%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP101^1 : 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 : n004.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 08:08:21 AM UTC 2026
% Result : Theorem 0.58s 0.41s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 144 ( 56 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 370 ( 32 ~; 18 |; 15 &; 279 @)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 150 ( 147 usr; 8 con; 0-4 aty)
% Number of variables : 7 ( 0 sgn 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
list_nat: $tType ).
thf(type_def_6,type,
set_nat: $tType ).
thf(type_def_7,type,
list_a: $tType ).
thf(type_def_8,type,
set_a: $tType ).
thf(type_def_9,type,
nat: $tType ).
thf(type_def_10,type,
a: $tType ).
thf(type_def_11,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_1,type,
one_one_nat: nat ).
thf(func_def_2,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_3,type,
if_a: $o > a > a > a ).
thf(func_def_4,type,
list_asc_nat: list_nat > $o ).
thf(func_def_5,type,
list_desc_nat: list_nat > $o ).
thf(func_def_6,type,
list_strict_asc_nat: list_nat > $o ).
thf(func_def_7,type,
list_strict_desc_nat: list_nat > $o ).
thf(func_def_8,type,
listIn923761578nd_nat: list_nat > ( nat > nat ) > nat > nat ).
thf(func_def_9,type,
listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).
thf(func_def_10,type,
append_nat: list_nat > list_nat > list_nat ).
thf(func_def_11,type,
append_a: list_a > list_a > list_a ).
thf(func_def_12,type,
butlast_nat: list_nat > list_nat ).
thf(func_def_13,type,
butlast_a: list_a > list_a ).
thf(func_def_14,type,
set_nat2: list_nat > set_nat ).
thf(func_def_15,type,
set_a2: list_a > set_a ).
thf(func_def_16,type,
list_ex_nat: ( nat > $o ) > list_nat > $o ).
thf(func_def_17,type,
list_ex_a: ( a > $o ) > list_a > $o ).
thf(func_def_18,type,
list_update_nat: list_nat > nat > nat > list_nat ).
thf(func_def_19,type,
list_update_a: list_a > nat > a > list_a ).
thf(func_def_20,type,
nth_nat: list_nat > nat > nat ).
thf(func_def_21,type,
nth_a: list_a > nat > a ).
thf(func_def_22,type,
size_size_list_nat: list_nat > nat ).
thf(func_def_23,type,
size_size_list_a: list_a > nat ).
thf(func_def_24,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_25,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_26,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_27,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_28,type,
member_nat: nat > set_nat > $o ).
thf(func_def_29,type,
member_a: a > set_a > $o ).
thf(func_def_30,type,
f: nat > a ).
thf(func_def_31,type,
g: nat > a ).
thf(func_def_32,type,
x: nat ).
thf(func_def_33,type,
xs: list_a ).
thf(func_def_34,type,
ys: list_a ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
sP0: nat > nat > nat > $o ).
thf(func_def_50,type,
sP1: nat > nat > nat > $o ).
thf(func_def_51,type,
sK2: ( nat > nat > $o ) > nat ).
thf(func_def_52,type,
sK3: ( nat > nat > $o ) > nat ).
thf(func_def_53,type,
sK4: ( nat > nat > $o ) > nat ).
thf(func_def_54,type,
sK5: ( nat > nat > $o ) > nat ).
thf(func_def_55,type,
sK6: ( nat > nat ) > nat ).
thf(func_def_56,type,
sK7: ( nat > nat ) > nat ).
thf(func_def_57,type,
sK8: list_a > ( a > $o ) > nat ).
thf(func_def_58,type,
sK9: ( nat > nat ) > nat ).
thf(func_def_59,type,
sK10: ( nat > nat ) > nat ).
thf(func_def_60,type,
sK11: list_a > ( a > $o ) > a ).
thf(func_def_61,type,
sK12: ( nat > $o ) > nat ).
thf(func_def_62,type,
sK13: ( nat > nat > $o ) > nat ).
thf(func_def_63,type,
sK14: ( nat > nat > $o ) > nat ).
