%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN049^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:27:15 AM UTC 2026
% Result : Theorem 1.63s 1.38s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 51 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 466 ( 12 ~; 3 |; 4 &; 443 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 4 con; 0-5 aty)
% Number of variables : 46 ( 0 ^; 42 !; 4 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_2,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_3,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_4,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_5,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_6,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_7,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_8,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_9,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_10,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_11,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_13,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK0: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_18,type,
sK1: 'type/nums/num' ).
thf(func_def_20,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f30,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK1 )
@ ( sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK1 )
@ ( sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(superposition,[status(thm)],[f23,f26]) ).
thf(f26,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 ) ),
inference(forward_demodulation,[status(thm)],[f25,f17]) ).
thf(f17,plain,
( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ),
file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/NEUTRAL_ADD_') ).
thf(f25,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/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/iterate/..' @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( $true != $true )
| ( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X0 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/iterate/..' @ X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ) ),
inference(superposition,[status(thm)],[f18,f22]) ).
thf(f22,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/MONOIDAL_ADD_') ).
thf(f18,plain,
! [X0: $tType,X2: X0 > X0 > X0,X1: 'type/nums/num' > X0,X5: 'type/nums/num'] :
( ( ( 'const/iterate/monoidal' @ X0 @ X2 )
!= $true )
| ( ( 'const/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X5 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X2 )
!= $true )
| ( ! [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 ) ) )
& ! [X5: 'type/nums/num'] :
( ( 'const/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X5 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X2 )
= $true )
=> ( ! [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 ) ) )
& ! [X5: 'type/nums/num'] :
( ( 'const/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X5 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > 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 ) ) )
& ! [X5: 'type/nums/num'] :
( ( 'const/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X5 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X5 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > 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/class/COND' @ X0
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X3 )
@ ( X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/iterate/neutral' @ X0 @ X2 ) )
= ( 'const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ( 'const/iterate/..' @ X3 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/ITERATE_CLAUSES_NUMSEG_') ).
thf(f23,plain,
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK1 )
@ ( sK0 @ ( '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/..' @ sK1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f20,f21]) ).
thf(f21,plain,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/nsum_') ).
thf(f20,plain,
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK1 )
@ ( sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK1 )
@ ( sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15]) ).
thf(f15,plain,
( ? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X0 )
!= ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X1 )
@ ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
=> ( ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= sK1 )
@ ( sK0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X0 )
!= ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X1 )
@ ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X0 )
= ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X1 )
@ ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X0 )
= ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X1 )
@ ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ X0 )
= ( 'const/class/COND' @ 'type/nums/num'
@ ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= X1 )
@ ( X0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/NSUM_CLAUSES_NUMSEG_0') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUN049^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n019.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 11:19:54 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : NUN049^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.39 % Domain : Number theory
% 0.16/0.39 % Problem : NSUM_CLAUSES_NUMSEG_0
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Kal16]
% 0.16/0.39 % Names : NSUM_CLAUSES_NUMSEG_0.p [Kal16]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.00 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.16/0.39 % Syntax : Number of formulae : 17 ( 4 unt; 12 typ; 1 def)
% 0.16/0.39 % Number of atoms : 15 ( 7 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 3 ( 3 avg)
% 0.16/0.39 % Number of connectives : 77 ( 0 ~; 0 |; 1 &; 75 @)
% 0.16/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 8 ( 3 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 12 ( 11 usr; 1 con; 0-5 aty)
% 0.16/0.39 % Number of variables : 15 ( 0 ^; 9 !; 0 ?; 15 :)
% 0.16/0.39 % ( 6 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.39 % SPC : TH1_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : Exported from core HOL Light.
