%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP069^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:12 AM UTC 2026
% Result : Theorem 0.23s 0.37s
% Output : Refutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 27 unt; 0 typ; 4 def)
% Number of atoms : 141 ( 38 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 311 ( 29 ~; 23 |; 0 &; 246 @)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 144 ( 141 usr; 11 con; 0-4 aty)
% Number of variables : 9 ( 0 sgn 9 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr158363655iset_a: $tType ).
thf(type_def_6,type,
produc1127127335iset_a: $tType ).
thf(type_def_7,type,
set_Product_prod_a_a: $tType ).
thf(type_def_8,type,
multiset_multiset_a: $tType ).
thf(type_def_9,type,
set_multiset_a: $tType ).
thf(type_def_10,type,
product_prod_a_a: $tType ).
thf(type_def_11,type,
multiset_a: $tType ).
thf(type_def_12,type,
tree_a: $tType ).
thf(type_def_13,type,
set_a: $tType ).
thf(type_def_14,type,
a: $tType ).
thf(type_def_15,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
minus_1649712171iset_a: multiset_a > multiset_a > multiset_a ).
thf(func_def_1,type,
plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
thf(func_def_2,type,
zero_zero_multiset_a: multiset_a ).
thf(func_def_3,type,
nO_MAT1617603563iset_a: multiset_a > multiset_a > $o ).
thf(func_def_4,type,
heapIm970322378pify_a: tree_a > tree_a ).
thf(func_def_5,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(func_def_6,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(func_def_7,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(func_def_8,type,
e_a: tree_a ).
thf(func_def_9,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(func_def_10,type,
in_tree_a: a > tree_a > $o ).
thf(func_def_11,type,
is_heap_a: tree_a > $o ).
thf(func_def_12,type,
multiset_a2: tree_a > multiset_a ).
thf(func_def_13,type,
val_a: tree_a > a ).
thf(func_def_14,type,
lattic146396397_Max_a: set_a > a ).
thf(func_def_15,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(func_def_16,type,
comm_m315775925iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
thf(func_def_17,type,
fold_m382157835iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
thf(func_def_18,type,
fold_m364285649iset_a: ( a > multiset_a > multiset_a ) > multiset_a > multiset_a > multiset_a ).
thf(func_def_19,type,
is_empty_a: multiset_a > $o ).
thf(func_def_20,type,
mult1_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
thf(func_def_21,type,
mult_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
thf(func_def_22,type,
set_mset_multiset_a: multiset_multiset_a > set_multiset_a ).
thf(func_def_23,type,
set_mset_a: multiset_a > set_a ).
thf(func_def_24,type,
ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
thf(func_def_25,type,
ord_less_eq_a: a > a > $o ).
thf(func_def_26,type,
order_Greatest_a: ( a > $o ) > a ).
thf(func_def_27,type,
produc2037245207iset_a: multiset_a > multiset_a > produc1127127335iset_a ).
thf(func_def_28,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(func_def_29,type,
irrefl_a: set_Product_prod_a_a > $o ).
thf(func_def_30,type,
trans_a: set_Product_prod_a_a > $o ).
thf(func_def_31,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_32,type,
member_multiset_a: multiset_a > set_multiset_a > $o ).
thf(func_def_33,type,
member340150864iset_a: produc1127127335iset_a > set_Pr158363655iset_a > $o ).
thf(func_def_34,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_35,type,
member_a: a > set_a > $o ).
thf(func_def_36,type,
l: tree_a ).
thf(func_def_37,type,
r: tree_a ).
thf(func_def_38,type,
v: a ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
sP0: a > a > a > $o ).
thf(func_def_48,type,
sP1: a > a > a > $o ).
thf(func_def_49,type,
sK2: ( a > a ) > a ).
thf(func_def_50,type,
sK3: ( a > a ) > a ).
thf(func_def_51,type,
sK4: tree_a > a ).
thf(func_def_52,type,
sK5: tree_a > a ).
thf(func_def_53,type,
sK6: tree_a > a ).