thf(func_def_64,type,
sK15: ( nat > nat > $o ) > nat ).
thf(func_def_65,type,
sK16: ( nat > nat > $o ) > nat ).
thf(func_def_66,type,
sK17: ( nat > nat > $o ) > nat ).
thf(func_def_67,type,
sK18: nat > nat ).
thf(func_def_68,type,
sK19: ( nat > $o ) > list_nat > nat ).
thf(func_def_69,type,
sK20: nat > nat ).
thf(func_def_70,type,
sK21: ( nat > nat ) > nat ).
thf(func_def_71,type,
sK22: ( nat > nat ) > nat ).
thf(func_def_72,type,
sK23: a > list_a > nat ).
thf(func_def_73,type,
sK24: list_nat > nat > nat ).
thf(func_def_74,type,
sK25: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_75,type,
sK26: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_76,type,
sK27: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_77,type,
sK28: nat > nat ).
thf(func_def_78,type,
sK29: nat > nat ).
thf(func_def_79,type,
sK30: ( nat > nat ) > nat ).
thf(func_def_80,type,
sK31: ( nat > nat ) > nat ).
thf(func_def_81,type,
sK32: nat > nat ).
thf(func_def_82,type,
sK33: nat > nat ).
thf(func_def_83,type,
sK34: ( a > $o ) > ( a > $o ) > list_a > a ).
thf(func_def_84,type,
sK35: ( list_nat > $o ) > list_nat ).
thf(func_def_85,type,
sK36: ( nat > $o ) > nat > nat ).
thf(func_def_86,type,
sK37: ( nat > $o ) > nat > nat ).
thf(func_def_87,type,
sK38: list_a > list_a > nat ).
thf(func_def_88,type,
sK39: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_89,type,
sK40: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_90,type,
sK41: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_91,type,
sK42: list_nat > ( nat > $o ) > nat ).
thf(func_def_92,type,
sK43: list_nat > ( nat > $o ) > nat ).
thf(func_def_93,type,
sK44: ( a > $o ) > list_a > a ).
thf(func_def_94,type,
sK45: ( a > $o ) > list_a > nat ).
thf(func_def_95,type,
sK46: ( nat > $o ) > nat ).
thf(func_def_96,type,
sK47: ( nat > $o ) > nat > nat ).
thf(func_def_97,type,
sK48: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_98,type,
sK49: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_99,type,
sK50: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_100,type,
sK51: nat > nat ).
thf(func_def_101,type,
sK52: set_a > list_a > a ).
thf(func_def_102,type,
sK53: ( list_a > $o ) > list_a ).
thf(func_def_103,type,
sK54: ( nat > nat ) > nat ).
thf(func_def_104,type,
sK55: ( nat > nat ) > nat ).
thf(func_def_105,type,
sK56: list_nat > list_nat > nat ).
thf(func_def_106,type,
sK57: ( nat > nat ) > nat ).
thf(func_def_107,type,
sK58: ( nat > nat ) > nat ).
thf(func_def_108,type,
sK59: nat > list_nat ).
thf(func_def_109,type,
sK60: ( nat > $o ) > nat ).
thf(func_def_110,type,
sK61: nat > nat ).
thf(func_def_111,type,
sK62: ( nat > nat ) > nat ).
thf(func_def_112,type,
sK63: ( nat > nat ) > nat ).
thf(func_def_113,type,
sK64: nat > nat ).
thf(func_def_114,type,
sK65: nat > nat ).
thf(func_def_115,type,
sK66: nat > ( nat > a > $o ) > a ).
thf(func_def_116,type,
sK67: list_a > nat > ( nat > a > $o ) > nat ).
thf(func_def_117,type,
sK68: nat > ( nat > a > $o ) > list_a ).
thf(func_def_118,type,
sK69: nat > ( nat > a > $o ) > nat ).
thf(func_def_119,type,
sK70: ( nat > $o ) > nat ).
thf(func_def_120,type,
sK71: ( nat > nat ) > nat ).
