------------------------
% 5.82/2.06 % (6254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.06 % (6254)Termination reason: Unknown
% 5.82/2.06 % (6254)Termination phase: Saturation
% 5.82/2.06
% 5.82/2.06 % (6254)Memory used [KB]: 6780
% 5.82/2.06 % (6254)Time elapsed: 0.039 s
% 5.82/2.06 % (6254)Instructions burned: 135 (million)
% 5.82/2.06 % (6254)------------------------------
% 5.82/2.06 % (6254)------------------------------
% 5.82/2.07 % (6257)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_5848 for (2994ds/258Mi)
% 5.82/2.09 % (6256)Instruction limit reached!
% 5.82/2.09 % (6256)------------------------------
% 5.82/2.09 % (6256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.09 % (6256)Termination reason: Unknown
% 5.82/2.09 % (6256)Termination phase: Saturation
% 5.82/2.09
% 5.82/2.09 % (6256)Memory used [KB]: 7547
% 5.82/2.09 % (6256)Time elapsed: 0.056 s
% 5.82/2.09 % (6256)Instructions burned: 193 (million)
% 5.82/2.09 % (6256)------------------------------
% 5.82/2.09 % (6256)------------------------------
% 5.82/2.10 % (6257)Refutation not found, incomplete strategy
% 5.82/2.10 % (6257)------------------------------
% 5.82/2.10 % (6257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.10 % (6257)Termination reason: Refutation not found, incomplete strategy
% 5.82/2.10
% 5.82/2.10
% 5.82/2.10 % (6257)Memory used [KB]: 6652
% 5.82/2.10 % (6257)Time elapsed: 0.030 s
% 5.82/2.10 % (6257)Instructions burned: 102 (million)
% 5.82/2.10 % (6257)------------------------------
% 5.82/2.10 % (6257)------------------------------
% 5.82/2.10 % (6258)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_5848 for (2993ds/90Mi)
% 5.82/2.10 % (6253)Instruction limit reached!
% 5.82/2.10 % (6253)------------------------------
% 5.82/2.10 % (6253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.10 % (6253)Termination reason: Unknown
% 5.82/2.10 % (6253)Termination phase: Saturation
% 5.82/2.10
% 5.82/2.10 % (6253)Memory used [KB]: 7291
% 5.82/2.10 % (6253)Time elapsed: 0.082 s
% 5.82/2.10 % (6253)Instructions burned: 283 (million)
% 5.82/2.10 % (6253)------------------------------
% 5.82/2.10 % (6253)------------------------------
% 5.82/2.11 % (6259)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_5848 for (2993ds/231Mi)
% 5.82/2.11 % (6260)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_5848 for (2993ds/458Mi)
% 5.82/2.11 % (6252)Instruction limit reached!
% 5.82/2.11 % (6252)------------------------------
% 5.82/2.11 % (6252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.11 % (6252)Termination reason: Unknown
% 5.82/2.11 % (6252)Termination phase: Saturation
% 5.82/2.11
% 5.82/2.11 % (6252)Memory used [KB]: 7803
% 5.82/2.11 % (6252)Time elapsed: 0.099 s
% 5.82/2.11 % (6252)Instructions burned: 341 (million)
% 5.82/2.11 % (6252)------------------------------
% 5.82/2.11 % (6252)------------------------------
% 6.42/2.12 % (6255)Instruction limit reached!
% 6.42/2.12 % (6255)------------------------------
% 6.42/2.12 % (6255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.12 % (6255)Termination reason: Unknown
% 6.42/2.12 % (6255)Termination phase: Saturation
% 6.42/2.12
% 6.42/2.12 % (6255)Memory used [KB]: 7675
% 6.42/2.12 % (6255)Time elapsed: 0.088 s
% 6.42/2.12 % (6255)Instructions burned: 301 (million)
% 6.42/2.12 % (6255)------------------------------
% 6.42/2.12 % (6255)------------------------------
% 6.42/2.12 % (6261)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_5848 for (2993ds/31Mi)
% 6.42/2.12 % (6258)Instruction limit reached!
% 6.42/2.12 % (6258)------------------------------
% 6.42/2.12 % (6258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.12 % (6258)Termination reason: Unknown
% 6.42/2.12 % (6258)Termination phase: Saturation
% 6.42/2.12
% 6.42/2.13 % (6258)Memory used [KB]: 6524
% 6.42/2.13 % (6258)Time elapsed: 0.027 s
% 6.42/2.13 % (6258)Instructions burned: 92 (million)
% 6.42/2.13 % (6258)------------------------------
% 6.42/2.13 % (6258)------------------------------
% 6.42/2.13 % (6262)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_5848 for (2993ds/297Mi)
% 6.42/2.13 % (6261)Instruction limit reached!
% 6.42/2.13 % (6261)------------------------------
% 6.42/2.13 % (6261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.13 % (6261)Termination reason: Unknown
% 6.42/2.13 % (6261)Termination phase: shuffling
% 6.42/2.13
% 6.42/2.13 % (6261)Memory used [KB]: 1535
% 6.42/2.13 % (6261)Time elapsed: 0.011 s
% 6.42/2.13 % (6261)Instructions burned: 33 (million)
% 6.42/2.13 % (6261)------------------------------
% 6.42/2.13 % (6261)------------------------------
% 6.42/2.13 % (6263)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_5848 for (2993ds/987Mi)
% 6.42/2.14 % (6264)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_5848 for (2993ds/182Mi)
% 6.42/2.15 % (6250)Instruction limit reached!
% 6.42/2.15 % (6250)------------------------------
% 6.42/2.15 % (6250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.15 % (6250)Termination reason: Unknown
% 6.42/2.15 % (6250)Termination phase: Saturation
% 6.42/2.15
% 6.42/2.15 % (6250)Memory used [KB]: 8699
% 6.42/2.15 % (6250)Time elapsed: 0.185 s
% 6.42/2.15 % (6250)Instructions burned: 614 (million)
% 6.42/2.15 % (6250)------------------------------
% 6.42/2.15 % (6250)------------------------------
% 6.42/2.16 % (6265)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_5848 for (2993ds/182Mi)
% 6.42/2.17 % (6259)Instruction limit reached!
% 6.42/2.17 % (6259)------------------------------
% 6.42/2.17 % (6259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.17 % (6259)Termination reason: Unknown
% 6.42/2.17 % (6259)Termination phase: Saturation
% 6.42/2.17
% 6.42/2.17 % (6259)Memory used [KB]: 6780
% 6.42/2.17 % (6259)Time elapsed: 0.060 s
% 6.42/2.17 % (6259)Instructions burned: 231 (million)
% 6.42/2.17 % (6259)------------------------------
% 6.42/2.17 % (6259)------------------------------
% 6.42/2.17 % (6193)Instruction limit reached!
% 6.42/2.17 % (6193)------------------------------
% 6.42/2.17 % (6193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.17 % (6193)Termination reason: Unknown
% 6.42/2.17 % (6193)Termination phase: Saturation
% 6.42/2.17
% 6.42/2.17 % (6193)Memory used [KB]: 7931
% 6.42/2.17 % (6193)Time elapsed: 0.350 s
% 6.42/2.17 % (6193)Instructions burned: 1089 (million)
% 6.42/2.17 % (6193)------------------------------
% 6.42/2.17 % (6193)------------------------------
% 6.42/2.18 % (6266)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_5848 for (2993ds/154Mi)
% 6.42/2.18 % (6267)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_5848 for (2993ds/79Mi)
% 6.42/2.19 % (6264)Instruction limit reached!
% 6.42/2.19 % (6264)------------------------------
% 6.42/2.19 % (6264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.19 % (6264)Termination reason: Unknown
% 6.42/2.19 % (6264)Termination phase: Saturation
% 6.42/2.19
% 6.42/2.19 % (6264)Memory used [KB]: 6908
% 6.42/2.19 % (6264)Time elapsed: 0.053 s
% 6.42/2.19 % (6264)Instructions burned: 182 (million)
% 6.42/2.19 % (6264)------------------------------
% 6.42/2.19 % (6264)------------------------------
% 6.81/2.20 % (6268)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_5848 for (2992ds/216Mi)
% 6.81/2.21 % (6267)Instruction limit reached!
% 6.81/2.21 % (6267)------------------------------
% 6.81/2.21 % (6267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.21 % (6267)Termination reason: Unknown
% 6.81/2.21 % (6267)Termination phase: Saturation
% 6.81/2.21
% 6.81/2.21 % (6267)Memory used [KB]: 6396
% 6.81/2.21 % (6267)Time elapsed: 0.023 s
% 6.81/2.21 % (6267)Instructions burned: 81 (million)
% 6.81/2.21 % (6267)------------------------------
% 6.81/2.21 % (6267)------------------------------
% 6.81/2.21 % (6262)Instruction limit reached!
% 6.81/2.21 % (6262)------------------------------
% 6.81/2.21 % (6262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.21 % (6262)Termination reason: Unknown
% 6.81/2.21 % (6262)Termination phase: Saturation
% 6.81/2.21
% 6.81/2.21 % (6262)Memory used [KB]: 7291
% 6.81/2.21 % (6262)Time elapsed: 0.087 s
% 6.81/2.21 % (6262)Instructions burned: 297 (million)
% 6.81/2.21 % (6262)------------------------------
% 6.81/2.21 % (6262)------------------------------
% 6.81/2.22 % (6266)Refutation not found, incomplete strategy
% 6.81/2.22 % (6266)------------------------------
% 6.81/2.22 % (6266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.22 % (6266)Termination reason: Refutation not found, incomplete strategy
% 6.81/2.22
% 6.81/2.22
% 6.81/2.22 % (6266)Memory used [KB]: 6908
% 6.81/2.22 % (6266)Time elapsed: 0.040 s
% 6.81/2.22 % (6266)Instructions burned: 145 (million)
% 6.81/2.22 % (6266)------------------------------
% 6.81/2.22 % (6266)------------------------------
% 6.81/2.22 % (6269)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_5848 for (2992ds/114Mi)
% 6.81/2.22 % (6265)Instruction limit reached!
% 6.81/2.22 % (6265)------------------------------
% 6.81/2.22 % (6265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.22 % (6265)Termination reason: Unknown
% 6.81/2.22 % (6265)Termination phase: Saturation
% 6.81/2.22
% 6.81/2.22 % (6265)Memory used [KB]: 6780
% 6.81/2.22 % (6265)Time elapsed: 0.057 s
% 6.81/2.22 % (6265)Instructions burned: 183 (million)
% 6.81/2.22 % (6265)------------------------------
% 6.81/2.22 % (6265)------------------------------
% 6.81/2.22 % (6270)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_5848 for (2992ds/922Mi)
% 6.81/2.22 % (6271)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_5848 for (2992ds/182Mi)
% 6.81/2.23 % (6272)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_5848 for (2992ds/164Mi)
% 6.81/2.25 % (6269)Instruction limit reached!
% 6.81/2.25 % (6269)------------------------------
% 6.81/2.25 % (6269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.25 % (6269)Termination reason: Unknown
% 6.81/2.25 % (6269)Termination phase: Saturation
% 6.81/2.25
% 6.81/2.25 % (6269)Memory used [KB]: 6780
% 6.81/2.25 % (6269)Time elapsed: 0.033 s
% 6.81/2.25 % (6269)Instructions burned: 115 (million)
% 6.81/2.25 % (6269)------------------------------
% 6.81/2.25 % (6269)------------------------------
% 6.81/2.25 % (6260)Instruction limit reached!
% 6.81/2.25 % (6260)------------------------------
% 6.81/2.25 % (6260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.25 % (6260)Termination reason: Unknown
% 6.81/2.25 % (6260)Termination phase: Saturation
% 6.81/2.25
% 6.81/2.25 % (6260)Memory used [KB]: 7803
% 6.81/2.25 % (6260)Time elapsed: 0.139 s
% 6.81/2.25 % (6260)Instructions burned: 458 (million)
% 6.81/2.25 % (6260)------------------------------
% 6.81/2.25 % (6260)------------------------------
% 6.81/2.26 % (6273)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_5848 for (2992ds/50Mi)
% 6.81/2.26 % (6274)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_5848 for (2992ds/368Mi)
% 6.81/2.26 % (6268)Instruction limit reached!
% 6.81/2.26 % (6268)------------------------------
% 6.81/2.26 % (6268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.26 % (6268)Termination reason: Unknown
% 6.81/2.26 % (6268)Termination phase: Saturation
% 6.81/2.26
% 6.81/2.26 % (6268)Memory used [KB]: 7036
% 6.81/2.26 % (6268)Time elapsed: 0.059 s
% 6.81/2.26 % (6268)Instructions burned: 217 (million)
% 6.81/2.26 % (6268)------------------------------
% 6.81/2.26 % (6268)------------------------------
% 6.81/2.27 % (6275)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_5848 for (2992ds/1021Mi)
% 6.81/2.27 % (6273)Instruction limit reached!
% 6.81/2.27 % (6273)------------------------------
% 6.81/2.27 % (6273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.27 % (6273)Termination reason: Unknown
% 6.81/2.27 % (6273)Termination phase: Property scanning
% 6.81/2.27
% 6.81/2.27 % (6273)Memory used [KB]: 1918
% 6.81/2.27 % (6273)Time elapsed: 0.014 s
% 6.81/2.27 % (6273)Instructions burned: 51 (million)
% 6.81/2.27 % (6273)------------------------------
% 6.81/2.27 % (6273)------------------------------
% 6.81/2.27 % (6272)Instruction limit reached!
% 6.81/2.27 % (6272)------------------------------
% 6.81/2.27 % (6272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.27 % (6272)Termination reason: Unknown
% 6.81/2.27 % (6272)Termination phase: Saturation
% 6.81/2.27
% 6.81/2.27 % (6272)Memory used [KB]: 2174
% 6.81/2.27 % (6272)Time elapsed: 0.045 s
% 6.81/2.27 % (6272)Instructions burned: 166 (million)
% 6.81/2.27 % (6272)------------------------------
% 6.81/2.27 % (6272)------------------------------
% 6.81/2.27 % (6271)Instruction limit reached!
% 6.81/2.27 % (6271)------------------------------
% 6.81/2.27 % (6271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.27 % (6271)Termination reason: Unknown
% 6.81/2.27 % (6271)Termination phase: Saturation
% 6.81/2.27
% 6.81/2.27 % (6271)Memory used [KB]: 6908
% 6.81/2.27 % (6271)Time elapsed: 0.049 s
% 6.81/2.27 % (6271)Instructions burned: 182 (million)
% 6.81/2.27 % (6271)------------------------------
% 6.81/2.27 % (6271)------------------------------
% 6.81/2.28 % (6276)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_5848 for (2992ds/267Mi)
% 6.81/2.28 % (6277)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_5848 for (2992ds/204Mi)
% 6.81/2.28 % (6278)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_5848 for (2992ds/26Mi)
% 6.81/2.29 % (6278)Instruction limit reached!
% 6.81/2.29 % (6278)------------------------------
% 6.81/2.29 % (6278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.29 % (6278)Termination reason: Unknown
% 6.81/2.29 % (6278)Termination phase: shuffling
% 6.81/2.29
% 6.81/2.29 % (6278)Memory used [KB]: 1663
% 6.81/2.29 % (6278)Time elapsed: 0.008 s
% 6.81/2.29 % (6278)Instructions burned: 27 (million)
% 6.81/2.29 % (6278)------------------------------
% 6.81/2.29 % (6278)------------------------------
% 7.47/2.30 % (6279)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_5848 for (2992ds/53Mi)
% 7.47/2.31 % (6279)Instruction limit reached!
% 7.47/2.31 % (6279)------------------------------
% 7.47/2.31 % (6279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.31 % (6279)Termination reason: Unknown
% 7.47/2.31 % (6279)Termination phase: Property scanning
% 7.47/2.31
% 7.47/2.31 % (6279)Memory used [KB]: 1918
% 7.47/2.31 % (6279)Time elapsed: 0.015 s
% 7.47/2.31 % (6279)Instructions burned: 55 (million)
% 7.47/2.31 % (6279)------------------------------
% 7.47/2.31 % (6279)------------------------------
% 7.47/2.32 % (6280)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_5848 for (2991ds/4436Mi)
% 7.47/2.34 % (6277)Instruction limit reached!
% 7.47/2.34 % (6277)------------------------------
% 7.47/2.34 % (6277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.34 % (6277)Termination reason: Unknown
% 7.47/2.34 % (6277)Termination phase: Saturation
% 7.47/2.34
% 7.47/2.34 % (6277)Memory used [KB]: 7036
% 7.47/2.34 % (6277)Time elapsed: 0.064 s
% 7.47/2.34 % (6277)Instructions burned: 206 (million)
% 7.47/2.34 % (6277)------------------------------
% 7.47/2.34 % (6277)------------------------------
% 7.47/2.35 % (6281)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_5848 for (2991ds/1539Mi)
% 7.47/2.36 % (6276)Instruction limit reached!