thf(func_def_54,type,
sK7: tree_a > tree_a ).
thf(func_def_55,type,
sK8: tree_a > tree_a ).
thf(func_def_56,type,
sK9: tree_a > tree_a ).
thf(func_def_57,type,
sK10: tree_a > tree_a ).
thf(func_def_58,type,
sK11: tree_a > a ).
thf(func_def_59,type,
sK12: tree_a > a ).
thf(func_def_60,type,
sK13: tree_a > tree_a ).
thf(func_def_61,type,
sK14: tree_a > a ).
thf(func_def_62,type,
sK15: tree_a > tree_a ).
thf(func_def_63,type,
sK16: tree_a > a ).
thf(func_def_64,type,
sK17: tree_a > tree_a ).
thf(func_def_65,type,
sK18: tree_a > a ).
thf(func_def_66,type,
sK19: tree_a > tree_a ).
thf(func_def_67,type,
sK20: ( multiset_a > $o ) > a ).
thf(func_def_68,type,
sK21: ( multiset_a > $o ) > multiset_a ).
thf(func_def_69,type,
sK22: multiset_a > a > multiset_a > a > multiset_a ).
thf(func_def_70,type,
sK23: set_Product_prod_a_a > a > multiset_a > a ).
thf(func_def_71,type,
sK24: multiset_a > a > set_Product_prod_a_a > multiset_a > multiset_a ).
thf(func_def_72,type,
sK25: multiset_a > a > set_Product_prod_a_a > multiset_a > multiset_a ).
thf(func_def_73,type,
sK26: ( multiset_a > $o ) > a ).
thf(func_def_74,type,
sK27: ( multiset_a > $o ) > multiset_a ).
thf(func_def_75,type,
sK28: ( multiset_a > $o ) > multiset_a ).
thf(func_def_76,type,
sK29: ( multiset_a > $o ) > a ).
thf(func_def_77,type,
sK30: ( a > $o ) > a > a ).
thf(func_def_78,type,
sK31: tree_a > a ).
thf(func_def_79,type,
sK32: tree_a > tree_a ).
thf(func_def_80,type,
sK33: tree_a > tree_a ).
thf(func_def_81,type,
sK34: tree_a > a ).
thf(func_def_82,type,
sK35: tree_a > tree_a ).
thf(func_def_83,type,
sK36: tree_a > a ).
thf(func_def_84,type,
sK37: tree_a > a ).
thf(func_def_85,type,
sK38: tree_a > tree_a ).
thf(func_def_86,type,
sK39: tree_a > a ).
thf(func_def_87,type,
sK40: tree_a > a ).
thf(func_def_88,type,
sK41: tree_a > tree_a ).
thf(func_def_89,type,
sK42: tree_a > tree_a ).
thf(func_def_90,type,
sK43: tree_a > a ).
thf(func_def_91,type,
sK44: tree_a > tree_a ).
thf(func_def_92,type,
sK45: tree_a > tree_a ).
thf(func_def_93,type,
sK46: tree_a > a ).
thf(func_def_94,type,
sK47: ( a > a ) > a ).
thf(func_def_95,type,
sK48: ( a > a ) > a ).
thf(func_def_96,type,
sK49: tree_a > tree_a ).
thf(func_def_97,type,
sK50: tree_a > tree_a ).
thf(func_def_98,type,
sK51: tree_a > a ).
thf(func_def_99,type,
sK52: multiset_a > multiset_a ).
thf(func_def_100,type,
sK53: multiset_a > a ).
thf(func_def_101,type,
sK54: ( a > a ) > a ).
thf(func_def_102,type,
sK55: ( a > a ) > a ).
thf(func_def_103,type,
sK56: set_Product_prod_a_a > multiset_a > multiset_a > a ).
thf(func_def_104,type,
sK57: ( a > $o ) > a > a ).
thf(func_def_105,type,
sK58: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_106,type,
sK59: multiset_a > multiset_a ).