thf(func_def_121,type,
sK72: ( nat > nat ) > nat ).
thf(func_def_122,type,
sK73: list_a > list_a > list_a > list_a > list_a ).
thf(func_def_123,type,
sK74: ( nat > nat ) > nat ).
thf(func_def_124,type,
sK75: ( nat > nat ) > nat ).
thf(func_def_125,type,
sK76: ( nat > nat ) > nat ).
thf(func_def_126,type,
sK77: ( nat > nat ) > nat ).
thf(func_def_127,type,
sK78: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_128,type,
sK79: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_129,type,
sK80: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_130,type,
sK81: ( nat > nat ) > nat ).
thf(func_def_131,type,
sK82: ( nat > nat ) > nat ).
thf(func_def_132,type,
sK83: nat > nat ).
thf(func_def_133,type,
sK84: ( nat > nat ) > nat ).
thf(func_def_134,type,
sK85: ( nat > nat ) > nat ).
thf(func_def_135,type,
sK86: list_nat > ( nat > $o ) > nat ).
thf(func_def_136,type,
sK87: nat > ( nat > nat > $o ) > nat ).
thf(func_def_137,type,
sK88: list_nat > nat > ( nat > nat > $o ) > nat ).
thf(func_def_138,type,
sK89: nat > ( nat > nat > $o ) > list_nat ).
thf(func_def_139,type,
sK90: nat > ( nat > nat > $o ) > nat ).
thf(func_def_140,type,
sK91: ( nat > $o ) > nat > nat > nat ).
thf(func_def_141,type,
sK92: nat > ( nat > $o ) > nat > nat ).
thf(func_def_142,type,
sK93: nat > list_a ).
thf(func_def_143,type,
sK94: nat > nat ).
thf(func_def_144,type,
sK95: ( nat > nat ) > nat ).
thf(func_def_145,type,
sK96: ( nat > nat ) > nat ).
thf(func_def_146,type,
sK97: nat > nat ).
thf(f265,axiom,
! [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) ) )
& ( ~ ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) )
= ( nth_a @ ys @ X0 ) ) ) ) )
& ( ~ ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( nth_a @ xs @ X0 )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) )
& ( ~ ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(f266,axiom,
ord_less_nat @ x @ ( size_size_list_a @ ys ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(f267,conjecture,
( ( nth_a @ xs @ x )
= ( nth_a @ ys @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(f268,negated_conjecture,
( ( nth_a @ xs @ x )
!= ( nth_a @ ys @ x ) ),
inference(negated_conjecture,[status(cth)],[f267]) ).
thf(f702,plain,
ord_less_nat @ x @ ( size_size_list_a @ ys ),
inference(rectify,[],[f266]) ).
thf(f703,plain,
( ( ord_less_nat @ x @ ( size_size_list_a @ ys ) )
= $true ),
inference(fool_elimination,[],[f702]) ).
thf(f706,plain,
! [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) ) )
& ( ~ ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) )
= ( nth_a @ ys @ X0 ) ) ) ) )
& ( ~ ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( nth_a @ xs @ X0 )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) )
& ( ~ ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
=> ( ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) ) ) ) ),
inference(rectify,[],[f265]) ).
thf(f707,plain,
! [X0: nat] :
( ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
= $true )
=> ( ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
= $true )
=> ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) ) )
& ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
=> ( ( nth_a @ ys @ X0 )
= ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) ) ) ) ) )
& ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
=> ( ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
= $true )
=> ( ( nth_a @ xs @ X0 )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) )
& ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
=> ( ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f706]) ).
thf(f760,plain,
( ( nth_a @ xs @ x )
!= ( nth_a @ ys @ x ) ),
inference(flattening,[],[f268]) ).
thf(f788,plain,
! [X0: nat] :
( ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
= $true )
=> ( ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
=> ( ( nth_a @ ys @ X0 )
= ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) ) ) )
& ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
= $true )
=> ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) ) ) ) )
& ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
=> ( ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
= $true )
=> ( ( nth_a @ xs @ X0 )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) )
& ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
=> ( ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) ) ) ) ),
inference(flattening,[],[f707]) ).