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf('thf_type_type/nums/num',type,
% 0.16/0.39 'type/nums/num': $tType ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/nums/SUC',type,
% 0.16/0.39 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/nums/NUMERAL',type,
% 0.16/0.39 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/nums/_0',type,
% 0.16/0.39 'const/nums/_0': 'type/nums/num' ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/iterate/nsum',type,
% 0.16/0.39 'const/iterate/nsum':
% 0.16/0.39 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/iterate/neutral',type,
% 0.16/0.39 'const/iterate/neutral':
% 0.16/0.39 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/iterate/monoidal',type,
% 0.16/0.39 'const/iterate/monoidal':
% 0.16/0.39 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/iterate/iterate',type,
% 0.16/0.39 'const/iterate/iterate':
% 0.16/0.39 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/iterate/..',type,
% 0.16/0.39 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/class/COND',type,
% 0.16/0.39 'const/class/COND':
% 0.16/0.39 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/arith/+',type,
% 0.16/0.39 'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 0.16/0.39
% 0.16/0.39 thf('thf_const_const/arith/<=',type,
% 0.16/0.39 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 0.16/0.39
% 0.16/0.39 thf('thm/iterate/nsum_',definition,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( 'const/iterate/nsum' @ A )
% 0.16/0.39 = ( 'const/iterate/iterate' @ A @ 'type/nums/num' @ 'const/arith/+' ) ) ).
% 0.16/0.39
% 0.16/0.39 thf('thm/iterate/NEUTRAL_ADD_',axiom,
% 0.16/0.39 ( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
% 0.16/0.39 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
% 0.16/0.39
% 0.16/0.39 thf('thm/iterate/ITERATE_CLAUSES_NUMSEG_',axiom,
% 0.16/0.39 ! [A: $tType,A0: 'type/nums/num' > A,A1: A > A > A] :
% 0.16/0.39 ( ( 'const/iterate/monoidal' @ A @ A1 )
% 0.16/0.39 => ( ! [A2: 'type/nums/num'] :
% 0.16/0.39 ( ( 'const/iterate/iterate' @ 'type/nums/num' @ A @ A1 @ ( 'const/iterate/..' @ A2 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ A0 )
% 0.16/0.39 = ( 'const/class/COND' @ A
% 0.16/0.39 @ ( A2
% 0.16/0.39 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 0.16/0.39 @ ( A0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 0.16/0.39 @ ( 'const/iterate/neutral' @ A @ A1 ) ) )
% 0.16/0.39 & ! [A2: 'type/nums/num',A3: 'type/nums/num'] :
% 0.16/0.39 ( ( 'const/iterate/iterate' @ 'type/nums/num' @ A @ A1 @ ( 'const/iterate/..' @ A2 @ ( 'const/nums/SUC' @ A3 ) ) @ A0 )
% 0.16/0.39 = ( 'const/class/COND' @ A @ ( 'const/arith/<=' @ A2 @ ( 'const/nums/SUC' @ A3 ) ) @ ( A1 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ A @ A1 @ ( 'const/iterate/..' @ A2 @ A3 ) @ A0 ) @ ( A0 @ ( 'const/nums/SUC' @ A3 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ A @ A1 @ ( 'const/iterate/..' @ A2 @ A3 ) @ A0 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf('thm/iterate/MONOIDAL_ADD_',axiom,
% 0.16/0.39 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' ).
% 0.16/0.39
% 0.16/0.39 thf('thm/iterate/NSUM_CLAUSES_NUMSEG_0',conjecture,
% 0.16/0.39 ! [A: 'type/nums/num' > 'type/nums/num',A0: 'type/nums/num'] :
% 0.16/0.39 ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ A )
% 0.16/0.39 = ( 'const/class/COND' @ 'type/nums/num'
% 0.16/0.39 @ ( A0
% 0.16/0.39 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 0.16/0.39 @ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 0.16/0.39 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.63/1.34 ---- Embedded in THF ---
% 1.63/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.34 %%% Generated on Tue Feb 24 11:19:55 EST 2026
% 1.63/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.34 %%% Logic specification used:
% 1.63/1.34 %%% thf(spec, logic, $$dhol).