thf(func_def_107,type,
sK60: multiset_a > a ).
thf(func_def_108,type,
sK61: ( tree_a > $o ) > a ).
thf(func_def_109,type,
sK62: ( tree_a > $o ) > tree_a ).
thf(func_def_110,type,
sK63: ( tree_a > $o ) > tree_a ).
thf(func_def_111,type,
sK64: multiset_a > a > multiset_a ).
thf(func_def_112,type,
sK65: multiset_a > a > multiset_a ).
thf(func_def_113,type,
sK66: multiset_a > a ).
thf(func_def_114,type,
sK67: ( a > a > $o ) > a ).
thf(func_def_115,type,
sK68: ( a > a > $o ) > a ).
thf(func_def_116,type,
sK69: ( a > a > $o ) > a ).
thf(func_def_117,type,
sK70: ( a > a > $o ) > a ).
thf(func_def_118,type,
sK71: set_Product_prod_a_a > multiset_a > multiset_a > a ).
thf(func_def_119,type,
sK72: set_Product_prod_a_a > multiset_a > multiset_a > multiset_a ).
thf(func_def_120,type,
sK73: set_Product_prod_a_a > multiset_a > multiset_a > multiset_a ).
thf(func_def_121,type,
sK74: tree_a > a > tree_a ).
thf(func_def_122,type,
sK75: tree_a > a > a ).
thf(func_def_123,type,
sK76: tree_a > a > tree_a ).
thf(func_def_124,type,
sK77: a > multiset_multiset_a > multiset_a ).
thf(func_def_125,type,
sK78: multiset_multiset_a > multiset_a ).
thf(func_def_126,type,
sK79: ( a > a ) > a ).
thf(func_def_127,type,
sK80: ( a > a ) > a ).
thf(func_def_128,type,
sK81: ( multiset_a > multiset_a > $o ) > multiset_a ).
thf(func_def_129,type,
sK82: ( multiset_a > multiset_a > $o ) > multiset_a ).
thf(func_def_130,type,
sK83: ( multiset_a > multiset_a > $o ) > a ).
thf(func_def_131,type,
sK84: ( multiset_a > multiset_a > $o ) > multiset_a ).
thf(func_def_132,type,
sK85: ( multiset_a > multiset_a > $o ) > multiset_a ).
thf(func_def_133,type,
sK86: ( multiset_a > multiset_a > $o ) > a ).
thf(func_def_134,type,
sK87: multiset_a > set_Product_prod_a_a > multiset_a > multiset_a ).
thf(func_def_135,type,
sK88: multiset_a > set_Product_prod_a_a > multiset_a > multiset_a ).
thf(func_def_136,type,
sK89: multiset_a > set_Product_prod_a_a > multiset_a > multiset_a ).
thf(func_def_137,type,
sK90: a > multiset_a > set_Product_prod_a_a > multiset_a > a ).
thf(func_def_138,type,
vNOT: $o > $o ).
thf(f1,axiom,
is_heap_a @ ( heapIm970322378pify_a @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_T_Ohyps_I2_J) ).
thf(f2,axiom,
is_heap_a @ ( heapIm970322378pify_a @ l ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_T_Ohyps_I1_J) ).
thf(f3,axiom,
( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
=> ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
=> ( ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062) ).
thf(f4,axiom,
! [X0: a,X2: tree_a,X1: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ X0 @ X1 @ X2 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X0 @ ( heapIm970322378pify_a @ X1 ) @ ( heapIm970322378pify_a @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_heapify_Osimps_I2_J) ).
thf(f143,conjecture,
is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f144,negated_conjecture,
~ ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ),
inference(negated_conjecture,[status(cth)],[f143]) ).
thf(f159,plain,
~ ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ),
inference(rectify,[],[f144]) ).
thf(f160,plain,
( ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) )
!= $true ),
inference(fool_elimination,[],[f159]) ).
thf(f171,plain,
( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
=> ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
=> ( ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f172,plain,
( ( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
= $true )
=> ( ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
= $true )
=> ( ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
=> ( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f171]) ).