thf(f964,plain,
! [X0: nat] :
( ( ( ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
| ( ( nth_a @ xs @ X0 )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) )
& ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
= $true )
| ( ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) )
= ( g @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ ys ) ) ) ) ) )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
= $true ) )
& ( ( ( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
| ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) ) )
& ( ( ( nth_a @ ys @ X0 )
= ( f @ ( minus_minus_nat @ X0 @ ( size_size_list_a @ xs ) ) ) )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
= $true ) ) )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f788]) ).
thf(f1316,plain,
( ( nth_a @ xs @ x )
!= ( nth_a @ ys @ x ) ),
inference(cnf_transformation,[],[f760]) ).
thf(f1370,plain,
! [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
| ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) ) ),
inference(cnf_transformation,[],[f964]) ).
thf(f1546,plain,
( ( ord_less_nat @ x @ ( size_size_list_a @ ys ) )
= $true ),
inference(cnf_transformation,[],[f703]) ).
thf(f2029,plain,
! [X0: nat] :
( ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true ) ),
inference(duplicate_literal_removal,[],[f1370]) ).
thf(f2082,definition,
( spl98_8
<=> ( ( ord_less_nat @ x @ ( size_size_list_a @ ys ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl98_8])],[avatar_definition]) ).
thf(f2084,plain,
( ( ( ord_less_nat @ x @ ( size_size_list_a @ ys ) )
= $true )
| ~ spl98_8 ),
inference(avatar_component_clause,[],[f2082]) ).
thf(f2085,plain,
spl98_8,
inference(avatar_split_clause,[],[f1546,f2082]) ).
thf(f2149,definition,
( spl98_22
<=> ( ( nth_a @ xs @ x )
= ( nth_a @ ys @ x ) ) ),
introduced(definition,[new_symbols(definition,[spl98_22])],[avatar_definition]) ).
thf(f2151,plain,
( ( ( nth_a @ xs @ x )
!= ( nth_a @ ys @ x ) )
| spl98_22 ),
inference(avatar_component_clause,[],[f2149]) ).
thf(f2152,plain,
~ spl98_22,
inference(avatar_split_clause,[],[f1316,f2149]) ).
thf(f2189,plain,
( ( ( ord_less_nat @ x @ ( size_size_list_a @ ys ) )
!= $true )
| ( ( nth_a @ ys @ x )
!= ( nth_a @ ys @ x ) )
| spl98_22 ),
inference(superposition,[],[f2151,f2029]) ).
thf(f2191,plain,
( ( ( ord_less_nat @ x @ ( size_size_list_a @ ys ) )
!= $true )
| spl98_22 ),
inference(trivial_inequality_removal,[],[f2189]) ).
thf(f2192,plain,
( $false
| ~ spl98_8
| spl98_22 ),
inference(forward_subsumption_resolution,[],[f2191,f2084]) ).
thf(f2193,plain,
( ~ spl98_8
| spl98_22 ),
inference(avatar_contradiction_clause,[],[f2192]) ).
cnf(s9,plain,
spl98_8,
inference(sat_conversion,[],[f2085]) ).
cnf(s25,plain,
~ spl98_22,
inference(sat_conversion,[],[f2152]) ).
cnf(s39,plain,
( ~ spl98_8
| spl98_22 ),
inference(sat_conversion,[],[f2193]) ).
cnf(s40,plain,
~ spl98_8,
inference(rat,[],[s39,s25]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s9,s40]) ).
thf(f2194,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP101^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 19:53:37 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.20/0.28 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
% 0.58/0.41 % (1756145)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.58/0.41 % (1756155)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=434375998:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.58/0.41 % (1756156)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.58/0.41 % (1756156)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
% 0.58/0.41 % (1756154)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3316083349:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.58/0.41 % (1756151)lrs+10_16_si=on:nwc=1.5:random_seed=9784889:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.58/0.41 % (1756152)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3038184212:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.58/0.41 % (1756153)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=1423179974: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)
% 0.58/0.41 % (1756156)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=855488206:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.58/0.41 % (1756152)Instruction limit reached!