% 7.47/2.36 % (6276)------------------------------
% 7.47/2.36 % (6276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.36 % (6276)Termination reason: Unknown
% 7.47/2.36 % (6276)Termination phase: Saturation
% 7.47/2.36
% 7.47/2.36 % (6276)Memory used [KB]: 7164
% 7.47/2.36 % (6276)Time elapsed: 0.080 s
% 7.47/2.36 % (6276)Instructions burned: 269 (million)
% 7.47/2.36 % (6276)------------------------------
% 7.47/2.36 % (6276)------------------------------
% 7.47/2.37 % (6282)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_5848 for (2991ds/408Mi)
% 7.47/2.37 % (6274)Instruction limit reached!
% 7.47/2.37 % (6274)------------------------------
% 7.47/2.37 % (6274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.37 % (6274)Termination reason: Unknown
% 7.47/2.37 % (6274)Termination phase: Saturation
% 7.47/2.37
% 7.47/2.37 % (6274)Memory used [KB]: 7931
% 7.47/2.37 % (6274)Time elapsed: 0.115 s
% 7.47/2.37 % (6274)Instructions burned: 370 (million)
% 7.47/2.37 % (6274)------------------------------
% 7.47/2.37 % (6274)------------------------------
% 7.47/2.38 % (6283)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_5848 for (2991ds/5205Mi)
% 7.79/2.43 % (6263)Instruction limit reached!
% 7.79/2.43 % (6263)------------------------------
% 7.79/2.43 % (6263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.43 % (6263)Termination reason: Unknown
% 7.79/2.43 % (6263)Termination phase: Saturation
% 7.79/2.43
% 7.79/2.43 % (6263)Memory used [KB]: 8315
% 7.79/2.43 % (6263)Time elapsed: 0.299 s
% 7.79/2.43 % (6263)Instructions burned: 987 (million)
% 7.79/2.43 % (6263)------------------------------
% 7.79/2.43 % (6263)------------------------------
% 7.79/2.44 % (6284)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_5848 for (2990ds/1913Mi)
% 7.79/2.49 % (6282)Instruction limit reached!
% 7.79/2.49 % (6282)------------------------------
% 7.79/2.49 % (6282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.49 % (6282)Termination reason: Unknown
% 7.79/2.49 % (6282)Termination phase: Saturation
% 7.79/2.49
% 7.79/2.49 % (6282)Memory used [KB]: 7419
% 7.79/2.49 % (6282)Time elapsed: 0.124 s
% 7.79/2.49 % (6282)Instructions burned: 408 (million)
% 7.79/2.49 % (6282)------------------------------
% 7.79/2.49 % (6282)------------------------------
% 8.23/2.50 % (6285)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_5848 for (2990ds/4350Mi)
% 8.23/2.51 % (6270)Instruction limit reached!
% 8.23/2.51 % (6270)------------------------------
% 8.23/2.51 % (6270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.51 % (6270)Termination reason: Unknown
% 8.23/2.51 % (6270)Termination phase: Saturation
% 8.23/2.51
% 8.23/2.51 % (6270)Memory used [KB]: 7419
% 8.23/2.51 % (6270)Time elapsed: 0.287 s
% 8.23/2.51 % (6270)Instructions burned: 925 (million)
% 8.23/2.51 % (6270)------------------------------
% 8.23/2.51 % (6270)------------------------------
% 8.23/2.51 % (6285)Refutation not found, incomplete strategy
% 8.23/2.51 % (6285)------------------------------
% 8.23/2.51 % (6285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.51 % (6285)Termination reason: Refutation not found, incomplete strategy
% 8.23/2.51
% 8.23/2.51
% 8.23/2.51 % (6285)Memory used [KB]: 6012
% 8.23/2.51 % (6285)Time elapsed: 0.012 s
% 8.23/2.51 % (6285)Instructions burned: 34 (million)
% 8.23/2.51 % (6285)------------------------------
% 8.23/2.51 % (6285)------------------------------
% 8.23/2.52 % (6286)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=68:si=on:rtra=on_0 on DTF2THF_5848 for (2989ds/68Mi)
% 8.23/2.52 % (6287)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_5848 for (2989ds/358Mi)
% 8.23/2.54 % (6286)Instruction limit reached!
% 8.23/2.54 % (6286)------------------------------
% 8.23/2.54 % (6286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.54 % (6286)Termination reason: Unknown
% 8.23/2.54 % (6286)Termination phase: Property scanning
% 8.23/2.54
% 8.23/2.54 % (6286)Memory used [KB]: 1791
% 8.23/2.54 % (6286)Time elapsed: 0.020 s
% 8.23/2.54 % (6286)Instructions burned: 69 (million)
% 8.23/2.54 % (6286)------------------------------
% 8.23/2.54 % (6286)------------------------------
% 8.23/2.55 % (6288)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_5848 for (2989ds/31Mi)
% 8.23/2.56 % (6288)Instruction limit reached!
% 8.23/2.56 % (6288)------------------------------
% 8.23/2.56 % (6288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.56 % (6288)Termination reason: Unknown
% 8.23/2.56 % (6288)Termination phase: Preprocessing 1
% 8.23/2.56
% 8.23/2.56 % (6288)Memory used [KB]: 1535
% 8.23/2.56 % (6288)Time elapsed: 0.010 s
% 8.23/2.56 % (6288)Instructions burned: 31 (million)
% 8.23/2.56 % (6288)------------------------------
% 8.23/2.56 % (6288)------------------------------
% 8.23/2.57 % (6289)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_5848 for (2989ds/279Mi)
% 8.23/2.58 % (6275)Instruction limit reached!
% 8.23/2.58 % (6275)------------------------------
% 8.23/2.58 % (6275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.58 % (6275)Termination reason: Unknown
% 8.23/2.58 % (6275)Termination phase: Saturation
% 8.23/2.58
% 8.23/2.58 % (6275)Memory used [KB]: 8315
% 8.23/2.58 % (6275)Time elapsed: 0.312 s
% 8.23/2.58 % (6275)Instructions burned: 1023 (million)
% 8.23/2.58 % (6275)------------------------------
% 8.23/2.58 % (6275)------------------------------
% 8.23/2.59 % (6290)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_5848 for (2988ds/258Mi)
% 8.91/2.60 % (6289)Refutation not found, incomplete strategy
% 8.91/2.60 % (6289)------------------------------
% 8.91/2.60 % (6289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.91/2.60 % (6289)Termination reason: Refutation not found, incomplete strategy
% 8.91/2.60
% 8.91/2.60
% 8.91/2.60 % (6289)Memory used [KB]: 6652
% 8.91/2.60 % (6289)Time elapsed: 0.031 s
% 8.91/2.60 % (6289)Instructions burned: 116 (million)
% 8.91/2.60 % (6289)------------------------------
% 8.91/2.60 % (6289)------------------------------
% 8.91/2.61 % (6291)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_5848 for (2988ds/26Mi)
% 8.91/2.61 % (6291)Instruction limit reached!
% 8.91/2.61 % (6291)------------------------------
% 8.91/2.61 % (6291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.91/2.61 % (6291)Termination reason: Unknown
% 8.91/2.61 % (6291)Termination phase: shuffling
% 8.91/2.61
% 8.91/2.61 % (6291)Memory used [KB]: 1663
% 8.91/2.61 % (6291)Time elapsed: 0.008 s
% 8.91/2.61 % (6291)Instructions burned: 27 (million)
% 8.91/2.61 % (6291)------------------------------
% 8.91/2.61 % (6291)------------------------------
% 8.91/2.62 % (6292)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_5848 for (2988ds/995Mi)
% 8.91/2.63 % (6287)Instruction limit reached!
% 8.91/2.63 % (6287)------------------------------
% 8.91/2.63 % (6287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.91/2.63 % (6287)Termination reason: Unknown
% 8.91/2.63 % (6287)Termination phase: Saturation
% 8.91/2.63
% 8.91/2.63 % (6287)Memory used [KB]: 7164
% 8.91/2.63 % (6287)Time elapsed: 0.133 s
% 8.91/2.63 % (6287)Instructions burned: 358 (million)
% 8.91/2.63 % (6287)------------------------------
% 8.91/2.63 % (6287)------------------------------
% 8.91/2.64 % (6293)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_5848 for (2988ds/373Mi)
% 8.91/2.67 % (6290)Instruction limit reached!
% 8.91/2.67 % (6290)------------------------------
% 8.91/2.67 % (6290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.91/2.67 % (6290)Termination reason: Unknown
% 8.91/2.67 % (6290)Termination phase: Saturation
% 8.91/2.67
% 8.91/2.67 % (6290)Memory used [KB]: 7036
% 8.91/2.67 % (6290)Time elapsed: 0.080 s
% 8.91/2.67 % (6290)Instructions burned: 258 (million)
% 8.91/2.67 % (6290)------------------------------
% 8.91/2.67 % (6290)------------------------------
% 8.91/2.68 % (6294)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_5848 for (2988ds/253Mi)
% 9.18/2.75 % (6294)Instruction limit reached!
% 9.18/2.75 % (6294)------------------------------
% 9.18/2.75 % (6294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.75 % (6294)Termination reason: Unknown
% 9.18/2.75 % (6294)Termination phase: Saturation
% 9.18/2.75
% 9.18/2.75 % (6294)Memory used [KB]: 7419
% 9.18/2.75 % (6294)Time elapsed: 0.071 s
% 9.18/2.75 % (6294)Instructions burned: 254 (million)
% 9.18/2.75 % (6294)------------------------------
% 9.18/2.75 % (6294)------------------------------
% 9.18/2.75 % (6293)Instruction limit reached!
% 9.18/2.75 % (6293)------------------------------
% 9.18/2.75 % (6293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.75 % (6293)Termination reason: Unknown
% 9.18/2.75 % (6293)Termination phase: Saturation
% 9.18/2.75
% 9.18/2.75 % (6293)Memory used [KB]: 7803
% 9.18/2.75 % (6293)Time elapsed: 0.112 s
% 9.18/2.75 % (6293)Instructions burned: 373 (million)
% 9.18/2.75 % (6293)------------------------------
% 9.18/2.75 % (6293)------------------------------
% 9.18/2.76 % (6295)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_5848 for (2987ds/832Mi)
% 9.18/2.76 % (6296)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_5848 for (2987ds/668Mi)
% 9.18/2.79 % (6295)Refutation not found, incomplete strategy
% 9.18/2.79 % (6295)------------------------------
% 9.18/2.79 % (6295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.79 % (6295)Termination reason: Refutation not found, incomplete strategy
% 9.18/2.79
% 9.18/2.79
% 9.18/2.79 % (6295)Memory used [KB]: 6780
% 9.18/2.79 % (6295)Time elapsed: 0.030 s
% 9.18/2.79 % (6295)Instructions burned: 101 (million)
% 9.18/2.79 % (6295)------------------------------
% 9.18/2.79 % (6295)------------------------------
% 9.42/2.80 % (6297)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=40:si=on:rtra=on_0 on DTF2THF_5848 for (2986ds/40Mi)
% 9.42/2.81 % (6297)Instruction limit reached!
% 9.42/2.81 % (6297)------------------------------
% 9.42/2.81 % (6297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.81 % (6297)Termination reason: Unknown
% 9.42/2.81 % (6297)Termination phase: Property scanning
% 9.42/2.81
% 9.42/2.81 % (6297)Memory used [KB]: 1918
% 9.42/2.81 % (6297)Time elapsed: 0.012 s
% 9.42/2.81 % (6297)Instructions burned: 43 (million)
% 9.42/2.81 % (6297)------------------------------
% 9.42/2.81 % (6297)------------------------------
% 9.42/2.82 % (6298)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_5848 for (2986ds/294Mi)
% 9.42/2.83 % (6281)Instruction limit reached!
% 9.42/2.83 % (6281)------------------------------
% 9.42/2.83 % (6281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.83 % (6281)Termination reason: Unknown
% 9.42/2.83 % (6281)Termination phase: Saturation
% 9.42/2.83
% 9.42/2.83 % (6281)Memory used [KB]: 9722
% 9.42/2.83 % (6281)Time elapsed: 0.475 s
% 9.42/2.83 % (6281)Instructions burned: 1539 (million)
% 9.42/2.83 % (6281)------------------------------
% 9.42/2.83 % (6281)------------------------------
% 9.42/2.84 % (6298)Refutation not found, incomplete strategy
% 9.42/2.84 % (6298)------------------------------
% 9.42/2.84 % (6298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.84 % (6298)Termination reason: Refutation not found, incomplete strategy
% 9.42/2.84
% 9.42/2.84
% 9.42/2.84 % (6298)Memory used [KB]: 6524
% 9.42/2.84 % (6298)Time elapsed: 0.021 s
% 9.42/2.84 % (6298)Instructions burned: 77 (million)
% 9.42/2.84 % (6298)------------------------------
% 9.42/2.84 % (6298)------------------------------
% 9.42/2.84 % (6299)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_5848 for (2986ds/187Mi)
% 9.42/2.85 % (6300)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_5848 for (2986ds/371Mi)
% 9.42/2.89 % (6299)Instruction limit reached!
% 9.42/2.89 % (6299)------------------------------
% 9.42/2.89 % (6299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.89 % (6299)Termination reason: Unknown
% 9.42/2.89 % (6299)Termination phase: Saturation
% 9.42/2.89
% 9.42/2.89 % (6299)Memory used [KB]: 7164
% 9.42/2.89 % (6299)Time elapsed: 0.056 s
% 9.42/2.89 % (6299)Instructions burned: 188 (million)
% 9.42/2.89 % (6299)------------------------------
% 9.42/2.89 % (6299)------------------------------
% 10.01/2.90 % (6301)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_5848 for (2985ds/1827Mi)
% 10.01/2.92 % (6292)Instruction limit reached!
% 10.01/2.92 % (6292)------------------------------
% 10.01/2.92 % (6292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.01/2.92 % (6292)Termination reason: Unknown
% 10.01/2.92 % (6292)Termination phase: Saturation
% 10.01/2.92
% 10.01/2.92 % (6292)Memory used [KB]: 9338
% 10.01/2.92 % (6292)Time elapsed: 0.295 s
% 10.01/2.92 % (6292)Instructions burned: 995 (million)
% 10.01/2.92 % (6292)------------------------------
% 10.01/2.92 % (6292)------------------------------
% 10.01/2.93 % (6302)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_5848 for (2985ds/70Mi)
% 10.01/2.94 % (6302)Instruction limit reached!
% 10.01/2.94 % (6302)------------------------------
% 10.01/2.94 % (6302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.01/2.94 % (6302)Termination reason: Unknown
% 10.01/2.94 % (6302)Termination phase: Property scanning
% 10.01/2.94
% 10.01/2.94 % (6302)Memory used [KB]: 1918
% 10.01/2.94 % (6302)Time elapsed: 0.019 s
% 10.01/2.94 % (6302)Instructions burned: 71 (million)
% 10.01/2.94 % (6302)------------------------------
% 10.01/2.94 % (6302)------------------------------
% 10.01/2.95 % (6303)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_5848 for (2985ds/316Mi)
% 10.01/2.96 % (6296)Instruction limit reached!
% 10.01/2.96 % (6296)------------------------------
% 10.01/2.96 % (6296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.01/2.96 % (6296)Termination reason: Unknown
% 10.01/2.96 % (6296)Termination phase: Saturation
% 10.01/2.96
% 10.01/2.96 % (6296)Memory used [KB]: 14072
% 10.01/2.96 % (6296)Time elapsed: 0.197 s
% 10.01/2.96 % (6296)Instructions burned: 669 (million)
% 10.01/2.96 % (6296)------------------------------
% 10.01/2.96 % (6296)------------------------------
% 10.01/2.96 % (6300)Instruction limit reached!
% 10.01/2.96 % (6300)------------------------------
% 10.01/2.96 % (6300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.01/2.96 % (6300)Termination reason: Unknown
% 10.01/2.96 % (6300)Termination phase: Saturation
% 10.01/2.96
% 10.01/2.96 % (6300)Memory used [KB]: 6908
% 10.01/2.96 % (6300)Time elapsed: 0.116 s
% 10.01/2.96 % (6300)Instructions burned: 373 (million)
% 10.01/2.96 % (6300)------------------------------
% 10.01/2.96 % (6300)------------------------------
% 10.01/2.97 % (6304)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_5848 for (2985ds/932Mi)
% 10.01/2.97 % (6305)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_5848 for (2985ds/4714Mi)
% 10.01/2.99 % (6303)Refutation not found, incomplete strategy
% 10.01/2.99 % (6303)------------------------------
% 10.01/2.99 % (6303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.01/2.99 % (6303)Termination reason: Refutation not found, incomplete strategy
% 10.01/2.99
% 10.01/2.99
% 10.01/2.99 % (6303)Memory used [KB]: 6780
% 10.01/2.99 % (6303)Time elapsed: 0.036 s
% 10.01/2.99 % (6303)Instructions burned: 136 (million)
% 10.01/2.99 % (6303)------------------------------
% 10.01/2.99 % (6303)------------------------------
% 10.01/3.00 % (6306)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_5848 for (2984ds/8250Mi)
% 10.01/3.01 % (6305)Refutation not found, incomplete strategy
% 10.01/3.01 % (6305)------------------------------
% 10.01/3.01 % (6305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.01/3.01 % (6305)Termination reason: Refutation not found, incomplete strategy
% 10.01/3.01
% 10.01/3.01
% 10.01/3.01 % (6305)Memory used [KB]: 6780
% 10.01/3.01 % (6305)Time elapsed: 0.037 s
% 10.01/3.01 % (6305)Instructions burned: 140 (million)
% 10.01/3.01 % (6305)------------------------------
% 10.01/3.01 % (6305)------------------------------
% 10.01/3.02 % (6307)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_5848 for (2984ds/770Mi)
% 10.01/3.02 % (6284)Instruction limit reached!