% 1.63/1.34
% 1.63/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2DTF9333.p
% See solution above
% 1.63/1.34 ------------------------
% 1.63/1.35 ---- Cleaned THF ---
% 1.63/1.35 thf('thf_type_type/nums/num',type,
% 1.63/1.35 'type/nums/num': $tType ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/nums/SUC',type,
% 1.63/1.35 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/nums/NUMERAL',type,
% 1.63/1.35 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/nums/_0',type,
% 1.63/1.35 'const/nums/_0': 'type/nums/num' ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/iterate/nsum',type,
% 1.63/1.35 'const/iterate/nsum':
% 1.63/1.35 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/iterate/neutral',type,
% 1.63/1.35 'const/iterate/neutral':
% 1.63/1.35 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/iterate/monoidal',type,
% 1.63/1.35 'const/iterate/monoidal':
% 1.63/1.35 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/iterate/iterate',type,
% 1.63/1.35 'const/iterate/iterate':
% 1.63/1.35 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/iterate/..',type,
% 1.63/1.35 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/class/COND',type,
% 1.63/1.35 'const/class/COND':
% 1.63/1.35 !>[A: $tType] : ( $o > A > A > A ) ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/arith/+',type,
% 1.63/1.35 'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 1.63/1.35
% 1.63/1.35 thf('thf_const_const/arith/<=',type,
% 1.63/1.35 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 1.63/1.35
% 1.63/1.35 thf('thm/iterate/nsum_',definition,
% 1.63/1.35 ! [A: $tType] :
% 1.63/1.35 ( ( 'const/iterate/nsum' @ A )
% 1.63/1.35 = ( 'const/iterate/iterate' @ A @ 'type/nums/num' @ 'const/arith/+' ) ) ).
% 1.63/1.35
% 1.63/1.35 thf('thm/iterate/NEUTRAL_ADD_',axiom,
% 1.63/1.35 ( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
% 1.63/1.35 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
% 1.63/1.35
% 1.63/1.35 thf('thm/iterate/ITERATE_CLAUSES_NUMSEG_',axiom,
% 1.63/1.35 ! [A: $tType,A0: 'type/nums/num' > A,A1: A > A > A] :
% 1.63/1.35 ( ( 'const/iterate/monoidal' @ A @ A1 )
% 1.63/1.35 => ( ! [A2: 'type/nums/num'] :
% 1.63/1.35 ( ( 'const/iterate/iterate' @ 'type/nums/num' @ A @ A1 @ ( 'const/iterate/..' @ A2 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ A0 )
% 1.63/1.35 = ( 'const/class/COND' @ A
% 1.63/1.35 @ ( A2
% 1.63/1.35 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 1.63/1.35 @ ( A0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 1.63/1.35 @ ( 'const/iterate/neutral' @ A @ A1 ) ) )
% 1.63/1.35 & ! [A2: 'type/nums/num',A3: 'type/nums/num'] :
% 1.63/1.35 ( ( 'const/iterate/iterate' @ 'type/nums/num' @ A @ A1 @ ( 'const/iterate/..' @ A2 @ ( 'const/nums/SUC' @ A3 ) ) @ A0 )
% 1.63/1.35 = ( 'const/class/COND' @ A @ ( 'const/arith/<=' @ A2 @ ( 'const/nums/SUC' @ A3 ) ) @ ( A1 @ ( 'const/iterate/iterate' @ 'type/nums/num' @ A @ A1 @ ( 'const/iterate/..' @ A2 @ A3 ) @ A0 ) @ ( A0 @ ( 'const/nums/SUC' @ A3 ) ) ) @ ( 'const/iterate/iterate' @ 'type/nums/num' @ A @ A1 @ ( 'const/iterate/..' @ A2 @ A3 ) @ A0 ) ) ) ) ) ).
% 1.63/1.35
% 1.63/1.35 thf('thm/iterate/MONOIDAL_ADD_',axiom,
% 1.63/1.35 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' ).
% 1.63/1.35
% 1.63/1.35 thf('thm/iterate/NSUM_CLAUSES_NUMSEG_0',conjecture,
% 1.63/1.35 ! [A: 'type/nums/num' > 'type/nums/num',A0: 'type/nums/num'] :
% 1.63/1.35 ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ A )
% 1.63/1.35 = ( 'const/class/COND' @ 'type/nums/num'
% 1.63/1.35 @ ( A0
% 1.63/1.35 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 1.63/1.35 @ ( A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 1.63/1.35 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 1.63/1.35 ------------------------
% 1.63/1.37 % (9432)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9333 for (2999ds/183Mi)
% 1.63/1.37 % (9433)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_9333 for (2999ds/4Mi)
% 1.63/1.37 % (9434)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_9333 for (2999ds/27Mi)
% 1.63/1.37 % (9435)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9333 for (2999ds/2Mi)
% 1.63/1.37 % (9436)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_9333 for (2999ds/2Mi)
% 1.63/1.37 % (9437)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_9333 for (2999ds/275Mi)
% 1.63/1.37 % (9438)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9333 for (2999ds/18Mi)
% 1.63/1.37 % (9435)Instruction limit reached!