% 0.58/0.41 % (1756152)------------------------------
% 0.58/0.41 % (1756152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756152)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756152)Termination reason: Instruction limit
% 0.58/0.41 % (1756152)Termination phase: shuffling
% 0.58/0.41 % (1756152)Time elapsed: 0.003 s
% 0.58/0.41 % (1756152)Peak memory usage: 10 MB
% 0.58/0.41 % (1756152)Instructions burned: 5 (million)
% 0.58/0.41 % (1756150)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3087431419:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.58/0.41 % (1756151)Instruction limit reached!
% 0.58/0.41 % (1756151)------------------------------
% 0.58/0.41 % (1756151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756151)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756151)Termination reason: Instruction limit
% 0.58/0.41 % (1756151)Termination phase: Property scanning
% 0.58/0.41 % (1756151)Time elapsed: 0.009 s
% 0.58/0.41 % (1756151)Peak memory usage: 10 MB
% 0.58/0.41 % (1756151)Instructions burned: 20 (million)
% 0.58/0.41 % (1756155)Instruction limit reached!
% 0.58/0.41 % (1756155)------------------------------
% 0.58/0.41 % (1756155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756155)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756155)Termination reason: Instruction limit
% 0.58/0.41 % (1756155)Termination phase: Function definition elimination
% 0.58/0.41 % (1756155)Time elapsed: 0.020 s
% 0.58/0.41 % (1756155)Peak memory usage: 12 MB
% 0.58/0.41 % (1756155)Instructions burned: 79 (million)
% 0.58/0.41 % (1756154)Instruction limit reached!
% 0.58/0.41 % (1756154)------------------------------
% 0.58/0.41 % (1756154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756154)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756154)Termination reason: Instruction limit
% 0.58/0.41 % (1756154)Termination phase: Preprocessing 1
% 0.58/0.41 % (1756154)Time elapsed: 0.014 s
% 0.58/0.41 % (1756154)Peak memory usage: 10 MB
% 0.58/0.41 % (1756154)Instructions burned: 31 (million)
% 0.58/0.41 % (1756163)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2396515493:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.58/0.41 % (1756163)Instruction limit reached!
% 0.58/0.41 % (1756163)------------------------------
% 0.58/0.41 % (1756163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756163)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756163)Termination reason: Instruction limit
% 0.58/0.41 % (1756163)Termination phase: shuffling
% 0.58/0.41 % (1756163)Time elapsed: 0.001 s
% 0.58/0.41 % (1756163)Peak memory usage: 10 MB
% 0.58/0.41 % (1756163)Instructions burned: 5 (million)
% 0.58/0.41 % (1756165)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1838932872:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.58/0.41 % (1756167)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2074677921:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.58/0.41 % (1756166)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.58/0.41 % (1756165)Instruction limit reached!
% 0.58/0.41 % (1756165)------------------------------
% 0.58/0.41 % (1756165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756165)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756165)Termination reason: Instruction limit
% 0.58/0.41 % (1756165)Termination phase: shuffling
% 0.58/0.41 % (1756165)Time elapsed: 0.003 s
% 0.58/0.41 % (1756165)Peak memory usage: 10 MB
% 0.58/0.41 % (1756165)Instructions burned: 6 (million)
% 0.58/0.41 % (1756167)Instruction limit reached!
% 0.58/0.41 % (1756167)------------------------------
% 0.58/0.41 % (1756167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756167)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756167)Termination reason: Instruction limit
% 0.58/0.41 % (1756167)Termination phase: shuffling
% 0.58/0.41 % (1756167)Time elapsed: 0.003 s
% 0.58/0.41 % (1756167)Peak memory usage: 10 MB
% 0.58/0.41 % (1756167)Instructions burned: 13 (million)
% 0.58/0.41 % (1756166)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2808772847:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.58/0.41 % (1756166)Instruction limit reached!