% 10.01/3.02 % (6284)------------------------------
% 10.01/3.02 % (6284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.01/3.02 % (6284)Termination reason: Unknown
% 10.01/3.02 % (6284)Termination phase: Saturation
% 10.01/3.02
% 10.01/3.02 % (6284)Memory used [KB]: 3709
% 10.01/3.02 % (6284)Time elapsed: 0.582 s
% 10.01/3.02 % (6284)Instructions burned: 1913 (million)
% 10.01/3.02 % (6284)------------------------------
% 10.01/3.02 % (6284)------------------------------
% 12.90/3.03 % (6307)Refutation not found, incomplete strategy
% 12.90/3.03 % (6307)------------------------------
% 12.90/3.03 % (6307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.90/3.03 % (6307)Termination reason: Refutation not found, incomplete strategy
% 12.90/3.03
% 12.90/3.03
% 12.90/3.03 % (6307)Memory used [KB]: 6012
% 12.90/3.03 % (6307)Time elapsed: 0.012 s
% 12.90/3.03 % (6307)Instructions burned: 37 (million)
% 12.90/3.03 % (6307)------------------------------
% 12.90/3.03 % (6307)------------------------------
% 12.90/3.03 % (6308)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_5848 for (2984ds/794Mi)
% 12.90/3.04 % (6309)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_5848 for (2984ds/464Mi)
% 13.43/3.18 % (6309)Instruction limit reached!
% 13.43/3.18 % (6309)------------------------------
% 13.43/3.18 % (6309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.43/3.18 % (6309)Termination reason: Unknown
% 13.43/3.18 % (6309)Termination phase: Saturation
% 13.43/3.18
% 13.43/3.18 % (6309)Memory used [KB]: 7419
% 13.43/3.18 % (6309)Time elapsed: 0.164 s
% 13.43/3.18 % (6309)Instructions burned: 466 (million)
% 13.43/3.18 % (6309)------------------------------
% 13.43/3.18 % (6309)------------------------------
% 13.43/3.19 % (6310)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_5848 for (2983ds/1376Mi)
% 13.97/3.24 % (6304)Instruction limit reached!
% 13.97/3.24 % (6304)------------------------------
% 13.97/3.24 % (6304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.97/3.24 % (6304)Termination reason: Unknown
% 13.97/3.24 % (6304)Termination phase: Saturation
% 13.97/3.24
% 13.97/3.24 % (6304)Memory used [KB]: 9083
% 13.97/3.24 % (6304)Time elapsed: 0.278 s
% 13.97/3.24 % (6304)Instructions burned: 933 (million)
% 13.97/3.24 % (6304)------------------------------
% 13.97/3.24 % (6304)------------------------------
% 13.97/3.25 % (6311)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_5848 for (2982ds/906Mi)
% 13.97/3.27 % (6308)Instruction limit reached!
% 13.97/3.27 % (6308)------------------------------
% 13.97/3.27 % (6308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.97/3.27 % (6308)Termination reason: Unknown
% 13.97/3.27 % (6308)Termination phase: Saturation
% 13.97/3.27
% 13.97/3.27 % (6308)Memory used [KB]: 5373
% 13.97/3.27 % (6308)Time elapsed: 0.260 s
% 13.97/3.27 % (6308)Instructions burned: 794 (million)
% 13.97/3.27 % (6308)------------------------------
% 13.97/3.27 % (6308)------------------------------
% 13.97/3.28 % (6312)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_5848 for (2982ds/434Mi)
% 15.08/3.41 % (6312)Instruction limit reached!
% 15.08/3.41 % (6312)------------------------------
% 15.08/3.41 % (6312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.08/3.41 % (6312)Termination reason: Unknown
% 15.08/3.41 % (6312)Termination phase: Saturation
% 15.08/3.41
% 15.08/3.41 % (6312)Memory used [KB]: 6780
% 15.08/3.41 % (6312)Time elapsed: 0.150 s
% 15.08/3.41 % (6312)Instructions burned: 435 (million)
% 15.08/3.41 % (6312)------------------------------
% 15.08/3.41 % (6312)------------------------------
% 15.08/3.42 % (6313)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_5848 for (2980ds/865Mi)
% 15.08/3.47 % (6301)Instruction limit reached!
% 15.08/3.47 % (6301)------------------------------
% 15.08/3.47 % (6301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.08/3.47 % (6301)Termination reason: Unknown
% 15.08/3.47 % (6301)Termination phase: Saturation
% 15.08/3.47
% 15.08/3.47 % (6301)Memory used [KB]: 9083
% 15.08/3.47 % (6301)Time elapsed: 0.570 s
% 15.08/3.47 % (6301)Instructions burned: 1828 (million)
% 15.08/3.47 % (6301)------------------------------
% 15.08/3.47 % (6301)------------------------------
% 15.08/3.48 % (6314)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_5848 for (2980ds/593Mi)
% 15.59/3.56 % (6311)Instruction limit reached!
% 15.59/3.56 % (6311)------------------------------
% 15.59/3.56 % (6311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.59/3.56 % (6311)Termination reason: Unknown
% 15.59/3.56 % (6311)Termination phase: Saturation
% 15.59/3.56
% 15.59/3.56 % (6311)Memory used [KB]: 12025
% 15.59/3.56 % (6311)Time elapsed: 0.332 s
% 15.59/3.56 % (6311)Instructions burned: 907 (million)
% 15.59/3.56 % (6311)------------------------------
% 15.59/3.56 % (6311)------------------------------
% 15.59/3.57 % (6315)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_5848 for (2979ds/443Mi)
% 16.22/3.61 % (6310)Instruction limit reached!
% 16.22/3.61 % (6310)------------------------------
% 16.22/3.61 % (6310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.22/3.61 % (6310)Termination reason: Unknown
% 16.22/3.61 % (6310)Termination phase: Saturation
% 16.22/3.61
% 16.22/3.61 % (6310)Memory used [KB]: 9722
% 16.22/3.61 % (6310)Time elapsed: 0.447 s
% 16.22/3.61 % (6310)Instructions burned: 1378 (million)
% 16.22/3.61 % (6310)------------------------------
% 16.22/3.61 % (6310)------------------------------
% 16.22/3.62 % (6316)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_5848 for (2978ds/594Mi)
% 16.22/3.65 % (6314)Instruction limit reached!
% 16.22/3.65 % (6314)------------------------------
% 16.22/3.65 % (6314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.22/3.65 % (6314)Termination reason: Unknown
% 16.22/3.65 % (6314)Termination phase: Saturation
% 16.22/3.65
% 16.22/3.65 % (6314)Memory used [KB]: 8955
% 16.22/3.65 % (6314)Time elapsed: 0.175 s
% 16.22/3.65 % (6314)Instructions burned: 595 (million)
% 16.22/3.65 % (6314)------------------------------
% 16.22/3.65 % (6314)------------------------------
% 16.22/3.66 % (6317)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_5848 for (2978ds/327Mi)
% 16.22/3.67 % (6280)Instruction limit reached!
% 16.22/3.67 % (6280)------------------------------
% 16.22/3.67 % (6280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.22/3.67 % (6280)Termination reason: Unknown
% 16.22/3.67 % (6280)Termination phase: Saturation
% 16.22/3.67
% 16.22/3.67 % (6280)Memory used [KB]: 10490
% 16.22/3.67 % (6280)Time elapsed: 1.350 s
% 16.22/3.67 % (6280)Instructions burned: 4437 (million)
% 16.22/3.67 % (6280)------------------------------
% 16.22/3.67 % (6280)------------------------------
% 16.22/3.67 % (6313)Instruction limit reached!
% 16.22/3.67 % (6313)------------------------------
% 16.22/3.67 % (6313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.22/3.67 % (6313)Termination reason: Unknown
% 16.22/3.67 % (6313)Termination phase: Saturation
% 16.22/3.67
% 16.22/3.67 % (6313)Memory used [KB]: 8827
% 16.22/3.67 % (6313)Time elapsed: 0.257 s
% 16.22/3.67 % (6313)Instructions burned: 866 (million)
% 16.22/3.67 % (6313)------------------------------
% 16.22/3.67 % (6313)------------------------------
% 16.22/3.68 % (6318)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_5848 for (2978ds/5411Mi)
% 16.22/3.68 % (6319)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_5848 for (2978ds/1762Mi)
% 17.36/3.70 % (6318)Refutation not found, incomplete strategy
% 17.36/3.70 % (6318)------------------------------
% 17.36/3.70 % (6318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.36/3.70 % (6318)Termination reason: Refutation not found, incomplete strategy
% 17.36/3.70
% 17.36/3.70
% 17.36/3.70 % (6318)Memory used [KB]: 6396
% 17.36/3.70 % (6318)Time elapsed: 0.019 s
% 17.36/3.70 % (6318)Instructions burned: 63 (million)
% 17.36/3.70 % (6318)------------------------------
% 17.36/3.70 % (6318)------------------------------
% 17.36/3.71 % (6320)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_5848 for (2977ds/96Mi)
% 17.36/3.71 % (6315)Instruction limit reached!
% 17.36/3.71 % (6315)------------------------------
% 17.36/3.71 % (6315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.36/3.71 % (6315)Termination reason: Unknown
% 17.36/3.71 % (6315)Termination phase: Saturation
% 17.36/3.71
% 17.36/3.71 % (6315)Memory used [KB]: 7291
% 17.36/3.71 % (6315)Time elapsed: 0.141 s
% 17.36/3.71 % (6315)Instructions burned: 445 (million)
% 17.36/3.71 % (6315)------------------------------
% 17.36/3.71 % (6315)------------------------------
% 17.36/3.72 % (6321)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_5848 for (2977ds/503Mi)
% 17.36/3.73 % (6320)Instruction limit reached!
% 17.36/3.73 % (6320)------------------------------
% 17.36/3.73 % (6320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.36/3.73 % (6320)Termination reason: Unknown
% 17.36/3.73 % (6320)Termination phase: Property scanning
% 17.36/3.73
% 17.36/3.73 % (6320)Memory used [KB]: 1918
% 17.36/3.73 % (6320)Time elapsed: 0.025 s
% 17.36/3.73 % (6320)Instructions burned: 96 (million)
% 17.36/3.73 % (6320)------------------------------
% 17.36/3.73 % (6320)------------------------------
% 17.36/3.74 % (6321)Refutation not found, incomplete strategy
% 17.36/3.74 % (6321)------------------------------
% 17.36/3.74 % (6321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.36/3.74 % (6321)Termination reason: Refutation not found, incomplete strategy
% 17.36/3.74
% 17.36/3.74
% 17.36/3.74 % (6321)Memory used [KB]: 6396
% 17.36/3.74 % (6321)Time elapsed: 0.021 s
% 17.36/3.74 % (6321)Instructions burned: 70 (million)
% 17.36/3.74 % (6321)------------------------------
% 17.36/3.74 % (6321)------------------------------
% 17.36/3.74 % (6322)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_5848 for (2977ds/90Mi)
% 17.36/3.75 % (6323)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_5848 for (2977ds/593Mi)
% 17.36/3.76 % (6317)Instruction limit reached!
% 17.36/3.76 % (6317)------------------------------
% 17.36/3.76 % (6317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.36/3.76 % (6317)Termination reason: Unknown
% 17.36/3.76 % (6317)Termination phase: Saturation
% 17.36/3.76
% 17.36/3.76 % (6317)Memory used [KB]: 7547
% 17.36/3.76 % (6317)Time elapsed: 0.100 s
% 17.36/3.76 % (6317)Instructions burned: 327 (million)
% 17.36/3.76 % (6317)------------------------------
% 17.36/3.76 % (6317)------------------------------
% 17.36/3.77 % (6322)Instruction limit reached!
% 17.36/3.77 % (6322)------------------------------
% 17.36/3.77 % (6322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.36/3.77 % (6322)Termination reason: Unknown
% 17.36/3.77 % (6322)Termination phase: Saturation
% 17.36/3.77
% 17.36/3.77 % (6322)Memory used [KB]: 6524
% 17.36/3.77 % (6322)Time elapsed: 0.027 s
% 17.36/3.77 % (6322)Instructions burned: 93 (million)
% 17.36/3.77 % (6322)------------------------------
% 17.36/3.77 % (6322)------------------------------
% 17.36/3.77 % (6324)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_5848 for (2977ds/1512Mi)
% 17.36/3.78 % (6325)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_5848 for (2977ds/569Mi)
% 17.95/3.80 % (6316)Instruction limit reached!
% 17.95/3.80 % (6316)------------------------------
% 17.95/3.80 % (6316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.95/3.80 % (6316)Termination reason: Unknown
% 17.95/3.80 % (6316)Termination phase: Saturation
% 17.95/3.80
% 17.95/3.80 % (6316)Memory used [KB]: 7547
% 17.95/3.80 % (6316)Time elapsed: 0.182 s
% 17.95/3.80 % (6316)Instructions burned: 596 (million)
% 17.95/3.80 % (6316)------------------------------
% 17.95/3.80 % (6316)------------------------------
% 17.95/3.80 % (6324)Refutation not found, incomplete strategy
% 17.95/3.80 % (6324)------------------------------
% 17.95/3.80 % (6324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.95/3.80 % (6324)Termination reason: Refutation not found, incomplete strategy
% 17.95/3.80
% 17.95/3.80
% 17.95/3.80 % (6324)Memory used [KB]: 6780
% 17.95/3.80 % (6324)Time elapsed: 0.032 s
% 17.95/3.80 % (6324)Instructions burned: 108 (million)
% 17.95/3.80 % (6324)------------------------------
% 17.95/3.80 % (6324)------------------------------
% 17.95/3.81 % (6326)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_5848 for (2976ds/501Mi)
% 17.95/3.81 % (6327)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_5848 for (2976ds/562Mi)
% 18.38/3.93 % (6323)Instruction limit reached!
% 18.38/3.93 % (6323)------------------------------
% 18.38/3.93 % (6323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.38/3.93 % (6323)Termination reason: Unknown
% 18.38/3.93 % (6323)Termination phase: Saturation
% 18.38/3.93
% 18.38/3.93 % (6323)Memory used [KB]: 7931
% 18.38/3.93 % (6323)Time elapsed: 0.185 s
% 18.38/3.93 % (6323)Instructions burned: 593 (million)
% 18.38/3.93 % (6323)------------------------------
% 18.38/3.93 % (6323)------------------------------
% 18.38/3.94 % (6328)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_5848 for (2975ds/406Mi)
% 18.38/3.95 % (6325)Instruction limit reached!
% 18.38/3.95 % (6325)------------------------------
% 18.38/3.95 % (6325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.38/3.95 % (6325)Termination reason: Unknown
% 18.38/3.95 % (6325)Termination phase: Saturation
% 18.38/3.95
% 18.38/3.95 % (6325)Memory used [KB]: 8571
% 18.38/3.95 % (6325)Time elapsed: 0.170 s
% 18.38/3.95 % (6325)Instructions burned: 569 (million)
% 18.38/3.95 % (6325)------------------------------
% 18.38/3.95 % (6325)------------------------------
% 18.38/3.96 % (6329)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_5848 for (2975ds/582Mi)
% 18.38/3.96 % (6326)Instruction limit reached!
% 18.38/3.96 % (6326)------------------------------
% 18.38/3.96 % (6326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.38/3.96 % (6326)Termination reason: Unknown
% 18.38/3.96 % (6326)Termination phase: Saturation
% 18.38/3.96
% 18.38/3.96 % (6326)Memory used [KB]: 7803
% 18.38/3.96 % (6326)Time elapsed: 0.151 s
% 18.38/3.96 % (6326)Instructions burned: 504 (million)
% 18.38/3.96 % (6326)------------------------------
% 18.38/3.96 % (6326)------------------------------
% 18.38/3.97 % (6330)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_5848 for (2975ds/456Mi)
% 18.38/3.98 % (6327)Instruction limit reached!
% 18.38/3.98 % (6327)------------------------------
% 18.38/3.98 % (6327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.38/3.98 % (6327)Termination reason: Unknown
% 18.38/3.98 % (6327)Termination phase: Saturation
% 18.38/3.98
% 18.38/3.98 % (6327)Memory used [KB]: 8315
% 18.38/3.98 % (6327)Time elapsed: 0.168 s
% 18.38/3.98 % (6327)Instructions burned: 563 (million)
% 18.38/3.98 % (6327)------------------------------
% 18.38/3.98 % (6327)------------------------------
% 18.38/3.98 % (6283)Instruction limit reached!
