%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN049^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:19:55 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 26 unt; 0 typ; 3 def)
% Number of atoms : 149 ( 57 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 557 ( 27 ~; 20 |; 5 &; 499 @)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 7 con; 0-5 aty)
% Number of variables : 55 ( 0 sgn 53 !; 2 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_1,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_2,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_3,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_4,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_5,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_6,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_7,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_8,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_9,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_10,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
sK0: 'type/nums/num' ).
thf(func_def_16,type,
sK1: 'type/nums/num' > 'type/nums/num' ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/nsum_') ).
thf(f2,axiom,
( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NEUTRAL_ADD_') ).
thf(f3,axiom,
! [X0: $tType,X2: X0 > X0 > X0,X1: 'type/nums/num' > X0] :
( ( 'const/iterate/monoidal' @ X0 @ X2 )
=> ( ! [X3: 'type/nums/num',X4: 'type/nums/num'] :
( ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ X1 )
= ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ ( X2 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) @ ( X1 @ ( 'const/nums/SUC' @ X4 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X1 ) ) )
& ! [X3: 'type/nums/num'] :
( ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 )
= ( 'const/class/COND' @ X0
@ ( X3
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_NUMSEG_') ).
thf(f4,axiom,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_ADD_') ).
thf(f5,conjecture,
! [X1: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num'] :
( ( 'const/class/COND' @ 'type/nums/num'
@ ( X1
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_CLAUSES_NUMSEG_0') ).
thf(f6,negated_conjecture,
~ ! [X1: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num'] :
( ( 'const/class/COND' @ 'type/nums/num'
@ ( X1
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
inference(rectify,[],[f4]) ).
thf(f8,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > X0 > X0,X2: 'type/nums/num' > X0] :
( ( 'const/iterate/monoidal' @ X0 @ X1 )
=> ( ! [X3: 'type/nums/num',X4: 'type/nums/num'] :
( ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ ( X1 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X2 ) @ ( X2 @ ( 'const/nums/SUC' @ X4 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X2 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ X2 ) )
& ! [X5: 'type/nums/num'] :
( ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X2 )
= ( 'const/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X5 )
@ ( X2 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > X0 > X0,X2: 'type/nums/num' > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true )
=> ( ! [X4: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ ( X1 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X2 ) @ ( X2 @ ( 'const/nums/SUC' @ X4 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X2 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ X2 ) )
& ! [X5: 'type/nums/num'] :
( ( 'const/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X5 )
@ ( X2 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X1 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X2 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X0 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
~ ! [X1: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num'] :
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X0 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > X0 > X0,X2: 'type/nums/num' > X0] :
( ( ! [X4: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ ( X1 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X2 ) @ ( X2 @ ( 'const/nums/SUC' @ X4 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X3 @ X4 ) @ X2 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/SUC' @ X4 ) ) @ X2 ) )
& ! [X5: 'type/nums/num'] :
( ( 'const/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X5 )
@ ( X2 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X1 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X2 ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f14,plain,
? [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X0 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > X0 > X0,X2: 'type/nums/num' > X0] :
( ( ! [X3: 'type/nums/num',X4: 'type/nums/num'] :
( ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X4 @ ( 'const/nums/SUC' @ X3 ) ) @ X2 )
= ( 'const/class/COND' @ X0 @ ( 'const/arith/<=' @ X4 @ ( 'const/nums/SUC' @ X3 ) ) @ ( X1 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X4 @ X3 ) @ X2 ) @ ( X2 @ ( 'const/nums/SUC' @ X3 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X4 @ X3 ) @ X2 ) ) )
& ! [X5: 'type/nums/num'] :
( ( 'const/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X5 )
@ ( X2 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X1 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X2 ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true ) ),
inference(rectify,[],[f13]) ).
thf(f16,plain,
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK0 )
@ ( sK1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
thf(f17,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f19,plain,
! [X0: $tType,X2: 'type/nums/num' > X0,X1: X0 > X0 > X0,X5: 'type/nums/num'] :
( ( ( 'const/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X5 )
@ ( X2 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X1 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X1 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X2 ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f21,plain,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f22,plain,
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK0 )
@ ( sK1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK1 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,definition,
( spl2_1
<=> ( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK0 )
@ ( sK1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f27,plain,
( ( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK0 )
@ ( sK1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK1 ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f28,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f22,f25]) ).
thf(f30,definition,
( spl2_2
<=> ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f32,plain,
( ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
spl2_2,
inference(avatar_split_clause,[],[f17,f30]) ).
thf(f35,definition,
( spl2_3
<=> ( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f37,plain,
( ( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
spl2_3,
inference(avatar_split_clause,[],[f18,f35]) ).
thf(f39,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ X1 )
= ( 'const/iterate/nsum' @ X0 @ X1 ) ),
inference(argument_congruence,[],[f21]) ).
thf(f51,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ X1 @ X2 ) ),
inference(argument_congruence,[],[f39]) ).
thf(f54,plain,
( ! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| ( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X0 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/iterate/..' @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ) )
| ~ spl2_3 ),
inference(superposition,[],[f19,f37]) ).
thf(f56,plain,
( ! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X0 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/iterate/..' @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f54,f32]) ).
thf(f66,plain,
( ( ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/iterate/..' @ sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK1 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK1 ) )
| spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[],[f27,f56]) ).
thf(f73,plain,
( $false
| spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f66,f51]) ).
thf(f74,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f73]) ).
cnf(s1,plain,
~ spl2_1,
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
spl2_2,
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
spl2_3,
inference(sat_conversion,[],[f38]) ).
cnf(s5,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f74]) ).
cnf(s6,plain,
spl2_1,
inference(rat,[],[s5,s3,s2]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6]) ).
thf(f76,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN049^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n020.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:08:20 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.22 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
% 0.07/0.26 % (1022741)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.26 % (1022749)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=4201805520: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)
% 0.07/0.26 % (1022752)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.07/0.26 % (1022752)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
% 0.07/0.26 % (1022749) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1022741-1022749"...
% 0.07/0.26 % (1022749)...printing done.
% 0.07/0.26 % (1022749)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.26 % (1022749)------------------------------
% 0.21/0.26 % (1022749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (1022749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (1022749)CaDiCaL version: 2.1.3
% 0.21/0.26 % (1022749)Termination reason: Refutation
% 0.21/0.26 % (1022749)Time elapsed: 0.005 s
% 0.21/0.26 % (1022749)Peak memory usage: 13 MB
% 0.21/0.26 % (1022749)Instructions burned: 14 (million)
% 0.21/0.26 % (1022741)Success in time 0.032 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------