% 1.63/1.37 % (9435)------------------------------
% 1.63/1.37 % (9435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (9435)Termination reason: Unknown
% 1.63/1.37 % (9435)Termination phase: Saturation
% 1.63/1.37 % (9436)Instruction limit reached!
% 1.63/1.37 % (9436)------------------------------
% 1.63/1.37 % (9436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (9436)Termination reason: Unknown
% 1.63/1.37 % (9436)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (9436)Memory used [KB]: 1023
% 1.63/1.37 % (9436)Time elapsed: 0.003 s
% 1.63/1.37 % (9436)Instructions burned: 3 (million)
% 1.63/1.37 % (9436)------------------------------
% 1.63/1.37 % (9436)------------------------------
% 1.63/1.37
% 1.63/1.37 % (9435)Memory used [KB]: 1023
% 1.63/1.37 % (9435)Time elapsed: 0.003 s
% 1.63/1.37 % (9435)Instructions burned: 3 (million)
% 1.63/1.37 % (9435)------------------------------
% 1.63/1.37 % (9435)------------------------------
% 1.63/1.37 % (9437)Refutation not found, incomplete strategy
% 1.63/1.37 % (9437)------------------------------
% 1.63/1.37 % (9437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (9437)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.37
% 1.63/1.37
% 1.63/1.37 % (9437)Memory used [KB]: 5500
% 1.63/1.37 % (9437)Time elapsed: 0.003 s
% 1.63/1.37 % (9437)Instructions burned: 3 (million)
% 1.63/1.37 % (9437)------------------------------
% 1.63/1.37 % (9437)------------------------------
% 1.63/1.37 % (9433)Instruction limit reached!
% 1.63/1.37 % (9433)------------------------------
% 1.63/1.37 % (9433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (9433)Termination reason: Unknown
% 1.63/1.37 % (9433)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (9433)Memory used [KB]: 5500
% 1.63/1.37 % (9433)Time elapsed: 0.004 s
% 1.63/1.37 % (9433)Instructions burned: 5 (million)
% 1.63/1.37 % (9433)------------------------------
% 1.63/1.37 % (9433)------------------------------
% 1.63/1.37 % (9434)First to succeed.
% 1.63/1.38 % (9434)Refutation found. Thanks to Tanya!
% 1.63/1.38 % SZS status Theorem for DTF2THF_9333
% 1.63/1.38 % SZS output start Proof for DTF2THF_9333
% 1.63/1.38 thf(type_def_5, type, 'type/nums/num': $tType).
% 1.63/1.38 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.63/1.38 thf(func_def_1, type, 'const/nums/SUC': 'type/nums/num' > 'type/nums/num').
% 1.63/1.38 thf(func_def_2, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.63/1.38 thf(func_def_3, type, 'const/nums/_0': 'type/nums/num').
% 1.63/1.38 thf(func_def_4, type, 'const/iterate/nsum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num')).
% 1.63/1.38 thf(func_def_5, type, 'const/iterate/neutral': !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.63/1.38 thf(func_def_6, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 1.63/1.38 thf(func_def_7, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 1.63/1.38 thf(func_def_8, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 1.63/1.38 thf(func_def_9, type, 'const/class/COND': !>[X0: $tType]:($o > X0 > X0 > X0)).
% 1.63/1.38 thf(func_def_10, type, 'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num').
% 1.63/1.38 thf(func_def_11, type, 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o).
% 1.63/1.38 thf(func_def_13, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.38 thf(func_def_17, type, sK0: 'type/nums/num' > 'type/nums/num').