% 18.38/3.98 % (6283)------------------------------
% 18.38/3.98 % (6283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.38/3.98 % (6283)Termination reason: Unknown
% 18.38/3.98 % (6283)Termination phase: Saturation
% 18.38/3.98
% 18.38/3.98 % (6283)Memory used [KB]: 18549
% 18.38/3.98 % (6283)Time elapsed: 1.604 s
% 18.38/3.98 % (6283)Instructions burned: 5207 (million)
% 18.38/3.98 % (6283)------------------------------
% 18.38/3.98 % (6283)------------------------------
% 18.38/3.99 % (6331)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_5848 for (2975ds/393Mi)
% 18.38/3.99 % (6332)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_5848 for (2975ds/1335Mi)
% 18.38/4.00 % (6330)Refutation not found, incomplete strategy
% 18.38/4.00 % (6330)------------------------------
% 18.38/4.00 % (6330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.38/4.00 % (6330)Termination reason: Refutation not found, incomplete strategy
% 18.38/4.00
% 18.38/4.00
% 18.38/4.00 % (6330)Memory used [KB]: 6780
% 18.38/4.00 % (6330)Time elapsed: 0.028 s
% 18.38/4.00 % (6330)Instructions burned: 94 (million)
% 18.38/4.00 % (6330)------------------------------
% 18.38/4.00 % (6330)------------------------------
% 18.38/4.01 % (6333)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_5848 for (2974ds/3373Mi)
% 19.91/4.07 % (6328)Instruction limit reached!
% 19.91/4.07 % (6328)------------------------------
% 19.91/4.07 % (6328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.07 % (6328)Termination reason: Unknown
% 19.91/4.07 % (6328)Termination phase: Saturation
% 19.91/4.07
% 19.91/4.07 % (6328)Memory used [KB]: 7291
% 19.91/4.07 % (6328)Time elapsed: 0.126 s
% 19.91/4.07 % (6328)Instructions burned: 409 (million)
% 19.91/4.07 % (6328)------------------------------
% 19.91/4.07 % (6328)------------------------------
% 19.91/4.08 % (6334)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_5848 for (2974ds/474Mi)
% 19.91/4.10 % (6331)Instruction limit reached!
% 19.91/4.10 % (6331)------------------------------
% 19.91/4.10 % (6331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.10 % (6331)Termination reason: Unknown
% 19.91/4.10 % (6331)Termination phase: Saturation
% 19.91/4.10
% 19.91/4.10 % (6331)Memory used [KB]: 7291
% 19.91/4.10 % (6331)Time elapsed: 0.112 s
% 19.91/4.10 % (6331)Instructions burned: 396 (million)
% 19.91/4.10 % (6331)------------------------------
% 19.91/4.10 % (6331)------------------------------
% 19.91/4.11 % (6335)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_5848 for (2973ds/157Mi)
% 20.47/4.14 % (6329)Instruction limit reached!
% 20.47/4.14 % (6329)------------------------------
% 20.47/4.14 % (6329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.47/4.14 % (6329)Termination reason: Unknown
% 20.47/4.14 % (6329)Termination phase: Saturation
% 20.47/4.14
% 20.47/4.14 % (6329)Memory used [KB]: 7547
% 20.47/4.14 % (6329)Time elapsed: 0.179 s
% 20.47/4.14 % (6329)Instructions burned: 582 (million)
% 20.47/4.14 % (6329)------------------------------
% 20.47/4.14 % (6329)------------------------------
% 20.47/4.14 % (6336)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_5848 for (2973ds/590Mi)
% 20.47/4.15 % (6335)Instruction limit reached!
% 20.47/4.15 % (6335)------------------------------
% 20.47/4.15 % (6335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.47/4.15 % (6335)Termination reason: Unknown
% 20.47/4.15 % (6335)Termination phase: Saturation
% 20.47/4.15
% 20.47/4.15 % (6335)Memory used [KB]: 6652
% 20.47/4.15 % (6335)Time elapsed: 0.042 s
% 20.47/4.15 % (6335)Instructions burned: 159 (million)
% 20.47/4.15 % (6335)------------------------------
% 20.47/4.15 % (6335)------------------------------
% 20.47/4.16 % (6337)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_5848 for (2973ds/104Mi)
% 20.47/4.19 % (6337)Instruction limit reached!
% 20.47/4.19 % (6337)------------------------------
% 20.47/4.19 % (6337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.47/4.19 % (6337)Termination reason: Unknown
% 20.47/4.19 % (6337)Termination phase: Saturation
% 20.47/4.19
% 20.47/4.19 % (6337)Memory used [KB]: 2302
% 20.47/4.19 % (6337)Time elapsed: 0.030 s
% 20.47/4.19 % (6337)Instructions burned: 104 (million)
% 20.47/4.19 % (6337)------------------------------
% 20.47/4.19 % (6337)------------------------------
% 20.78/4.20 % (6338)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_5848 for (2973ds/414Mi)
% 20.78/4.21 % (6319)Instruction limit reached!
% 20.78/4.21 % (6319)------------------------------
% 20.78/4.21 % (6319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.78/4.21 % (6319)Termination reason: Unknown
% 20.78/4.21 % (6319)Termination phase: Saturation
% 20.78/4.21
% 20.78/4.21 % (6319)Memory used [KB]: 8315
% 20.78/4.21 % (6319)Time elapsed: 0.530 s
% 20.78/4.21 % (6319)Instructions burned: 1764 (million)
% 20.78/4.21 % (6319)------------------------------
% 20.78/4.21 % (6319)------------------------------
% 20.78/4.22 % (6334)Instruction limit reached!
% 20.78/4.22 % (6334)------------------------------
% 20.78/4.22 % (6334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.78/4.22 % (6334)Termination reason: Unknown
% 20.78/4.22 % (6334)Termination phase: Saturation
% 20.78/4.22
% 20.78/4.22 % (6334)Memory used [KB]: 7419
% 20.78/4.22 % (6334)Time elapsed: 0.144 s
% 20.78/4.22 % (6334)Instructions burned: 475 (million)
% 20.78/4.22 % (6334)------------------------------
% 20.78/4.22 % (6334)------------------------------
% 20.78/4.22 % (6339)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_5848 for (2972ds/715Mi)
% 20.78/4.23 % (6340)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_5848 for (2972ds/961Mi)
% 21.17/4.32 % (6336)Instruction limit reached!
% 21.17/4.32 % (6336)------------------------------
% 21.17/4.32 % (6336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.32 % (6336)Termination reason: Unknown
% 21.17/4.32 % (6336)Termination phase: Saturation
% 21.17/4.32
% 21.17/4.32 % (6336)Memory used [KB]: 8699
% 21.17/4.32 % (6336)Time elapsed: 0.172 s
% 21.17/4.32 % (6336)Instructions burned: 590 (million)
% 21.17/4.32 % (6336)------------------------------
% 21.17/4.32 % (6336)------------------------------
% 21.17/4.33 % (6338)Instruction limit reached!
% 21.17/4.33 % (6338)------------------------------
% 21.17/4.33 % (6338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.33 % (6338)Termination reason: Unknown
% 21.17/4.33 % (6338)Termination phase: Saturation
% 21.17/4.33
% 21.17/4.33 % (6338)Memory used [KB]: 7291
% 21.17/4.33 % (6338)Time elapsed: 0.126 s
% 21.17/4.33 % (6338)Instructions burned: 416 (million)
% 21.17/4.33 % (6338)------------------------------
% 21.17/4.33 % (6338)------------------------------
% 21.17/4.33 % (6341)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_5848 for (2971ds/1213Mi)
% 21.17/4.33 % (6342)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_5848 for (2971ds/1979Mi)
% 21.17/4.38 % (6332)Instruction limit reached!
% 21.17/4.38 % (6332)------------------------------
% 21.17/4.38 % (6332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.38 % (6332)Termination reason: Unknown
% 21.17/4.38 % (6332)Termination phase: Saturation
% 21.17/4.38
% 21.17/4.38 % (6332)Memory used [KB]: 8699
% 21.17/4.38 % (6332)Time elapsed: 0.387 s
% 21.17/4.38 % (6332)Instructions burned: 1335 (million)
% 21.17/4.38 % (6332)------------------------------
% 21.17/4.38 % (6332)------------------------------
% 21.17/4.39 % (6343)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_5848 for (2971ds/481Mi)
% 21.68/4.44 % (6339)Instruction limit reached!
% 21.68/4.44 % (6339)------------------------------
% 21.68/4.44 % (6339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.68/4.44 % (6339)Termination reason: Unknown
% 21.68/4.44 % (6339)Termination phase: Saturation
% 21.68/4.44
% 21.68/4.44 % (6339)Memory used [KB]: 4477
% 21.68/4.44 % (6339)Time elapsed: 0.219 s
% 21.68/4.44 % (6339)Instructions burned: 716 (million)
% 21.68/4.44 % (6339)------------------------------
% 21.68/4.44 % (6339)------------------------------
% 21.68/4.45 % (6344)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_5848 for (2970ds/783Mi)
% 22.01/4.53 % (6340)Instruction limit reached!
% 22.01/4.53 % (6340)------------------------------
% 22.01/4.53 % (6340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/4.53 % (6340)Termination reason: Unknown
% 22.01/4.53 % (6340)Termination phase: Saturation
% 22.01/4.53
% 22.01/4.53 % (6340)Memory used [KB]: 7675
% 22.01/4.53 % (6340)Time elapsed: 0.322 s
% 22.01/4.53 % (6340)Instructions burned: 961 (million)
% 22.01/4.53 % (6340)------------------------------
% 22.01/4.53 % (6340)------------------------------
% 22.01/4.54 % (6343)Instruction limit reached!
% 22.01/4.54 % (6343)------------------------------
% 22.01/4.54 % (6343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/4.54 % (6343)Termination reason: Unknown
% 22.01/4.54 % (6343)Termination phase: Saturation
% 22.01/4.54
% 22.01/4.54 % (6343)Memory used [KB]: 7675
% 22.01/4.54 % (6343)Time elapsed: 0.173 s
% 22.01/4.54 % (6343)Instructions burned: 483 (million)
% 22.01/4.54 % (6343)------------------------------
% 22.01/4.54 % (6343)------------------------------
% 22.01/4.54 % (6345)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_5848 for (2969ds/432Mi)
% 22.01/4.55 % (6346)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_5848 for (2969ds/1670Mi)
% 22.01/4.55 % (6345)Refutation not found, incomplete strategy
% 22.01/4.55 % (6345)------------------------------
% 22.01/4.55 % (6345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/4.55 % (6345)Termination reason: Refutation not found, incomplete strategy
% 22.01/4.55
% 22.01/4.55
% 22.01/4.55 % (6345)Memory used [KB]: 6012
% 22.01/4.55 % (6345)Time elapsed: 0.013 s
% 22.01/4.55 % (6345)Instructions burned: 39 (million)
% 22.01/4.55 % (6345)------------------------------
% 22.01/4.55 % (6345)------------------------------
% 22.01/4.56 % (6347)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_5848 for (2969ds/90Mi)
% 22.01/4.59 % (6347)Instruction limit reached!
% 22.01/4.59 % (6347)------------------------------
% 22.01/4.59 % (6347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/4.59 % (6347)Termination reason: Unknown
% 22.01/4.59 % (6347)Termination phase: Saturation
% 22.01/4.59
% 22.01/4.59 % (6347)Memory used [KB]: 6396
% 22.01/4.59 % (6347)Time elapsed: 0.026 s
% 22.01/4.59 % (6347)Instructions burned: 93 (million)
% 22.01/4.59 % (6347)------------------------------
% 22.01/4.59 % (6347)------------------------------
% 22.64/4.60 % (6348)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_5848 for (2968ds/346Mi)
% 22.64/4.69 % (6344)Instruction limit reached!
% 22.64/4.69 % (6344)------------------------------
% 22.64/4.69 % (6344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.64/4.69 % (6344)Termination reason: Unknown
% 22.64/4.69 % (6344)Termination phase: Saturation
% 22.64/4.69
% 22.64/4.69 % (6344)Memory used [KB]: 7675
% 22.64/4.69 % (6344)Time elapsed: 0.266 s
% 22.64/4.69 % (6344)Instructions burned: 784 (million)
% 22.64/4.69 % (6344)------------------------------
% 22.64/4.69 % (6344)------------------------------
% 22.99/4.70 % (6349)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_5848 for (2967ds/401Mi)
% 22.99/4.70 % (6348)Instruction limit reached!
% 22.99/4.70 % (6348)------------------------------
% 22.99/4.70 % (6348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.99/4.70 % (6348)Termination reason: Unknown
% 22.99/4.70 % (6348)Termination phase: Saturation
% 22.99/4.70
% 22.99/4.70 % (6348)Memory used [KB]: 7291
% 22.99/4.70 % (6348)Time elapsed: 0.107 s
% 22.99/4.70 % (6348)Instructions burned: 348 (million)
% 22.99/4.70 % (6348)------------------------------
% 22.99/4.70 % (6348)------------------------------
% 22.99/4.70 % (6341)Instruction limit reached!
% 22.99/4.70 % (6341)------------------------------
% 22.99/4.70 % (6341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.99/4.70 % (6341)Termination reason: Unknown
% 22.99/4.70 % (6341)Termination phase: Saturation
% 22.99/4.70
% 22.99/4.70 % (6341)Memory used [KB]: 8827
% 22.99/4.70 % (6341)Time elapsed: 0.400 s
% 22.99/4.70 % (6341)Instructions burned: 1214 (million)
% 22.99/4.70 % (6341)------------------------------
% 22.99/4.70 % (6341)------------------------------
% 22.99/4.71 % (6350)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_5848 for (2967ds/6454Mi)
% 22.99/4.71 % (6351)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_5848 for (2967ds/283Mi)
% 23.60/4.80 % (6351)Instruction limit reached!
% 23.60/4.80 % (6351)------------------------------
% 23.60/4.80 % (6351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.60/4.80 % (6351)Termination reason: Unknown
% 23.60/4.80 % (6351)Termination phase: Saturation
% 23.60/4.80
% 23.60/4.80 % (6351)Memory used [KB]: 7547
% 23.60/4.80 % (6351)Time elapsed: 0.086 s
% 23.60/4.80 % (6351)Instructions burned: 283 (million)
% 23.60/4.80 % (6351)------------------------------
% 23.60/4.80 % (6351)------------------------------
% 23.60/4.81 % (6352)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_5848 for (2966ds/865Mi)
% 23.60/4.81 % (6349)Instruction limit reached!
% 23.60/4.81 % (6349)------------------------------
% 23.60/4.81 % (6349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.60/4.81 % (6349)Termination reason: Unknown
% 23.60/4.81 % (6349)Termination phase: Saturation
% 23.60/4.81
% 23.60/4.81 % (6349)Memory used [KB]: 8443
% 23.60/4.81 % (6349)Time elapsed: 0.113 s
% 23.60/4.81 % (6349)Instructions burned: 402 (million)
% 23.60/4.81 % (6349)------------------------------
% 23.60/4.81 % (6349)------------------------------
% 23.60/4.82 % (6353)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_5848 for (2966ds/4528Mi)
% 23.60/4.84 % (6353)Refutation not found, incomplete strategy
% 23.60/4.84 % (6353)------------------------------
% 23.60/4.84 % (6353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.60/4.84 % (6353)Termination reason: Refutation not found, incomplete strategy
% 23.60/4.84
% 23.60/4.84
% 23.60/4.84 % (6353)Memory used [KB]: 1663
% 23.60/4.84 % (6353)Time elapsed: 0.012 s
% 23.60/4.84 % (6353)Instructions burned: 38 (million)
% 23.60/4.84 % (6353)------------------------------
% 23.60/4.84 % (6353)------------------------------
% 23.60/4.85 % (6354)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_5848 for (2966ds/1001Mi)
% 23.93/4.94 % (6342)Instruction limit reached!
% 23.93/4.94 % (6342)------------------------------
% 23.93/4.94 % (6342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.93/4.94 % (6342)Termination reason: Unknown
% 23.93/4.94 % (6342)Termination phase: Saturation
% 23.93/4.94
% 23.93/4.94 % (6342)Memory used [KB]: 7931
% 23.93/4.94 % (6342)Time elapsed: 0.623 s
% 23.93/4.94 % (6342)Instructions burned: 1982 (million)
% 23.93/4.94 % (6342)------------------------------
% 23.93/4.94 % (6342)------------------------------
% 23.93/4.95 % (6355)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_5848 for (2965ds/102Mi)
% 23.93/4.97 % (6355)Instruction limit reached!
% 23.93/4.97 % (6355)------------------------------
% 23.93/4.97 % (6355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.93/4.97 % (6355)Termination reason: Unknown
% 23.93/4.97 % (6355)Termination phase: Property scanning
% 23.93/4.97
% 23.93/4.97 % (6355)Memory used [KB]: 1918
% 23.93/4.97 % (6355)Time elapsed: 0.027 s
% 23.93/4.97 % (6355)Instructions burned: 103 (million)
% 23.93/4.97 % (6355)------------------------------
% 23.93/4.97 % (6355)------------------------------
% 23.93/4.98 % (6356)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_5848 for (2965ds/952Mi)
% 26.94/5.04 % (6346)Instruction limit reached!
% 26.94/5.04 % (6346)------------------------------
% 26.94/5.04 % (6346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.94/5.04 % (6346)Termination reason: Unknown
% 26.94/5.04 % (6346)Termination phase: Saturation
% 26.94/5.04
% 26.94/5.04 % (6346)Memory used [KB]: 9594
% 26.94/5.04 % (6346)Time elapsed: 0.513 s
% 26.94/5.04 % (6346)Instructions burned: 1672 (million)
% 26.94/5.04 % (6346)------------------------------
% 26.94/5.04 % (6346)------------------------------
% 26.94/5.04 % (6333)Instruction limit reached!