thf(f246,plain,
is_heap_a @ ( heapIm970322378pify_a @ r ),
inference(rectify,[],[f1]) ).
thf(f247,plain,
( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
= $true ),
inference(fool_elimination,[],[f246]) ).
thf(f301,plain,
is_heap_a @ ( heapIm970322378pify_a @ l ),
inference(rectify,[],[f2]) ).
thf(f302,plain,
( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
= $true ),
inference(fool_elimination,[],[f301]) ).
thf(f350,plain,
( ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) )
!= $true ),
inference(flattening,[],[f160]) ).
thf(f418,plain,
( ( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) )
= $true )
| ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
!= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
| ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
!= $true )
| ( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
!= $true ) ),
inference(ennf_transformation,[],[f172]) ).
thf(f419,plain,
( ( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) )
= $true )
| ( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
!= $true )
| ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
!= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
| ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
!= $true ) ),
inference(flattening,[],[f418]) ).
thf(f580,plain,
! [X0: a,X1: tree_a,X2: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ X0 @ X2 @ X1 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X0 @ ( heapIm970322378pify_a @ X2 ) @ ( heapIm970322378pify_a @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f753,plain,
( ( ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) )
!= ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
| ( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
!= $true )
| ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
!= $true )
| ( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) )
= $true ) ),
inference(cnf_transformation,[],[f419]) ).
thf(f774,plain,
( ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) )
!= $true ),
inference(cnf_transformation,[],[f350]) ).
thf(f797,plain,
! [X2: tree_a,X0: a,X1: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ X0 @ X2 @ X1 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X0 @ ( heapIm970322378pify_a @ X2 ) @ ( heapIm970322378pify_a @ X1 ) ) ) ),
inference(cnf_transformation,[],[f580]) ).
thf(f835,plain,
( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
= $true ),
inference(cnf_transformation,[],[f247]) ).
thf(f935,plain,
( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
= $true ),
inference(cnf_transformation,[],[f302]) ).
thf(f1004,plain,
( ( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
!= $true )
| ( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) )
= $true )
| ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f753]) ).
thf(f1018,definition,
( spl91_2
<=> ( ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl91_2])],[avatar_definition]) ).
thf(f1020,plain,
( ( ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) )
!= $true )
| spl91_2 ),
inference(avatar_component_clause,[],[f1018]) ).
thf(f1021,plain,
~ spl91_2,
inference(avatar_split_clause,[],[f774,f1018]) ).
thf(f1048,definition,
( spl91_8
<=> ( ( is_heap_a @ ( heapIm970322378pify_a @ r ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl91_8])],[avatar_definition]) ).
thf(f1051,plain,
spl91_8,
inference(avatar_split_clause,[],[f835,f1048]) ).
thf(f1068,definition,
( spl91_12
<=> ( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl91_12])],[avatar_definition]) ).
thf(f1070,plain,
( ( ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) )
= $true )
| ~ spl91_12 ),
inference(avatar_component_clause,[],[f1068]) ).
thf(f1072,definition,
( spl91_13
<=> ( ( is_heap_a @ ( heapIm970322378pify_a @ l ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl91_13])],[avatar_definition]) ).
thf(f1075,plain,
( spl91_12
| ~ spl91_13
| ~ spl91_8 ),
inference(avatar_split_clause,[],[f1004,f1048,f1072,f1068]) ).
thf(f1076,plain,
spl91_13,
inference(avatar_split_clause,[],[f935,f1072]) ).
thf(f1172,plain,
( ( ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) )
= $true )
| ~ spl91_12 ),
inference(superposition,[],[f1070,f797]) ).
thf(f1174,plain,
( $false
| spl91_2
| ~ spl91_12 ),
inference(forward_subsumption_resolution,[],[f1172,f1020]) ).
thf(f1175,plain,
( spl91_2
| ~ spl91_12 ),
inference(avatar_contradiction_clause,[],[f1174]) ).