% 0.58/0.41 % (1756166)------------------------------
% 0.58/0.41 % (1756166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756166)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756166)Termination reason: Instruction limit
% 0.58/0.41 % (1756166)Termination phase: shuffling
% 0.58/0.41 % (1756166)Time elapsed: 0.004 s
% 0.58/0.41 % (1756166)Peak memory usage: 10 MB
% 0.58/0.41 % (1756166)Instructions burned: 7 (million)
% 0.58/0.41 % (1756173)lrs+10_1_si=on:cs=on:random_seed=139984072:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.58/0.41 % (1756150)Instruction limit reached!
% 0.58/0.41 % (1756150)------------------------------
% 0.58/0.41 % (1756150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756150)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756150)Termination reason: Instruction limit
% 0.58/0.41 % (1756150)Termination phase: Property scanning
% 0.58/0.41 % (1756150)Time elapsed: 0.041 s
% 0.58/0.41 % (1756150)Peak memory usage: 12 MB
% 0.58/0.41 % (1756150)Instructions burned: 88 (million)
% 0.58/0.41 % (1756169)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
% 0.58/0.41 % (1756173)Instruction limit reached!
% 0.58/0.41 % (1756173)------------------------------
% 0.58/0.41 % (1756173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756173)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756173)Termination reason: Instruction limit
% 0.58/0.41 % (1756173)Termination phase: shuffling
% 0.58/0.41 % (1756173)Time elapsed: 0.002 s
% 0.58/0.41 % (1756173)Peak memory usage: 10 MB
% 0.58/0.41 % (1756173)Instructions burned: 10 (million)
% 0.58/0.41 % (1756169)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.58/0.41 % (1756169)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2380798915:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.58/0.41 % (1756172)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=464422912:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.58/0.41 % (1756175)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.58/0.41 % (1756178)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1613808191:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.58/0.41 % (1756175)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1696068870:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.58/0.41 % (1756175)Instruction limit reached!
% 0.58/0.41 % (1756175)------------------------------
% 0.58/0.41 % (1756175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756175)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756175)Termination reason: Instruction limit
% 0.58/0.41 % (1756175)Termination phase: shuffling
% 0.58/0.41 % (1756175)Time elapsed: 0.003 s
% 0.58/0.41 % (1756175)Peak memory usage: 10 MB
% 0.58/0.41 % (1756175)Instructions burned: 7 (million)
% 0.58/0.41 % (1756153) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1756145-1756153"...
% 0.58/0.41 % (1756169)Instruction limit reached!
% 0.58/0.41 % (1756169)------------------------------
% 0.58/0.41 % (1756169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756169)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756169)Termination reason: Instruction limit
% 0.58/0.41 % (1756169)Termination phase: shuffling
% 0.58/0.41 % (1756169)Time elapsed: 0.013 s
% 0.58/0.41 % (1756169)Peak memory usage: 10 MB
% 0.58/0.41 % (1756169)Instructions burned: 29 (million)
% 0.58/0.41 % (1756177)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1985971701:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.58/0.41 % (1756153)...printing done.
% 0.58/0.41 % (1756156)Instruction limit reached!
% 0.58/0.41 % (1756156)------------------------------
% 0.58/0.41 % (1756156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756153)Refutation found. Thanks to Tanya!
% 0.58/0.41 % SZS status Theorem for theBenchmark
% 0.58/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.58/0.41 % (1756153)------------------------------
% 0.58/0.41 % (1756153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (1756153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (1756153)CaDiCaL version: 2.1.3
% 0.58/0.41 % (1756153)Termination reason: Refutation
% 0.58/0.41 % (1756153)Time elapsed: 0.070 s
% 0.58/0.41 % (1756153)Peak memory usage: 14 MB
% 0.58/0.41 % (1756153)Instructions burned: 151 (million)
% 0.58/0.41 % (1756145)Success in time 0.118 s
% 0.58/0.41 % Vampire exiting
%------------------------------------------------------------------------------