% 26.94/5.04 % (6333)------------------------------
% 26.94/5.04 % (6333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.94/5.04 % (6333)Termination reason: Unknown
% 26.94/5.04 % (6333)Termination phase: Saturation
% 26.94/5.04
% 26.94/5.04 % (6333)Memory used [KB]: 11897
% 26.94/5.04 % (6333)Time elapsed: 1.032 s
% 26.94/5.04 % (6333)Instructions burned: 3373 (million)
% 26.94/5.04 % (6333)------------------------------
% 26.94/5.04 % (6333)------------------------------
% 26.94/5.05 % (6357)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_5848 for (2964ds/578Mi)
% 26.94/5.05 % (6352)Instruction limit reached!
% 26.94/5.05 % (6352)------------------------------
% 26.94/5.05 % (6352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.94/5.05 % (6352)Termination reason: Unknown
% 26.94/5.05 % (6352)Termination phase: Saturation
% 26.94/5.05
% 26.94/5.05 % (6352)Memory used [KB]: 7931
% 26.94/5.05 % (6352)Time elapsed: 0.246 s
% 26.94/5.05 % (6352)Instructions burned: 868 (million)
% 26.94/5.05 % (6352)------------------------------
% 26.94/5.05 % (6352)------------------------------
% 26.94/5.05 % (6358)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_5848 for (2964ds/643Mi)
% 26.94/5.06 % (6359)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_5848 for (2964ds/865Mi)
% 27.45/5.15 % (6354)Instruction limit reached!
% 27.45/5.15 % (6354)------------------------------
% 27.45/5.15 % (6354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.45/5.15 % (6354)Termination reason: Unknown
% 27.45/5.15 % (6354)Termination phase: Saturation
% 27.45/5.15
% 27.45/5.15 % (6354)Memory used [KB]: 11129
% 27.45/5.15 % (6354)Time elapsed: 0.301 s
% 27.45/5.15 % (6354)Instructions burned: 1001 (million)
% 27.45/5.15 % (6354)------------------------------
% 27.45/5.15 % (6354)------------------------------
% 27.45/5.16 % (6360)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_5848 for (2963ds/1174Mi)
% 27.69/5.20 % (6360)Refutation not found, incomplete strategy
% 27.69/5.20 % (6360)------------------------------
% 27.69/5.20 % (6360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.69/5.20 % (6360)Termination reason: Refutation not found, incomplete strategy
% 27.69/5.20
% 27.69/5.20
% 27.69/5.20 % (6360)Memory used [KB]: 7291
% 27.69/5.20 % (6360)Time elapsed: 0.042 s
% 27.69/5.20 % (6360)Instructions burned: 142 (million)
% 27.69/5.20 % (6360)------------------------------
% 27.69/5.20 % (6360)------------------------------
% 27.69/5.21 % (6361)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_5848 for (2962ds/644Mi)
% 27.69/5.23 % (6357)Instruction limit reached!
% 27.69/5.23 % (6357)------------------------------
% 27.69/5.23 % (6357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.69/5.23 % (6357)Termination reason: Unknown
% 27.69/5.23 % (6357)Termination phase: Saturation
% 27.69/5.23
% 27.69/5.23 % (6357)Memory used [KB]: 7164
% 27.69/5.23 % (6357)Time elapsed: 0.180 s
% 27.69/5.23 % (6357)Instructions burned: 581 (million)
% 27.69/5.23 % (6357)------------------------------
% 27.69/5.23 % (6357)------------------------------
% 27.69/5.24 % (6362)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_5848 for (2962ds/1201Mi)
% 27.69/5.24 % (6358)Instruction limit reached!
% 27.69/5.24 % (6358)------------------------------
% 27.69/5.24 % (6358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.69/5.24 % (6358)Termination reason: Unknown
% 27.69/5.24 % (6358)Termination phase: Saturation
% 27.69/5.24
% 27.69/5.24 % (6358)Memory used [KB]: 8955
% 27.69/5.24 % (6358)Time elapsed: 0.192 s
% 27.69/5.24 % (6358)Instructions burned: 644 (million)
% 27.69/5.24 % (6358)------------------------------
% 27.69/5.24 % (6358)------------------------------
% 27.69/5.25 % (6363)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_5848 for (2962ds/1046Mi)
% 27.69/5.27 % (6356)Instruction limit reached!
% 27.69/5.27 % (6356)------------------------------
% 27.69/5.27 % (6356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.69/5.27 % (6356)Termination reason: Unknown
% 27.69/5.27 % (6356)Termination phase: Saturation
% 27.69/5.27
% 27.69/5.27 % (6356)Memory used [KB]: 8315
% 27.69/5.27 % (6356)Time elapsed: 0.294 s
% 27.69/5.27 % (6356)Instructions burned: 953 (million)
% 27.69/5.27 % (6356)------------------------------
% 27.69/5.27 % (6356)------------------------------
% 27.69/5.28 % (6364)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_5848 for (2962ds/222Mi)
% 28.42/5.33 % (6359)Instruction limit reached!
% 28.42/5.33 % (6359)------------------------------
% 28.42/5.33 % (6359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.42/5.33 % (6359)Termination reason: Unknown
% 28.42/5.33 % (6359)Termination phase: Saturation
% 28.42/5.33
% 28.42/5.33 % (6359)Memory used [KB]: 9083
% 28.42/5.33 % (6359)Time elapsed: 0.266 s
% 28.42/5.33 % (6359)Instructions burned: 867 (million)
% 28.42/5.33 % (6359)------------------------------
% 28.42/5.33 % (6359)------------------------------
% 28.42/5.34 % (6365)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=68:si=on:rtra=on_0 on DTF2THF_5848 for (2961ds/68Mi)
% 28.42/5.34 % (6364)Instruction limit reached!
% 28.42/5.34 % (6364)------------------------------
% 28.42/5.34 % (6364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.42/5.34 % (6364)Termination reason: Unknown
% 28.42/5.34 % (6364)Termination phase: Saturation
% 28.42/5.34
% 28.42/5.34 % (6364)Memory used [KB]: 7036
% 28.42/5.34 % (6364)Time elapsed: 0.061 s
% 28.42/5.34 % (6364)Instructions burned: 222 (million)
% 28.42/5.34 % (6364)------------------------------
% 28.42/5.34 % (6364)------------------------------
% 28.42/5.35 % (6366)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_5848 for (2961ds/454Mi)
% 28.42/5.36 % (6365)Instruction limit reached!
% 28.42/5.36 % (6365)------------------------------
% 28.42/5.36 % (6365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.42/5.36 % (6365)Termination reason: Unknown
% 28.42/5.36 % (6365)Termination phase: Property scanning
% 28.42/5.36
% 28.42/5.36 % (6365)Memory used [KB]: 1791
% 28.42/5.36 % (6365)Time elapsed: 0.020 s
% 28.42/5.36 % (6365)Instructions burned: 68 (million)
% 28.42/5.36 % (6365)------------------------------
% 28.42/5.36 % (6365)------------------------------
% 28.42/5.37 % (6367)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_5848 for (2961ds/360Mi)
% 28.99/5.41 % (6361)Instruction limit reached!
% 28.99/5.41 % (6361)------------------------------
% 28.99/5.41 % (6361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.99/5.41 % (6361)Termination reason: Unknown
% 28.99/5.41 % (6361)Termination phase: Saturation
% 28.99/5.41
% 28.99/5.41 % (6361)Memory used [KB]: 8315
% 28.99/5.41 % (6361)Time elapsed: 0.200 s
% 28.99/5.41 % (6361)Instructions burned: 645 (million)
% 28.99/5.41 % (6361)------------------------------
% 28.99/5.41 % (6361)------------------------------
% 28.99/5.42 % (6368)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_5848 for (2960ds/157Mi)
% 28.99/5.46 % (6368)Instruction limit reached!
% 28.99/5.46 % (6368)------------------------------
% 28.99/5.46 % (6368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.99/5.46 % (6368)Termination reason: Unknown
% 28.99/5.46 % (6368)Termination phase: Saturation
% 28.99/5.46
% 28.99/5.46 % (6368)Memory used [KB]: 6652
% 28.99/5.46 % (6368)Time elapsed: 0.044 s
% 28.99/5.46 % (6368)Instructions burned: 159 (million)
% 28.99/5.46 % (6368)------------------------------
% 28.99/5.46 % (6368)------------------------------
% 28.99/5.47 % (6367)Instruction limit reached!
% 28.99/5.47 % (6367)------------------------------
% 28.99/5.47 % (6367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.99/5.47 % (6367)Termination reason: Unknown
% 28.99/5.47 % (6367)Termination phase: Saturation
% 28.99/5.47
% 28.99/5.47 % (6367)Memory used [KB]: 8443
% 28.99/5.47 % (6367)Time elapsed: 0.103 s
% 28.99/5.47 % (6367)Instructions burned: 362 (million)
% 28.99/5.47 % (6367)------------------------------
% 28.99/5.47 % (6367)------------------------------
% 28.99/5.47 % (6369)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_5848 for (2960ds/5061Mi)
% 28.99/5.48 % (6370)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_5848 for (2960ds/2401Mi)
% 28.99/5.49 % (6366)Instruction limit reached!
% 28.99/5.49 % (6366)------------------------------
% 28.99/5.49 % (6366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.99/5.49 % (6366)Termination reason: Unknown
% 28.99/5.49 % (6366)Termination phase: Saturation
% 28.99/5.49
% 28.99/5.49 % (6366)Memory used [KB]: 13176
% 28.99/5.49 % (6366)Time elapsed: 0.135 s
% 28.99/5.49 % (6366)Instructions burned: 456 (million)
% 28.99/5.49 % (6366)------------------------------
% 28.99/5.49 % (6366)------------------------------
% 28.99/5.50 % (6371)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_5848 for (2959ds/5798Mi)
% 29.72/5.56 % (6363)Instruction limit reached!
% 29.72/5.56 % (6363)------------------------------
% 29.72/5.56 % (6363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.72/5.56 % (6363)Termination reason: Unknown
% 29.72/5.56 % (6363)Termination phase: Saturation
% 29.72/5.56
% 29.72/5.56 % (6363)Memory used [KB]: 8955
% 29.72/5.56 % (6363)Time elapsed: 0.309 s
% 29.72/5.56 % (6363)Instructions burned: 1047 (million)
% 29.72/5.56 % (6363)------------------------------
% 29.72/5.56 % (6363)------------------------------
% 29.72/5.57 % (6306)Instruction limit reached!
% 29.72/5.57 % (6306)------------------------------
% 29.72/5.57 % (6306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.72/5.57 % (6306)Termination reason: Unknown
% 29.72/5.57 % (6306)Termination phase: Saturation
% 29.72/5.57
% 29.72/5.57 % (6306)Memory used [KB]: 15351
% 29.72/5.57 % (6306)Time elapsed: 2.569 s
% 29.72/5.57 % (6306)Instructions burned: 8252 (million)
% 29.72/5.57 % (6306)------------------------------
% 29.72/5.57 % (6306)------------------------------
% 29.72/5.57 % (6372)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_5848 for (2959ds/346Mi)
% 29.72/5.58 % (6373)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_5848 for (2959ds/1321Mi)
% 29.72/5.59 % (6362)Instruction limit reached!
% 29.72/5.59 % (6362)------------------------------
% 29.72/5.59 % (6362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.72/5.59 % (6362)Termination reason: Unknown
% 29.72/5.59 % (6362)Termination phase: Saturation
% 29.72/5.59
% 29.72/5.59 % (6362)Memory used [KB]: 9722
% 29.72/5.59 % (6362)Time elapsed: 0.353 s
% 29.72/5.59 % (6362)Instructions burned: 1202 (million)
% 29.72/5.59 % (6362)------------------------------
% 29.72/5.59 % (6362)------------------------------
% 30.59/5.60 % (6374)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_5848 for (2958ds/1312Mi)
% 30.59/5.61 % (6373)Refutation not found, incomplete strategy
% 30.59/5.61 % (6373)------------------------------
% 30.59/5.61 % (6373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.61 % (6373)Termination reason: Refutation not found, incomplete strategy
% 30.59/5.61
% 30.59/5.61
% 30.59/5.61 % (6373)Memory used [KB]: 2430
% 30.59/5.61 % (6373)Time elapsed: 0.033 s
% 30.59/5.61 % (6373)Instructions burned: 107 (million)
% 30.59/5.61 % (6373)------------------------------
% 30.59/5.61 % (6373)------------------------------
% 30.59/5.62 % (6375)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_5848 for (2958ds/672Mi)
% 30.59/5.68 % (6372)Instruction limit reached!
% 30.59/5.68 % (6372)------------------------------
% 30.59/5.68 % (6372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.68 % (6372)Termination reason: Unknown
% 30.59/5.68 % (6372)Termination phase: Saturation
% 30.59/5.68
% 30.59/5.68 % (6372)Memory used [KB]: 7291
% 30.59/5.68 % (6372)Time elapsed: 0.106 s
% 30.59/5.68 % (6372)Instructions burned: 349 (million)
% 30.59/5.68 % (6372)------------------------------
% 30.59/5.68 % (6372)------------------------------
% 30.59/5.69 % (6376)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_5848 for (2958ds/1897Mi)
% 30.95/5.82 % (6375)Instruction limit reached!
% 30.95/5.82 % (6375)------------------------------
% 30.95/5.82 % (6375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.95/5.82 % (6375)Termination reason: Unknown
% 30.95/5.82 % (6375)Termination phase: Saturation
% 30.95/5.82
% 30.95/5.82 % (6375)Memory used [KB]: 7931
% 30.95/5.82 % (6375)Time elapsed: 0.203 s
% 30.95/5.82 % (6375)Instructions burned: 672 (million)
% 30.95/5.82 % (6375)------------------------------
% 30.95/5.82 % (6375)------------------------------
% 30.95/5.83 % (6377)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_5848 for (2956ds/1202Mi)
% 31.26/5.99 % (6374)Instruction limit reached!
% 31.26/5.99 % (6374)------------------------------
% 31.26/5.99 % (6374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.26/5.99 % (6374)Termination reason: Unknown
% 31.26/5.99 % (6374)Termination phase: Saturation
% 31.26/5.99
% 31.26/5.99 % (6374)Memory used [KB]: 9338
% 31.26/5.99 % (6374)Time elapsed: 0.393 s
% 31.26/5.99 % (6374)Instructions burned: 1314 (million)
% 31.26/5.99 % (6374)------------------------------
% 31.26/5.99 % (6374)------------------------------
% 31.26/6.00 % (6378)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_5848 for (2954ds/1493Mi)
% 33.92/6.03 % (6378)Refutation not found, incomplete strategy
% 33.92/6.03 % (6378)------------------------------
% 33.92/6.03 % (6378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.92/6.03 % (6378)Termination reason: Refutation not found, incomplete strategy
% 33.92/6.03
% 33.92/6.03
% 33.92/6.03 % (6378)Memory used [KB]: 6652
% 33.92/6.03 % (6378)Time elapsed: 0.031 s
% 33.92/6.03 % (6378)Instructions burned: 115 (million)
% 33.92/6.03 % (6378)------------------------------
% 33.92/6.03 % (6378)------------------------------
% 33.92/6.04 % (6379)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_5848 for (2954ds/7679Mi)
% 34.59/6.17 % (6370)Instruction limit reached!
% 34.59/6.17 % (6370)------------------------------
% 34.59/6.17 % (6370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.59/6.17 % (6370)Termination reason: Unknown
% 34.59/6.17 % (6370)Termination phase: Saturation
% 34.59/6.17
% 34.59/6.17 % (6370)Memory used [KB]: 9978
% 34.59/6.17 % (6370)Time elapsed: 0.694 s
% 34.59/6.17 % (6370)Instructions burned: 2401 (million)
% 34.59/6.17 % (6370)------------------------------
% 34.59/6.17 % (6370)------------------------------
% 34.59/6.18 % (6380)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_5848 for (2953ds/340Mi)
% 34.59/6.19 % (6377)Instruction limit reached!
% 34.59/6.19 % (6377)------------------------------
% 34.59/6.19 % (6377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.59/6.19 % (6377)Termination reason: Unknown
% 34.59/6.19 % (6377)Termination phase: Saturation
% 34.59/6.19
% 34.59/6.19 % (6377)Memory used [KB]: 4221
% 34.59/6.19 % (6377)Time elapsed: 0.363 s
% 34.59/6.19 % (6377)Instructions burned: 1205 (million)
% 34.59/6.19 % (6377)------------------------------
% 34.59/6.19 % (6377)------------------------------
% 35.03/6.20 % (6381)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_5848 for (2952ds/3672Mi)
% 35.03/6.25 % (6376)First to succeed.
% 35.03/6.26 % (6376)Refutation found. Thanks to Tanya!
% 35.03/6.26 % SZS status Theorem for DTF2THF_5848
% 35.03/6.26 % SZS output start Proof for DTF2THF_5848
% 35.03/6.26 thf(type_def_5, type, multiset_a: $tType).
% 35.03/6.26 thf(type_def_7, type, set_a: $tType).