cnf(s2,plain,
~ spl91_2,
inference(sat_conversion,[],[f1021]) ).
cnf(s9,plain,
spl91_8,
inference(sat_conversion,[],[f1051]) ).
cnf(s14,plain,
( ~ spl91_8
| spl91_12
| ~ spl91_13 ),
inference(sat_conversion,[],[f1075]) ).
cnf(s15,plain,
spl91_13,
inference(sat_conversion,[],[f1076]) ).
cnf(s24,plain,
( spl91_2
| ~ spl91_12 ),
inference(sat_conversion,[],[f1175]) ).
cnf(s27,plain,
( ~ spl91_8
| spl91_12 ),
inference(rat,[],[s14,s15]) ).
cnf(s28,plain,
spl91_12,
inference(rat,[],[s27,s9]) ).
cnf(s29,plain,
spl91_2,
inference(rat,[],[s24,s28]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s2,s29]) ).
thf(f1176,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP069^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:45:51 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.36 % (2568577)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.36 % (2568586)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1161459581:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.36 % (2568588)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.36 % (2568588)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.36 % (2568582)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2624955537:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.36 % (2568586)Instruction limit reached!
% 0.23/0.36 % (2568586)------------------------------
% 0.23/0.36 % (2568586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (2568586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (2568586)CaDiCaL version: 2.1.3
% 0.23/0.36 % (2568584)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2195954885:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.37 % (2568586)Termination reason: Instruction limit
% 0.23/0.37 % (2568586)Termination phase: Preprocessing 3
% 0.23/0.37 % (2568586)Time elapsed: 0.006 s
% 0.23/0.37 % (2568586)Peak memory usage: 10 MB
% 0.23/0.37 % (2568586)Instructions burned: 27 (million)
% 0.23/0.37 % (2568583)lrs+10_16_si=on:nwc=1.5:random_seed=4155676105:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.37 % (2568587)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3594884220:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.37 % (2568585)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1853393861:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.37 % (2568588)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1762330175:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.37 % (2568584)Instruction limit reached!
% 0.23/0.37 % (2568584)------------------------------
% 0.23/0.37 % (2568584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (2568584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (2568584)CaDiCaL version: 2.1.3
% 0.23/0.37 % (2568584)Termination reason: Instruction limit
% 0.23/0.37 % (2568584)Termination phase: shuffling
% 0.23/0.37 % (2568584)Time elapsed: 0.002 s
% 0.23/0.37 % (2568584)Peak memory usage: 10 MB
% 0.23/0.37 % (2568584)Instructions burned: 5 (million)
% 0.23/0.37 % (2568583)Instruction limit reached!
% 0.23/0.37 % (2568583)------------------------------
% 0.23/0.37 % (2568583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (2568583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (2568583)CaDiCaL version: 2.1.3
% 0.23/0.37 % (2568583)Termination reason: Instruction limit
% 0.23/0.37 % (2568583)Termination phase: Property scanning
% 0.23/0.37 % (2568583)Time elapsed: 0.009 s
% 0.23/0.37 % (2568583)Peak memory usage: 10 MB
% 0.23/0.37 % (2568583)Instructions burned: 20 (million)
% 0.23/0.37 % (2568595)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2913695717:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.37 % (2568595)Instruction limit reached!
% 0.23/0.37 % (2568595)------------------------------
% 0.23/0.37 % (2568595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (2568595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (2568595)CaDiCaL version: 2.1.3
% 0.23/0.37 % (2568595)Termination reason: Instruction limit
% 0.23/0.37 % (2568595)Termination phase: Property scanning
% 0.23/0.37 % (2568595)Time elapsed: 0.003 s
% 0.23/0.37 % (2568595)Peak memory usage: 10 MB
% 0.23/0.37 % (2568595)Instructions burned: 16 (million)
% 0.23/0.37 % (2568597)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=523634973:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.37 % (2568597)Instruction limit reached!