% 1.63/1.38 thf(func_def_18, type, sK1: 'type/nums/num').
% 1.63/1.38 thf(func_def_20, type, ph3: !>[X0: $tType]:(X0)).
% 1.63/1.38 thf(f30,plain,(
% 1.63/1.38 $false),
% 1.63/1.38 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.63/1.38 thf(f29,plain,(
% 1.63/1.38 (('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = sK1) @ (sK0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = sK1) @ (sK0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.63/1.38 inference(superposition,[status(thm)],[f23,f26])).
% 1.63/1.38 thf(f26,plain,(
% 1.63/1.38 ( ! [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))) )),
% 1.63/1.38 inference(forward_demodulation,[status(thm)],[f25,f17])).
% 1.63/1.38 thf(f17,plain,(
% 1.63/1.38 (('const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+') = ('const/nums/NUMERAL' @ 'const/nums/_0'))),
% 1.63/1.38 inference(cnf_transformation,[status(thm)],[f2])).
% 1.63/1.38 thf(f2,axiom,(
% 1.63/1.38 (('const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+') = ('const/nums/NUMERAL' @ 'const/nums/_0'))),
% 1.63/1.38 file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/NEUTRAL_ADD_')).
% 1.63/1.38 thf(f25,plain,(
% 1.63/1.38 ( ! [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/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+')) = ('const/iterate/iterate' @ 'type/nums/num' @ 'type/nums/num' @ 'const/arith/+' @ ('const/iterate/..' @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X1))) )),
% 1.63/1.38 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.63/1.38 thf(f24,plain,(
% 1.63/1.38 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num' > 'type/nums/num'] : (($true != $true) | (('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X0) @ (X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+')) = ('const/iterate/iterate' @ 'type/nums/num' @ 'type/nums/num' @ 'const/arith/+' @ ('const/iterate/..' @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X1))) )),
% 1.63/1.38 inference(superposition,[status(thm)],[f18,f22])).
% 1.63/1.38 thf(f22,plain,(
% 1.63/1.38 (('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+') = $true)),
% 1.63/1.38 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.38 thf(f12,plain,(
% 1.63/1.38 (('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+') = $true)),
% 1.63/1.38 inference(fool_elimination,[status(thm)],[f11])).
% 1.63/1.38 thf(f11,plain,(
% 1.63/1.38 ('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')),
% 1.63/1.38 inference(rectify,[status(thm)],[f4])).
% 1.63/1.38 thf(f4,axiom,(
% 1.63/1.38 ('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')),
% 1.63/1.38 file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/MONOIDAL_ADD_')).
% 1.63/1.38 thf(f18,plain,(
% 1.63/1.38 ( ! [X0 : $tType,X2 : X0 > X0 > X0,X1 : 'type/nums/num' > X0,X5 : 'type/nums/num'] : ((('const/iterate/monoidal' @ X0 @ X2) != $true) | (('const/class/COND' @ X0 @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X5) @ (X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/neutral' @ X0 @ X2)) = ('const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ('const/iterate/..' @ X5 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X1))) )),
% 1.63/1.38 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.38 thf(f14,plain,(
% 1.63/1.38 ! [X0 : $tType,X1 : 'type/nums/num' > X0,X2 : X0 > X0 > X0] : ((('const/iterate/monoidal' @ X0 @ X2) != $true) | (! [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))) & ! [X5 : 'type/nums/num'] : (('const/class/COND' @ X0 @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X5) @ (X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/neutral' @ X0 @ X2)) = ('const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ('const/iterate/..' @ X5 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X1))))),
% 1.63/1.38 inference(ennf_transformation,[status(thm)],[f9])).
% 1.63/1.38 thf(f9,plain,(
% 1.63/1.38 ! [X0 : $tType,X1 : 'type/nums/num' > X0,X2 : X0 > X0 > X0] : ((('const/iterate/monoidal' @ X0 @ X2) = $true) => (! [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))) & ! [X5 : 'type/nums/num'] : (('const/class/COND' @ X0 @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X5) @ (X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/neutral' @ X0 @ X2)) = ('const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ('const/iterate/..' @ X5 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X1))))),
% 1.63/1.38 inference(fool_elimination,[status(thm)],[f8])).