% 35.03/6.26 thf(type_def_8, type, tree_a: $tType).
% 35.03/6.26 thf(type_def_9, type, a: $tType).
% 35.03/6.26 thf(func_def_0, type, multiset_a: $tType).
% 35.03/6.26 thf(func_def_1, type, tree_a: $tType).
% 35.03/6.26 thf(func_def_2, type, set_a: $tType).
% 35.03/6.26 thf(func_def_3, type, a: $tType).
% 35.03/6.26 thf(func_def_4, type, minus_1649712171iset_a: multiset_a > multiset_a > multiset_a).
% 35.03/6.26 thf(func_def_5, type, minus_minus_set_a: set_a > set_a > set_a).
% 35.03/6.26 thf(func_def_6, type, plus_plus_multiset_a: multiset_a > multiset_a > multiset_a).
% 35.03/6.26 thf(func_def_7, type, zero_zero_multiset_a: multiset_a).
% 35.03/6.26 thf(func_def_8, type, heapIm1140443833left_a: tree_a > tree_a).
% 35.03/6.26 thf(func_def_9, type, heapIm1257206334ight_a: tree_a > tree_a).
% 35.03/6.26 thf(func_def_10, type, heapIm1091024090Down_a: tree_a > tree_a).
% 35.03/6.26 thf(func_def_11, type, e_a: tree_a).
% 35.03/6.26 thf(func_def_12, type, t_a: a > tree_a > tree_a > tree_a).
% 35.03/6.26 thf(func_def_13, type, pred_Tree_a: (a > $o) > tree_a > $o).
% 35.03/6.26 thf(func_def_14, type, set_Tree_a: tree_a > set_a).
% 35.03/6.26 thf(func_def_15, type, in_tree_a: a > tree_a > $o).
% 35.03/6.26 thf(func_def_16, type, is_heap_a: tree_a > $o).
% 35.03/6.26 thf(func_def_17, type, multiset_a2: tree_a > multiset_a).
% 35.03/6.26 thf(func_def_18, type, val_a: tree_a > a).
% 35.03/6.26 thf(func_def_19, type, lattic146396397_Max_a: set_a > a).
% 35.03/6.26 thf(func_def_20, type, add_mset_a: a > multiset_a > multiset_a).
% 35.03/6.26 thf(func_def_21, type, set_mset_a: multiset_a > set_a).
% 35.03/6.26 thf(func_def_22, type, bot_bot_a_o: a > $o).
% 35.03/6.26 thf(func_def_23, type, bot_bot_set_a: set_a).
% 35.03/6.26 thf(func_def_24, type, ord_less_eq_o_o_a: ($o > $o > a) > ($o > $o > a) > $o).
% 35.03/6.26 thf(func_def_25, type, ord_less_eq_o_a: ($o > a) > ($o > a) > $o).
% 35.03/6.26 thf(func_def_26, type, ord_less_eq_Tree_a_o: (tree_a > $o) > (tree_a > $o) > $o).
% 35.03/6.26 thf(func_def_27, type, ord_less_eq_a_o: (a > $o) > (a > $o) > $o).
% 35.03/6.26 thf(func_def_28, type, ord_le1199012836iset_a: multiset_a > multiset_a > $o).
% 35.03/6.26 thf(func_def_29, type, ord_less_eq_set_a: set_a > set_a > $o).
% 35.03/6.26 thf(func_def_30, type, ord_less_eq_a: a > a > $o).
% 35.03/6.26 thf(func_def_31, type, order_Greatest_o_a: (($o > a) > $o) > $o > a).
% 35.03/6.26 thf(func_def_32, type, order_Greatest_a: (a > $o) > a).
% 35.03/6.26 thf(func_def_33, type, ball_a: set_a > (a > $o) > $o).
% 35.03/6.26 thf(func_def_34, type, collect_a: (a > $o) > set_a).
% 35.03/6.26 thf(func_def_35, type, insert_a: a > set_a > set_a).
% 35.03/6.26 thf(func_def_36, type, is_singleton_a: set_a > $o).
% 35.03/6.26 thf(func_def_37, type, member_a: a > set_a > $o).
% 35.03/6.26 thf(func_def_38, type, l1: tree_a).
% 35.03/6.26 thf(func_def_39, type, l2: tree_a).
% 35.03/6.26 thf(func_def_40, type, r1: tree_a).
% 35.03/6.26 thf(func_def_41, type, r2: tree_a).
% 35.03/6.26 thf(func_def_42, type, t: tree_a).
% 35.03/6.26 thf(func_def_43, type, v: a).
% 35.03/6.26 thf(func_def_44, type, v1: a).
% 35.03/6.26 thf(func_def_45, type, v2: a).
% 35.03/6.26 thf(func_def_46, type, v3: a).
% 35.03/6.26 thf(func_def_58, type, sP0: a > a > a > $o).
% 35.03/6.26 thf(func_def_59, type, sP1: a > a > a > $o).
% 35.03/6.26 thf(func_def_60, type, sP2: a > a > a > $o).
% 35.03/6.26 thf(func_def_61, type, sK3: (a > a > $o) > a).
% 35.03/6.26 thf(func_def_62, type, sK4: (a > a > $o) > a).
% 35.03/6.26 thf(func_def_63, type, sK5: (a > a > $o) > a).
% 35.03/6.26 thf(func_def_64, type, sK6: (a > a > $o) > a).
% 35.03/6.26 thf(func_def_65, type, sK7: tree_a > tree_a).
% 35.03/6.26 thf(func_def_66, type, sK8: tree_a > a).
% 35.03/6.26 thf(func_def_67, type, sK9: tree_a > tree_a).
% 35.03/6.26 thf(func_def_68, type, sK10: tree_a > tree_a).
% 35.03/6.26 thf(func_def_69, type, sK11: tree_a > a).
% 35.03/6.26 thf(func_def_70, type, sK12: tree_a > a).
% 35.03/6.26 thf(func_def_71, type, sK13: tree_a > tree_a).
% 35.03/6.26 thf(func_def_72, type, sK14: tree_a > tree_a).
% 35.03/6.26 thf(func_def_73, type, sK15: tree_a > a).
% 35.03/6.26 thf(func_def_74, type, sK16: tree_a > tree_a).
% 35.03/6.26 thf(func_def_75, type, sK17: tree_a > a).
% 35.03/6.26 thf(func_def_76, type, sK18: tree_a > a).
% 35.03/6.26 thf(func_def_77, type, sK19: tree_a > tree_a).
% 35.03/6.26 thf(func_def_78, type, sK20: tree_a > tree_a).
% 35.03/6.26 thf(func_def_79, type, sK21: tree_a > a).
% 35.03/6.26 thf(func_def_80, type, sK22: tree_a > a).
% 35.03/6.26 thf(func_def_81, type, sK23: tree_a > tree_a).
% 35.03/6.26 thf(func_def_82, type, sK24: tree_a > tree_a).
% 35.03/6.26 thf(func_def_83, type, sK25: tree_a > a).
% 35.03/6.26 thf(func_def_84, type, sK26: (a > a) > a).
% 35.03/6.26 thf(func_def_85, type, sK27: (a > a) > a).
% 35.03/6.26 thf(func_def_86, type, sK28: (a > a) > a).
% 35.03/6.26 thf(func_def_87, type, sK29: (a > a) > a).
% 35.03/6.26 thf(func_def_88, type, sK30: (a > a) > a).
% 35.03/6.26 thf(func_def_89, type, sK31: (a > a) > a).
% 35.03/6.26 thf(func_def_90, type, sK32: (a > a) > a).
% 35.03/6.26 thf(func_def_91, type, sK33: (a > a) > a).
% 35.03/6.26 thf(func_def_92, type, sK34: (tree_a > $o) > tree_a).
% 35.03/6.26 thf(func_def_93, type, sK35: (tree_a > $o) > a).
% 35.03/6.26 thf(func_def_94, type, sK36: (tree_a > $o) > tree_a).
% 35.03/6.26 thf(func_def_95, type, sK37: tree_a > a).
% 35.03/6.26 thf(func_def_96, type, sK38: tree_a > a).
% 35.03/6.26 thf(func_def_97, type, sK39: tree_a > tree_a).
% 35.03/6.26 thf(func_def_98, type, sK40: tree_a > a).
% 35.03/6.26 thf(func_def_99, type, sK41: tree_a > tree_a).
% 35.03/6.26 thf(func_def_100, type, sK42: tree_a > tree_a).
% 35.03/6.26 thf(func_def_101, type, sK43: tree_a > a).
% 35.03/6.26 thf(func_def_102, type, sK44: tree_a > tree_a).
% 35.03/6.26 thf(func_def_103, type, sK45: tree_a > a).
% 35.03/6.26 thf(func_def_104, type, sK46: tree_a > tree_a).
% 35.03/6.26 thf(func_def_105, type, sK47: tree_a > a).
% 35.03/6.26 thf(func_def_106, type, sK48: tree_a > a).
% 35.03/6.26 thf(func_def_107, type, sK49: tree_a > tree_a).
% 35.03/6.26 thf(func_def_108, type, sK50: tree_a > a).
% 35.03/6.26 thf(func_def_109, type, sK51: tree_a > tree_a).
% 35.03/6.26 thf(func_def_110, type, sK52: tree_a > tree_a).
% 35.03/6.26 thf(func_def_111, type, sK53: tree_a > a > tree_a).
% 35.03/6.26 thf(func_def_112, type, sK54: tree_a > a > a).
% 35.03/6.26 thf(func_def_113, type, sK55: tree_a > a > tree_a).
% 35.03/6.26 thf(func_def_115, type, ph57: !>[X0: $tType]:(X0)).
% 35.03/6.26 thf(f5174,plain,(
% 35.03/6.26 $false),
% 35.03/6.26 inference(avatar_sat_refutation,[status(thm)],[f3919,f4271,f4454,f4468,f4789,f5012,f5173])).
% 35.03/6.26 thf(f5173,plain,(
% 35.03/6.26 spl56_3 | ~spl56_25),
% 35.03/6.26 inference(avatar_split_clause,[status(thm)],[f5172,f4465,f833])).
% 35.03/6.26 thf(f833,definition,(
% 35.03/6.26 spl56_3 <=> (v = v3)),
% 35.03/6.26 introduced(definition,[new_symbols(naming,[spl56_3])],[avatar_definition])).
% 35.03/6.26 thf(f4465,definition,(
% 35.03/6.26 spl56_25 <=> ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true)),
% 35.03/6.26 introduced(definition,[new_symbols(naming,[spl56_25])],[avatar_definition])).
% 35.03/6.26 thf(f5172,plain,(
% 35.03/6.26 (v = v3) | ~spl56_25),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f5171])).
% 35.03/6.26 thf(f5171,plain,(
% 35.03/6.26 (v = v3) | ($true = $false) | ~spl56_25),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f5170,f758])).
% 35.03/6.26 thf(f758,plain,(
% 35.03/6.26 ((in_tree_a @ v @ r1) = $false)),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f749])).
% 35.03/6.26 thf(f749,plain,(
% 35.03/6.26 ($true != $true) | ((in_tree_a @ v @ r1) = $false)),
% 35.03/6.26 inference(fool_paramodulation,[status(thm)],[f741])).
% 35.03/6.26 thf(f741,plain,(
% 35.03/6.26 ((in_tree_a @ v @ r1) != $true)),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f734])).
% 35.03/6.26 thf(f734,plain,(
% 35.03/6.26 ($true != $true) | ((in_tree_a @ v @ r1) != $true)),
% 35.03/6.26 inference(superposition,[status(thm)],[f729,f657])).
% 35.03/6.26 thf(f657,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : tree_a,X0 : a,X1 : a] : (((in_tree_a @ X0 @ X2) != $true) | ((in_tree_a @ X0 @ (t_a @ X1 @ X3 @ X2)) = $true)) )),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f580])).
% 35.03/6.26 thf(f580,plain,(
% 35.03/6.26 ! [X0 : a,X1 : a,X2 : tree_a,X3 : tree_a] : ((($true = (in_tree_a @ X0 @ X3)) | ((in_tree_a @ X0 @ X2) = $true) | (X0 = X1) | ((in_tree_a @ X0 @ (t_a @ X1 @ X3 @ X2)) != $true)) & (((in_tree_a @ X0 @ (t_a @ X1 @ X3 @ X2)) = $true) | (($true != (in_tree_a @ X0 @ X3)) & ((in_tree_a @ X0 @ X2) != $true) & (X0 != X1))))),
% 35.03/6.26 inference(flattening,[status(thm)],[f579])).
% 35.03/6.26 thf(f579,plain,(
% 35.03/6.26 ! [X0 : a,X1 : a,X2 : tree_a,X3 : tree_a] : (((($true = (in_tree_a @ X0 @ X3)) | ((in_tree_a @ X0 @ X2) = $true) | (X0 = X1)) | ((in_tree_a @ X0 @ (t_a @ X1 @ X3 @ X2)) != $true)) & (((in_tree_a @ X0 @ (t_a @ X1 @ X3 @ X2)) = $true) | (($true != (in_tree_a @ X0 @ X3)) & ((in_tree_a @ X0 @ X2) != $true) & (X0 != X1))))),
% 35.03/6.26 inference(nnf_transformation,[status(thm)],[f219])).
% 35.03/6.26 thf(f219,plain,(
% 35.03/6.26 ! [X0 : a,X1 : a,X2 : tree_a,X3 : tree_a] : ((($true = (in_tree_a @ X0 @ X3)) | ((in_tree_a @ X0 @ X2) = $true) | (X0 = X1)) <=> ((in_tree_a @ X0 @ (t_a @ X1 @ X3 @ X2)) = $true))),
% 35.03/6.26 inference(fool_elimination,[status(thm)],[f218])).
% 35.03/6.26 thf(f218,plain,(
% 35.03/6.26 ! [X0 : a,X1 : a,X2 : tree_a,X3 : tree_a] : ((in_tree_a @ X0 @ (t_a @ X1 @ X3 @ X2)) = (X0 = X1) | (in_tree_a @ X0 @ X2) | (in_tree_a @ X0 @ X3))),
% 35.03/6.26 inference(rectify,[status(thm)],[f6])).
% 35.03/6.26 thf(f6,axiom,(
% 35.03/6.26 ! [X6 : a,X7 : a,X9 : tree_a,X8 : tree_a] : ((in_tree_a @ X6 @ (t_a @ X7 @ X8 @ X9)) = (X6 = X7) | (in_tree_a @ X6 @ X9) | (in_tree_a @ X6 @ X8))),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_5_in__tree_Osimps_I2_J)).
% 35.03/6.26 thf(f729,plain,(
% 35.03/6.26 ($true != (in_tree_a @ v @ (t_a @ v1 @ l1 @ r1)))),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f719])).
% 35.03/6.26 thf(f719,plain,(
% 35.03/6.26 ($true != (in_tree_a @ v @ (t_a @ v1 @ l1 @ r1))) | ($true != $true)),
% 35.03/6.26 inference(superposition,[status(thm)],[f602,f658])).
% 35.03/6.26 thf(f658,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : tree_a,X0 : a,X1 : a] : (((in_tree_a @ X0 @ (t_a @ X1 @ X3 @ X2)) = $true) | ($true != (in_tree_a @ X0 @ X3))) )),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f580])).
% 35.03/6.26 thf(f602,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) != $true)),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f474])).
% 35.03/6.26 thf(f474,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) != $true)),
% 35.03/6.26 inference(flattening,[status(thm)],[f191])).
% 35.03/6.26 thf(f191,plain,(
% 35.03/6.26 ~((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $true)),
% 35.03/6.26 inference(fool_elimination,[status(thm)],[f190])).
% 35.03/6.26 thf(f190,plain,(
% 35.03/6.26 ~(in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2)))),
% 35.03/6.26 inference(rectify,[status(thm)],[f170])).
% 35.03/6.26 thf(f170,negated_conjecture,(
% 35.03/6.26 ~(in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2)))),
% 35.03/6.26 inference(negated_conjecture,[status(cth)],[f169])).
% 35.03/6.26 thf(f169,conjecture,(
% 35.03/6.26 (in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2)))),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',conj_0)).
% 35.03/6.26 thf(f5170,plain,(
% 35.03/6.26 (v = v3) | ((in_tree_a @ v @ r1) = $true) | ~spl56_25),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f5169])).
% 35.03/6.26 thf(f5169,plain,(
% 35.03/6.26 (v = v3) | ($true = $false) | ((in_tree_a @ v @ r1) = $true) | ~spl56_25),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f5159,f788])).
% 35.03/6.26 thf(f788,plain,(
% 35.03/6.26 ($false = (in_tree_a @ v @ l1))),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f777])).
% 35.03/6.26 thf(f777,plain,(
% 35.03/6.26 ($false = (in_tree_a @ v @ l1)) | ($true != $true)),
% 35.03/6.26 inference(fool_paramodulation,[status(thm)],[f744])).
% 35.03/6.26 thf(f744,plain,(
% 35.03/6.26 ($true != (in_tree_a @ v @ l1))),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f735])).
% 35.03/6.26 thf(f735,plain,(
% 35.03/6.26 ($true != (in_tree_a @ v @ l1)) | ($true != $true)),
% 35.03/6.26 inference(superposition,[status(thm)],[f729,f658])).