% 0.23/0.37 % (2568597)------------------------------
% 0.23/0.37 % (2568597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (2568597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (2568597)CaDiCaL version: 2.1.3
% 0.23/0.37 % (2568597)Termination reason: Instruction limit
% 0.23/0.37 % (2568597)Termination phase: shuffling
% 0.23/0.37 % (2568597)Time elapsed: 0.003 s
% 0.23/0.37 % (2568597)Peak memory usage: 10 MB
% 0.23/0.37 % (2568597)Instructions burned: 6 (million)
% 0.23/0.37 % (2568600)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3720964436:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.23/0.37 % (2568600)Instruction limit reached!
% 0.23/0.37 % (2568600)------------------------------
% 0.23/0.37 % (2568600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (2568600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (2568600)CaDiCaL version: 2.1.3
% 0.23/0.37 % (2568600)Termination reason: Instruction limit
% 0.23/0.37 % (2568600)Termination phase: Property scanning
% 0.23/0.37 % (2568600)Time elapsed: 0.003 s
% 0.23/0.37 % (2568600)Peak memory usage: 10 MB
% 0.23/0.37 % (2568600)Instructions burned: 16 (million)
% 0.23/0.37 % (2568598)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.37 % (2568587)Instruction limit reached!
% 0.23/0.37 % (2568587)------------------------------
% 0.23/0.37 % (2568587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (2568587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (2568587)CaDiCaL version: 2.1.3
% 0.23/0.37 % (2568587)Termination reason: Instruction limit
% 0.23/0.37 % (2568587)Termination phase: Saturation
% 0.23/0.37 % (2568587)Time elapsed: 0.034 s
% 0.23/0.37 % (2568587)Peak memory usage: 12 MB
% 0.23/0.37 % (2568587)Instructions burned: 76 (million)
% 0.23/0.37 % (2568598)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=513029927:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.37 % (2568602)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.37 % (2568604)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2041970023:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.23/0.37 % (2568602)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.37 % (2568582)Instruction limit reached!
% 0.23/0.37 % (2568582)------------------------------
% 0.23/0.37 % (2568582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (2568582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (2568582)CaDiCaL version: 2.1.3
% 0.23/0.37 % (2568582)Termination reason: Instruction limit
% 0.23/0.37 % (2568582)Termination phase: Saturation
% 0.23/0.37 % (2568582)Time elapsed: 0.042 s
% 0.23/0.37 % (2568582)Peak memory usage: 13 MB
% 0.23/0.37 % (2568582)Instructions burned: 92 (million)
% 0.23/0.37 % (2568602)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2343601943:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.23/0.37 % (2568598)Instruction limit reached!
% 0.23/0.37 % (2568598)------------------------------
% 0.23/0.37 % (2568598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (2568598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (2568598)CaDiCaL version: 2.1.3
% 0.23/0.37 % (2568598)Termination reason: Instruction limit
% 0.23/0.37 % (2568598)Termination phase: shuffling
% 0.23/0.37 % (2568598)Time elapsed: 0.006 s
% 0.23/0.37 % (2568598)Peak memory usage: 10 MB
% 0.23/0.37 % (2568598)Instructions burned: 7 (million)
% 0.23/0.37 % (2568585) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2568577-2568585"...
% 0.23/0.37 % (2568585)...printing done.
% 0.23/0.37 % (2568585)Refutation found. Thanks to Tanya!
% 0.23/0.37 % SZS status Theorem for theBenchmark
% 0.23/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.71/0.37 % (2568585)------------------------------
% 0.71/0.37 % (2568585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.37 % (2568585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.37 % (2568585)CaDiCaL version: 2.1.3
% 0.71/0.37 % (2568585)Termination reason: Refutation
% 0.71/0.37 % (2568585)Time elapsed: 0.048 s
% 0.71/0.37 % (2568585)Peak memory usage: 14 MB
% 0.71/0.37 % (2568585)Instructions burned: 99 (million)
% 0.71/0.37 % (2568577)Success in time 0.102 s
% 0.71/0.37 % Vampire exiting
%------------------------------------------------------------------------------