% 1.63/1.38 thf(f8,plain,(
% 1.63/1.38 ! [X0 : $tType,X1 : 'type/nums/num' > X0,X2 : X0 > X0 > 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))) & ! [X5 : 'type/nums/num'] : (('const/class/COND' @ X0 @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X5) @ (X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/neutral' @ X0 @ X2)) = ('const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ('const/iterate/..' @ X5 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X1))))),
% 1.63/1.38 inference(rectify,[status(thm)],[f3])).
% 1.63/1.38 thf(f3,axiom,(
% 1.63/1.38 ! [X0 : $tType,X1 : 'type/nums/num' > X0,X2 : X0 > X0 > 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/class/COND' @ X0 @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X3) @ (X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/neutral' @ X0 @ X2)) = ('const/iterate/iterate' @ 'type/nums/num' @ X0 @ X2 @ ('const/iterate/..' @ X3 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X1))))),
% 1.63/1.38 file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/ITERATE_CLAUSES_NUMSEG_')).
% 1.63/1.38 thf(f23,plain,(
% 1.63/1.38 (('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = sK1) @ (sK0 @ ('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/..' @ sK1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ sK0))),
% 1.63/1.38 inference(definition_unfolding,[status(thm)],[f20,f21])).
% 1.63/1.38 thf(f21,plain,(
% 1.63/1.38 ( ! [X0 : $tType] : (('const/iterate/nsum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+'))) )),
% 1.63/1.38 inference(cnf_transformation,[status(thm)],[f1])).
% 1.63/1.38 thf(f1,axiom,(
% 1.63/1.38 ! [X0 : $tType] : ('const/iterate/nsum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+'))),
% 1.63/1.38 file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/nsum_')).
% 1.63/1.38 thf(f20,plain,(
% 1.63/1.38 (('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = sK1) @ (sK0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ sK0))),
% 1.63/1.38 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.38 thf(f16,plain,(
% 1.63/1.38 (('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = sK1) @ (sK0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ sK0))),
% 1.63/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15])).
% 1.63/1.38 thf(f15,plain,(
% 1.63/1.38 ? [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num'] : (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X0) != ('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X1) @ (X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) => (('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = sK1) @ (sK0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ sK0))),
% 1.63/1.38 introduced(definition,[],[choice_axiom])).
% 1.63/1.38 thf(f13,plain,(
% 1.63/1.38 ? [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num'] : (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X0) != ('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X1) @ (X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.63/1.38 inference(ennf_transformation,[status(thm)],[f10])).
% 1.63/1.38 thf(f10,plain,(
% 1.63/1.38 ~! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num'] : (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X0) = ('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X1) @ (X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.63/1.38 inference(fool_elimination,[status(thm)],[f6])).
% 1.63/1.38 thf(f6,negated_conjecture,(
% 1.63/1.38 ~! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num'] : (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X0) = ('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X1) @ (X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.63/1.38 inference(negated_conjecture,[status(cth)],[f5])).
% 1.63/1.38 thf(f5,conjecture,(
% 1.63/1.38 ! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num'] : (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ X0) = ('const/class/COND' @ 'type/nums/num' @ (('const/nums/NUMERAL' @ 'const/nums/_0') = X1) @ (X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.63/1.38 file('/export/starexec/sandbox/tmp/tmp.9pCjD4X4q7/DTF2THF_9333.p','thm/iterate/NSUM_CLAUSES_NUMSEG_0')).
% 1.63/1.38 % SZS output end Proof for DTF2THF_9333
% 1.63/1.38 % (9434)------------------------------
% 1.63/1.38 % (9434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (9434)Termination reason: Refutation
% 1.63/1.38
% 1.63/1.38 % (9434)Memory used [KB]: 5628
% 1.63/1.38 % (9434)Time elapsed: 0.007 s
% 1.63/1.38 % (9434)Instructions burned: 6 (million)
% 1.63/1.38 % (9434)------------------------------
% 1.63/1.38 % (9434)------------------------------
% 1.63/1.38 % (9431)Success in time 0.01 s
%------------------------------------------------------------------------------