% 35.03/6.26 thf(f5159,plain,(
% 35.03/6.26 (v = v3) | ($true = (in_tree_a @ v @ l1)) | ((in_tree_a @ v @ r1) = $true) | ~spl56_25),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f5155])).
% 35.03/6.26 thf(f5155,plain,(
% 35.03/6.26 ((in_tree_a @ v @ r1) = $true) | ($true = (in_tree_a @ v @ l1)) | (v = v3) | ($true != $true) | ~spl56_25),
% 35.03/6.26 inference(superposition,[status(thm)],[f659,f4467])).
% 35.03/6.26 thf(f4467,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true) | ~spl56_25),
% 35.03/6.26 inference(avatar_component_clause,[status(thm)],[f4465])).
% 35.03/6.26 thf(f659,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : tree_a,X0 : a,X1 : a] : (((in_tree_a @ X0 @ X2) = $true) | (X0 = X1) | ((in_tree_a @ X0 @ (t_a @ X1 @ X3 @ X2)) != $true) | ($true = (in_tree_a @ X0 @ X3))) )),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f580])).
% 35.03/6.26 thf(f5012,plain,(
% 35.03/6.26 ~spl56_26),
% 35.03/6.26 inference(avatar_contradiction_clause,[status(thm)],[f5011])).
% 35.03/6.26 thf(f5011,plain,(
% 35.03/6.26 $false | ~spl56_26),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f5010])).
% 35.03/6.26 thf(f5010,plain,(
% 35.03/6.26 ($true = $false) | ~spl56_26),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4495,f726])).
% 35.03/6.26 thf(f726,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $false)),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f717])).
% 35.03/6.26 thf(f717,plain,(
% 35.03/6.26 ($true != $true) | ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $false)),
% 35.03/6.26 inference(fool_paramodulation,[status(thm)],[f602])).
% 35.03/6.26 thf(f4495,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $true) | ~spl56_26),
% 35.03/6.26 inference(avatar_component_clause,[status(thm)],[f4493])).
% 35.03/6.26 thf(f4493,definition,(
% 35.03/6.26 spl56_26 <=> ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $true)),
% 35.03/6.26 introduced(definition,[new_symbols(naming,[spl56_26])],[avatar_definition])).
% 35.03/6.26 thf(f4789,plain,(
% 35.03/6.26 ~spl56_12 | spl56_26),
% 35.03/6.26 inference(avatar_split_clause,[status(thm)],[f4788,f4493,f3912])).
% 35.03/6.26 thf(f3912,definition,(
% 35.03/6.26 spl56_12 <=> ($true = (ord_less_eq_a @ v1 @ v3))),
% 35.03/6.26 introduced(definition,[new_symbols(naming,[spl56_12])],[avatar_definition])).
% 35.03/6.26 thf(f4788,plain,(
% 35.03/6.26 ($true != (ord_less_eq_a @ v1 @ v3)) | ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4787,f677])).
% 35.03/6.26 thf(f677,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X0 : a,X1 : tree_a] : (((val_a @ (t_a @ X0 @ X1 @ X2)) = X0)) )),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f483])).
% 35.03/6.26 thf(f483,plain,(
% 35.03/6.26 ! [X0 : a,X1 : tree_a,X2 : tree_a] : ((val_a @ (t_a @ X0 @ X1 @ X2)) = X0)),
% 35.03/6.26 inference(rectify,[status(thm)],[f30])).
% 35.03/6.26 thf(f30,axiom,(
% 35.03/6.26 ! [X6 : a,X43 : tree_a,X44 : tree_a] : ((val_a @ (t_a @ X6 @ X43 @ X44)) = X6)),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_29_val_Osimps)).
% 35.03/6.26 thf(f4787,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) != $true)),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f4786])).
% 35.03/6.26 thf(f4786,plain,(
% 35.03/6.26 ($true != $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) != $true) | ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4785,f686])).
% 35.03/6.26 thf(f686,plain,(
% 35.03/6.26 ((ord_less_eq_a @ v2 @ v1) = $true)),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f247])).
% 35.03/6.26 thf(f247,plain,(
% 35.03/6.26 ((ord_less_eq_a @ v2 @ v1) = $true)),
% 35.03/6.26 inference(fool_elimination,[status(thm)],[f246])).
% 35.03/6.26 thf(f246,plain,(
% 35.03/6.26 (ord_less_eq_a @ v2 @ v1)),
% 35.03/6.26 inference(rectify,[status(thm)],[f3])).
% 35.03/6.26 thf(f3,axiom,(
% 35.03/6.26 (ord_less_eq_a @ v2 @ v1)),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_2_True)).
% 35.03/6.26 thf(f4785,plain,(
% 35.03/6.26 ((ord_less_eq_a @ v2 @ v1) != $true) | ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) != $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4784,f677])).
% 35.03/6.26 thf(f4784,plain,(
% 35.03/6.26 ($true != (ord_less_eq_a @ v2 @ (val_a @ (t_a @ v1 @ l1 @ r1)))) | ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) != $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4771,f677])).
% 35.03/6.26 thf(f4771,plain,(
% 35.03/6.26 ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) != $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) != $true) | ((in_tree_a @ v @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))) = $true)),
% 35.03/6.26 inference(superposition,[status(thm)],[f608,f672])).
% 35.03/6.26 thf(f672,plain,(
% 35.03/6.26 ( ! [X2 : a,X3 : a,X0 : tree_a,X1 : tree_a,X6 : a,X4 : tree_a,X5 : tree_a] : (((t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)))) | ((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X2) != $true) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (val_a @ (t_a @ X3 @ X0 @ X1))))) )),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f500])).
% 35.03/6.26 thf(f500,plain,(
% 35.03/6.26 ! [X0 : tree_a,X1 : tree_a,X2 : a,X3 : a,X4 : tree_a,X5 : tree_a,X6 : a] : ((((((t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)))) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ X2))) & (($true = (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ X2)) | ((heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))) = (t_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (t_a @ X3 @ X0 @ X1) @ (heapIm1091024090Down_a @ (t_a @ X2 @ (heapIm1140443833left_a @ (t_a @ X6 @ X5 @ X4)) @ (heapIm1257206334ight_a @ (t_a @ X6 @ X5 @ X4)))))))) | ($true = (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (val_a @ (t_a @ X3 @ X0 @ X1))))) & (((((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X2) = $true) | ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1091024090Down_a @ (t_a @ X2 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X1)))) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))) & (((t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)))) | ((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X2) != $true))) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (val_a @ (t_a @ X3 @ X0 @ X1))))))),
% 35.03/6.26 inference(ennf_transformation,[status(thm)],[f489])).
% 35.03/6.26 thf(f489,plain,(
% 35.03/6.26 ! [X0 : tree_a,X1 : tree_a,X2 : a,X3 : a,X4 : tree_a,X5 : tree_a,X6 : a] : ((($true != (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (val_a @ (t_a @ X3 @ X0 @ X1)))) => ((($true = (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ X2)) => ((t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))) & (($true != (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ X2)) => ((heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))) = (t_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (t_a @ X3 @ X0 @ X1) @ (heapIm1091024090Down_a @ (t_a @ X2 @ (heapIm1140443833left_a @ (t_a @ X6 @ X5 @ X4)) @ (heapIm1257206334ight_a @ (t_a @ X6 @ X5 @ X4))))))))) & (($true = (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (val_a @ (t_a @ X3 @ X0 @ X1)))) => ((((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X2) = $true) => ((t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))) & (((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X2) != $true) => ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1091024090Down_a @ (t_a @ X2 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X1)))) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))))))),
% 35.03/6.26 inference(flattening,[status(thm)],[f287])).
% 35.03/6.26 thf(f287,plain,(
% 35.03/6.26 ! [X0 : tree_a,X1 : tree_a,X2 : a,X3 : a,X4 : tree_a,X5 : tree_a,X6 : a] : ((($true = (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (val_a @ (t_a @ X3 @ X0 @ X1)))) => ((((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X2) = $true) => ((t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))) & (~((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X2) = $true) => ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1091024090Down_a @ (t_a @ X2 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X1)))) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))))) & (~($true = (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (val_a @ (t_a @ X3 @ X0 @ X1)))) => ((($true = (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ X2)) => ((t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))) & (~($true = (ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ X2)) => ((heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))) = (t_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (t_a @ X3 @ X0 @ X1) @ (heapIm1091024090Down_a @ (t_a @ X2 @ (heapIm1140443833left_a @ (t_a @ X6 @ X5 @ X4)) @ (heapIm1257206334ight_a @ (t_a @ X6 @ X5 @ X4))))))))))),
% 35.03/6.26 inference(fool_elimination,[status(thm)],[f286])).
% 35.03/6.26 thf(f286,plain,(
% 35.03/6.26 ! [X0 : tree_a,X1 : tree_a,X2 : a,X3 : a,X4 : tree_a,X5 : tree_a,X6 : a] : (((ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (val_a @ (t_a @ X3 @ X0 @ X1))) => (((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X2) => ((t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X2) => ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1091024090Down_a @ (t_a @ X2 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X1)))) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (val_a @ (t_a @ X3 @ X0 @ X1))) => (((ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ X2) => ((t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4)) = (heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ X2) => ((heapIm1091024090Down_a @ (t_a @ X2 @ (t_a @ X3 @ X0 @ X1) @ (t_a @ X6 @ X5 @ X4))) = (t_a @ (val_a @ (t_a @ X6 @ X5 @ X4)) @ (t_a @ X3 @ X0 @ X1) @ (heapIm1091024090Down_a @ (t_a @ X2 @ (heapIm1140443833left_a @ (t_a @ X6 @ X5 @ X4)) @ (heapIm1257206334ight_a @ (t_a @ X6 @ X5 @ X4))))))))))),
% 35.03/6.26 inference(rectify,[status(thm)],[f16])).
% 35.03/6.26 thf(f16,axiom,(
% 35.03/6.26 ! [X27 : tree_a,X28 : tree_a,X6 : a,X26 : a,X25 : tree_a,X24 : tree_a,X23 : a] : (((ord_less_eq_a @ (val_a @ (t_a @ X23 @ X24 @ X25)) @ (val_a @ (t_a @ X26 @ X27 @ X28))) => (((ord_less_eq_a @ (val_a @ (t_a @ X26 @ X27 @ X28)) @ X6) => ((t_a @ X6 @ (t_a @ X26 @ X27 @ X28) @ (t_a @ X23 @ X24 @ X25)) = (heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X26 @ X27 @ X28) @ (t_a @ X23 @ X24 @ X25))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X26 @ X27 @ X28)) @ X6) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X26 @ X27 @ X28) @ (t_a @ X23 @ X24 @ X25))) = (t_a @ (val_a @ (t_a @ X26 @ X27 @ X28)) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X26 @ X27 @ X28)) @ (heapIm1257206334ight_a @ (t_a @ X26 @ X27 @ X28)))) @ (t_a @ X23 @ X24 @ X25)))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X23 @ X24 @ X25)) @ (val_a @ (t_a @ X26 @ X27 @ X28))) => (((ord_less_eq_a @ (val_a @ (t_a @ X23 @ X24 @ X25)) @ X6) => ((t_a @ X6 @ (t_a @ X26 @ X27 @ X28) @ (t_a @ X23 @ X24 @ X25)) = (heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X26 @ X27 @ X28) @ (t_a @ X23 @ X24 @ X25))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X23 @ X24 @ X25)) @ X6) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X26 @ X27 @ X28) @ (t_a @ X23 @ X24 @ X25))) = (t_a @ (val_a @ (t_a @ X23 @ X24 @ X25)) @ (t_a @ X26 @ X27 @ X28) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X23 @ X24 @ X25)) @ (heapIm1257206334ight_a @ (t_a @ X23 @ X24 @ X25))))))))))),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_15_siftDown_Osimps_I6_J)).
% 35.03/6.26 thf(f608,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2)))) = $true)),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f273])).
% 35.03/6.26 thf(f273,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2)))) = $true)),
% 35.03/6.26 inference(fool_elimination,[status(thm)],[f272])).
% 35.03/6.26 thf(f272,plain,(
% 35.03/6.26 (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))))),
% 35.03/6.26 inference(rectify,[status(thm)],[f4])).
% 35.03/6.26 thf(f4,axiom,(
% 35.03/6.26 (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (t_a @ v1 @ l1 @ r1) @ (t_a @ v2 @ l2 @ r2))))),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_3__C5__1_Oprems_C)).
% 35.03/6.26 thf(f4468,plain,(
% 35.03/6.26 spl56_12 | spl56_25 | ~spl56_11),
% 35.03/6.26 inference(avatar_split_clause,[status(thm)],[f4463,f3908,f4465,f3912])).
% 35.03/6.26 thf(f3908,definition,(
% 35.03/6.26 spl56_11 <=> ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) = $true)),
% 35.03/6.26 introduced(definition,[new_symbols(naming,[spl56_11])],[avatar_definition])).
% 35.03/6.26 thf(f4463,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) != $true) | ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true) | ($true = (ord_less_eq_a @ v1 @ v3))),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f4462])).
% 35.03/6.26 thf(f4462,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) != $true) | ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true) | ($true != $true) | ($true = (ord_less_eq_a @ v1 @ v3))),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4461,f686])).
% 35.03/6.26 thf(f4461,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true) | ($true = (ord_less_eq_a @ v1 @ v3)) | ((ord_less_eq_a @ v2 @ v1) != $true) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) != $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4460,f677])).
% 35.03/6.26 thf(f4460,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true) | ($true != (ord_less_eq_a @ v2 @ (val_a @ (t_a @ v1 @ l1 @ r1)))) | ($true = (ord_less_eq_a @ v1 @ v3)) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) != $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4459,f677])).
% 35.03/6.26 thf(f4459,plain,(
% 35.03/6.26 ($true = (ord_less_eq_a @ v1 @ v3)) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) != $true) | ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) != $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4458,f687])).
% 35.03/6.26 thf(f687,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X0 : a,X1 : tree_a] : (((heapIm1257206334ight_a @ (t_a @ X0 @ X1 @ X2)) = X2)) )),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f492])).
% 35.03/6.26 thf(f492,plain,(
% 35.03/6.26 ! [X0 : a,X1 : tree_a,X2 : tree_a] : ((heapIm1257206334ight_a @ (t_a @ X0 @ X1 @ X2)) = X2)),
% 35.03/6.26 inference(rectify,[status(thm)],[f10])).
% 35.03/6.26 thf(f10,axiom,(
% 35.03/6.26 ! [X6 : a,X8 : tree_a,X9 : tree_a] : ((heapIm1257206334ight_a @ (t_a @ X6 @ X8 @ X9)) = X9)),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_9_right_Osimps)).
% 35.03/6.26 thf(f4458,plain,(
% 35.03/6.26 ($true != (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1)))))) | ($true = (ord_less_eq_a @ v1 @ v3)) | ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) != $true) | ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4457,f623])).
% 35.03/6.26 thf(f623,plain,(
% 35.03/6.26 ( ! [X2 : a,X0 : tree_a,X1 : tree_a] : (((heapIm1140443833left_a @ (t_a @ X2 @ X0 @ X1)) = X0)) )),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f487])).
% 35.03/6.26 thf(f487,plain,(
% 35.03/6.26 ! [X0 : tree_a,X1 : tree_a,X2 : a] : ((heapIm1140443833left_a @ (t_a @ X2 @ X0 @ X1)) = X0)),
% 35.03/6.26 inference(rectify,[status(thm)],[f9])).
% 35.03/6.26 thf(f9,axiom,(
% 35.03/6.26 ! [X8 : tree_a,X9 : tree_a,X6 : a] : ((heapIm1140443833left_a @ (t_a @ X6 @ X8 @ X9)) = X8)),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_8_left_Osimps)).
% 35.03/6.26 thf(f4457,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) != $true) | ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) != $true) | ($true = (ord_less_eq_a @ v1 @ v3))),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4456,f677])).
% 35.03/6.26 thf(f4456,plain,(
% 35.03/6.26 ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) = $true) | ((in_tree_a @ v @ (t_a @ v3 @ l1 @ r1)) = $true) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) != $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) != $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f4455,f687])).
% 35.03/6.26 thf(f4455,plain,(
% 35.03/6.26 ($true = (in_tree_a @ v @ (t_a @ v3 @ l1 @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) != $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) != $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) = $true)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f643,f623])).
% 35.03/6.26 thf(f643,plain,(
% 35.03/6.26 ((in_tree_a @ v @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1)))) = $true) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) != $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) = $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) != $true)),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f531])).
% 35.03/6.26 thf(f531,plain,(
% 35.03/6.26 ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) = $true) | ((in_tree_a @ v @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1)))) = $true) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) != $true) | ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) != $true)),
% 35.03/6.26 inference(flattening,[status(thm)],[f530])).
% 35.03/6.26 thf(f530,plain,(
% 35.03/6.26 ((((in_tree_a @ v @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1)))) = $true) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) != $true)) | ((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) = $true)) | ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) != $true)),
% 35.03/6.26 inference(ennf_transformation,[status(thm)],[f476])).
% 35.03/6.26 thf(f476,plain,(
% 35.03/6.26 ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) = $true) => (((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) != $true) => (((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) = $true) => ((in_tree_a @ v @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1)))) = $true)))),
% 35.03/6.26 inference(flattening,[status(thm)],[f387])).
% 35.03/6.26 thf(f387,plain,(
% 35.03/6.26 ((ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) = $true) => (~((ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) = $true) => (((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) = $true) => ((in_tree_a @ v @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1)))) = $true)))),
% 35.03/6.26 inference(fool_elimination,[status(thm)],[f386])).
% 35.03/6.26 thf(f386,plain,(
% 35.03/6.26 (ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) => (~(ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) => ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) => (in_tree_a @ v @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))))),
% 35.03/6.26 inference(rectify,[status(thm)],[f8])).
% 35.03/6.26 thf(f8,axiom,(
% 35.03/6.26 (ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ v1 @ l1 @ r1))) => (~(ord_less_eq_a @ (val_a @ (t_a @ v1 @ l1 @ r1)) @ v3) => ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))) => (in_tree_a @ v @ (t_a @ v3 @ (heapIm1140443833left_a @ (t_a @ v1 @ l1 @ r1)) @ (heapIm1257206334ight_a @ (t_a @ v1 @ l1 @ r1))))))),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_7__C5__1_Ohyps_C_I1_J)).
% 35.03/6.26 thf(f4454,plain,(
% 35.03/6.26 ~spl56_3),
% 35.03/6.26 inference(avatar_split_clause,[status(thm)],[f668,f833])).
% 35.03/6.26 thf(f668,plain,(
% 35.03/6.26 (v != v3)),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f520])).
% 35.03/6.26 thf(f520,plain,(
% 35.03/6.26 (v != v1) & (v != v2) & (v != v3)),
% 35.03/6.26 inference(ennf_transformation,[status(thm)],[f1])).
% 35.03/6.26 thf(f1,axiom,(
% 35.03/6.26 ~((v = v3) | (v = v1) | (v = v2))),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_0_False)).
% 35.03/6.26 thf(f4271,plain,(
% 35.03/6.26 ~spl56_13),
% 35.03/6.26 inference(avatar_contradiction_clause,[status(thm)],[f4270])).
% 35.03/6.26 thf(f4270,plain,(
% 35.03/6.26 $false | ~spl56_13),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f4269])).
% 35.03/6.26 thf(f4269,plain,(
% 35.03/6.26 (v1 != v1) | ~spl56_13),
% 35.03/6.26 inference(superposition,[status(thm)],[f670,f3918])).
% 35.03/6.26 thf(f3918,plain,(
% 35.03/6.26 (v = v1) | ~spl56_13),
% 35.03/6.26 inference(avatar_component_clause,[status(thm)],[f3916])).
% 35.03/6.26 thf(f3916,definition,(
% 35.03/6.26 spl56_13 <=> (v = v1)),
% 35.03/6.26 introduced(definition,[new_symbols(naming,[spl56_13])],[avatar_definition])).
% 35.03/6.26 thf(f670,plain,(
% 35.03/6.26 (v != v1)),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f520])).
% 35.03/6.26 thf(f3919,plain,(
% 35.03/6.26 spl56_11 | spl56_12 | spl56_13),
% 35.03/6.26 inference(avatar_split_clause,[status(thm)],[f3906,f3916,f3912,f3908])).
% 35.03/6.26 thf(f3906,plain,(
% 35.03/6.26 (v = v1) | ($true = (ord_less_eq_a @ v1 @ v3)) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) = $true)),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f3905])).
% 35.03/6.26 thf(f3905,plain,(
% 35.03/6.26 ($true = (ord_less_eq_a @ v1 @ v3)) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) = $true) | ($true != $true) | (v = v1)),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f3886,f686])).
% 35.03/6.26 thf(f3886,plain,(
% 35.03/6.26 (v = v1) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) = $true) | ($true = (ord_less_eq_a @ v1 @ v3)) | ((ord_less_eq_a @ v2 @ v1) != $true)),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f3876])).
% 35.03/6.26 thf(f3876,plain,(
% 35.03/6.26 ($true = (ord_less_eq_a @ v1 @ v3)) | ($true != $true) | (v = v1) | ((ord_less_eq_a @ v2 @ v1) != $true) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ v3 @ l1 @ r1))) = $true)),
% 35.03/6.26 inference(superposition,[status(thm)],[f1282,f608])).
% 35.03/6.26 thf(f1282,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : a,X0 : a,X1 : tree_a] : (($true != (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (t_a @ X0 @ X1 @ X2) @ (t_a @ v2 @ l2 @ r2))))) | ($true = (ord_less_eq_a @ X0 @ X3)) | ($true = (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ X1 @ X2)))) | (v = X0) | ($true != (ord_less_eq_a @ v2 @ X0))) )),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f1281,f677])).
% 35.03/6.26 thf(f1281,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : a,X0 : a,X1 : tree_a] : (($true = (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ X1 @ X2)))) | ($true = (ord_less_eq_a @ X0 @ X3)) | (v = X0) | ($true != (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (t_a @ X0 @ X1 @ X2) @ (t_a @ v2 @ l2 @ r2))))) | ($true != (ord_less_eq_a @ v2 @ (val_a @ (t_a @ X0 @ X1 @ X2))))) )),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f1280,f687])).
% 35.03/6.26 thf(f1280,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : a,X0 : a,X1 : tree_a] : (($true = (ord_less_eq_a @ X0 @ X3)) | ((in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ X1 @ (heapIm1257206334ight_a @ (t_a @ X0 @ X1 @ X2))))) = $true) | (v = X0) | ($true != (ord_less_eq_a @ v2 @ (val_a @ (t_a @ X0 @ X1 @ X2)))) | ($true != (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (t_a @ X0 @ X1 @ X2) @ (t_a @ v2 @ l2 @ r2)))))) )),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f1279,f623])).
% 35.03/6.26 thf(f1279,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : a,X0 : a,X1 : tree_a] : ((v = X0) | ($true = (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (heapIm1140443833left_a @ (t_a @ X0 @ X1 @ X2)) @ (heapIm1257206334ight_a @ (t_a @ X0 @ X1 @ X2)))))) | ($true != (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (t_a @ X0 @ X1 @ X2) @ (t_a @ v2 @ l2 @ r2))))) | ($true != (ord_less_eq_a @ v2 @ (val_a @ (t_a @ X0 @ X1 @ X2)))) | ($true = (ord_less_eq_a @ X0 @ X3))) )),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f1278,f677])).
% 35.03/6.26 thf(f1278,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : a,X0 : a,X1 : tree_a] : (($true = (ord_less_eq_a @ (val_a @ (t_a @ X0 @ X1 @ X2)) @ X3)) | ($true != (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (t_a @ X0 @ X1 @ X2) @ (t_a @ v2 @ l2 @ r2))))) | ($true = (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (heapIm1140443833left_a @ (t_a @ X0 @ X1 @ X2)) @ (heapIm1257206334ight_a @ (t_a @ X0 @ X1 @ X2)))))) | ($true != (ord_less_eq_a @ v2 @ (val_a @ (t_a @ X0 @ X1 @ X2)))) | (v = X0)) )),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f1277,f677])).
% 35.03/6.26 thf(f1277,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : a,X0 : a,X1 : tree_a] : (($true != (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (t_a @ X0 @ X1 @ X2) @ (t_a @ v2 @ l2 @ r2))))) | (v = X0) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ X0 @ X1 @ X2)))) | ($true = (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (heapIm1140443833left_a @ (t_a @ X0 @ X1 @ X2)) @ (heapIm1257206334ight_a @ (t_a @ X0 @ X1 @ X2)))))) | ($true = (ord_less_eq_a @ (val_a @ (t_a @ X0 @ X1 @ X2)) @ X3))) )),
% 35.03/6.26 inference(forward_demodulation,[status(thm)],[f1260,f677])).
% 35.03/6.26 thf(f1260,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : a,X0 : a,X1 : tree_a] : ((v = (val_a @ (t_a @ X0 @ X1 @ X2))) | ($true = (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (heapIm1140443833left_a @ (t_a @ X0 @ X1 @ X2)) @ (heapIm1257206334ight_a @ (t_a @ X0 @ X1 @ X2)))))) | ($true != (in_tree_a @ v @ (heapIm1091024090Down_a @ (t_a @ X3 @ (t_a @ X0 @ X1 @ X2) @ (t_a @ v2 @ l2 @ r2))))) | ($true = (ord_less_eq_a @ (val_a @ (t_a @ X0 @ X1 @ X2)) @ X3)) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ v2 @ l2 @ r2)) @ (val_a @ (t_a @ X0 @ X1 @ X2))))) )),
% 35.03/6.26 inference(superposition,[status(thm)],[f776,f696])).
% 35.03/6.26 thf(f696,plain,(
% 35.03/6.26 ( ! [X2 : tree_a,X3 : a,X0 : tree_a,X1 : tree_a,X6 : a,X4 : tree_a,X5 : a] : (((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1257206334ight_a @ (t_a @ X5 @ X2 @ X4)))) @ (t_a @ X3 @ X0 @ X1))) | ((ord_less_eq_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ X6) = $true) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (val_a @ (t_a @ X5 @ X2 @ X4))))) )),
% 35.03/6.26 inference(cnf_transformation,[status(thm)],[f512])).
% 35.03/6.26 thf(f512,plain,(
% 35.03/6.26 ! [X0 : tree_a,X1 : tree_a,X2 : tree_a,X3 : a,X4 : tree_a,X5 : a,X6 : a] : ((($true = (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (val_a @ (t_a @ X5 @ X2 @ X4)))) | ((($true = (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X6)) | ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (t_a @ X5 @ X2 @ X4) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X1))))) = (heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))))) & (((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X6))))) & (((((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1257206334ight_a @ (t_a @ X5 @ X2 @ X4)))) @ (t_a @ X3 @ X0 @ X1))) | ((ord_less_eq_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ X6) = $true)) & (((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) | ((ord_less_eq_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ X6) != $true))) | ($true != (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (val_a @ (t_a @ X5 @ X2 @ X4))))))),
% 35.03/6.26 inference(ennf_transformation,[status(thm)],[f491])).
% 35.03/6.26 thf(f491,plain,(
% 35.03/6.26 ! [X0 : tree_a,X1 : tree_a,X2 : tree_a,X3 : a,X4 : tree_a,X5 : a,X6 : a] : ((($true != (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (val_a @ (t_a @ X5 @ X2 @ X4)))) => ((($true != (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X6)) => ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (t_a @ X5 @ X2 @ X4) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X1))))) = (heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))))) & (($true = (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X6)) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1)))))) & (($true = (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (val_a @ (t_a @ X5 @ X2 @ X4)))) => ((((ord_less_eq_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ X6) != $true) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1257206334ight_a @ (t_a @ X5 @ X2 @ X4)))) @ (t_a @ X3 @ X0 @ X1)))) & (((ord_less_eq_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ X6) = $true) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1)))))))),
% 35.03/6.26 inference(flattening,[status(thm)],[f209])).
% 35.03/6.26 thf(f209,plain,(
% 35.03/6.26 ! [X0 : tree_a,X1 : tree_a,X2 : tree_a,X3 : a,X4 : tree_a,X5 : a,X6 : a] : ((($true = (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (val_a @ (t_a @ X5 @ X2 @ X4)))) => ((((ord_less_eq_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ X6) = $true) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1)))) & (~((ord_less_eq_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ X6) = $true) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1257206334ight_a @ (t_a @ X5 @ X2 @ X4)))) @ (t_a @ X3 @ X0 @ X1)))))) & (~($true = (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (val_a @ (t_a @ X5 @ X2 @ X4)))) => ((($true = (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X6)) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1)))) & (~($true = (ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X6)) => ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (t_a @ X5 @ X2 @ X4) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X1))))) = (heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))))))))),
% 35.03/6.26 inference(fool_elimination,[status(thm)],[f208])).
% 35.03/6.26 thf(f208,plain,(
% 35.03/6.26 ! [X0 : tree_a,X1 : tree_a,X2 : tree_a,X3 : a,X4 : tree_a,X5 : a,X6 : a] : (((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (val_a @ (t_a @ X5 @ X2 @ X4))) => (((ord_less_eq_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ X6) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1)))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ X6) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ (val_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X5 @ X2 @ X4)) @ (heapIm1257206334ight_a @ (t_a @ X5 @ X2 @ X4)))) @ (t_a @ X3 @ X0 @ X1)))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (val_a @ (t_a @ X5 @ X2 @ X4))) => (((ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X6) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))) = (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1)))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ X6) => ((t_a @ (val_a @ (t_a @ X3 @ X0 @ X1)) @ (t_a @ X5 @ X2 @ X4) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X3 @ X0 @ X1)) @ (heapIm1257206334ight_a @ (t_a @ X3 @ X0 @ X1))))) = (heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X5 @ X2 @ X4) @ (t_a @ X3 @ X0 @ X1))))))))),
% 35.03/6.26 inference(rectify,[status(thm)],[f17])).
% 35.03/6.26 thf(f17,axiom,(
% 35.03/6.26 ! [X27 : tree_a,X28 : tree_a,X24 : tree_a,X26 : a,X25 : tree_a,X23 : a,X6 : a] : (((ord_less_eq_a @ (val_a @ (t_a @ X26 @ X27 @ X28)) @ (val_a @ (t_a @ X23 @ X24 @ X25))) => (((ord_less_eq_a @ (val_a @ (t_a @ X23 @ X24 @ X25)) @ X6) => ((t_a @ X6 @ (t_a @ X23 @ X24 @ X25) @ (t_a @ X26 @ X27 @ X28)) = (heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X23 @ X24 @ X25) @ (t_a @ X26 @ X27 @ X28))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X23 @ X24 @ X25)) @ X6) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X23 @ X24 @ X25) @ (t_a @ X26 @ X27 @ X28))) = (t_a @ (val_a @ (t_a @ X23 @ X24 @ X25)) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X23 @ X24 @ X25)) @ (heapIm1257206334ight_a @ (t_a @ X23 @ X24 @ X25)))) @ (t_a @ X26 @ X27 @ X28)))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X26 @ X27 @ X28)) @ (val_a @ (t_a @ X23 @ X24 @ X25))) => (((ord_less_eq_a @ (val_a @ (t_a @ X26 @ X27 @ X28)) @ X6) => ((t_a @ X6 @ (t_a @ X23 @ X24 @ X25) @ (t_a @ X26 @ X27 @ X28)) = (heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X23 @ X24 @ X25) @ (t_a @ X26 @ X27 @ X28))))) & (~(ord_less_eq_a @ (val_a @ (t_a @ X26 @ X27 @ X28)) @ X6) => ((heapIm1091024090Down_a @ (t_a @ X6 @ (t_a @ X23 @ X24 @ X25) @ (t_a @ X26 @ X27 @ X28))) = (t_a @ (val_a @ (t_a @ X26 @ X27 @ X28)) @ (t_a @ X23 @ X24 @ X25) @ (heapIm1091024090Down_a @ (t_a @ X6 @ (heapIm1140443833left_a @ (t_a @ X26 @ X27 @ X28)) @ (heapIm1257206334ight_a @ (t_a @ X26 @ X27 @ X28))))))))))),
% 35.03/6.26 file('/export/starexec/sandbox/tmp/tmp.cqUclvVj2Z/DTF2THF_5848.p',fact_16_siftDown_Osimps_I5_J)).
% 35.03/6.26 thf(f776,plain,(
% 35.03/6.26 ( ! [X0 : a,X1 : tree_a] : (($true != (in_tree_a @ v @ (t_a @ X0 @ X1 @ (t_a @ v2 @ l2 @ r2)))) | (v = X0) | ($true = (in_tree_a @ v @ X1))) )),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f765])).
% 35.03/6.26 thf(f765,plain,(
% 35.03/6.26 ( ! [X0 : a,X1 : tree_a] : (($true != $true) | (v = X0) | ($true != (in_tree_a @ v @ (t_a @ X0 @ X1 @ (t_a @ v2 @ l2 @ r2)))) | ($true = (in_tree_a @ v @ X1))) )),
% 35.03/6.26 inference(superposition,[status(thm)],[f732,f659])).
% 35.03/6.26 thf(f732,plain,(
% 35.03/6.26 ($true != (in_tree_a @ v @ (t_a @ v2 @ l2 @ r2)))),
% 35.03/6.26 inference(trivial_inequality_removal,[status(thm)],[f718])).
% 35.03/6.26 thf(f718,plain,(
% 35.03/6.26 ($true != (in_tree_a @ v @ (t_a @ v2 @ l2 @ r2))) | ($true != $true)),
% 35.03/6.26 inference(superposition,[status(thm)],[f602,f657])).
% 35.03/6.26 % SZS output end Proof for DTF2THF_5848
% 35.03/6.26 % (6376)------------------------------
% 35.03/6.26 % (6376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.03/6.26 % (6376)Termination reason: Refutation
% 35.03/6.26
% 35.03/6.26 % (6376)Memory used [KB]: 8443
% 35.03/6.26 % (6376)Time elapsed: 0.569 s
% 35.03/6.26 % (6376)Instructions burned: 1873 (million)
% 35.03/6.26 % (6376)------------------------------
% 35.03/6.26 % (6376)------------------------------
% 35.03/6.26 % (6029)Success in time 4.773 s
%------------------------------------------------------------------------------