%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV494^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 09:41:23 AM UTC 2026
% Result : Theorem 1.68s 1.31s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 253 ( 12 ~; 3 |; 4 &; 226 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 24 ( 0 ^; 20 !; 4 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_2,type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_3,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_4,type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_5,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_6,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_7,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_8,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_10,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK0: 'type/nums/num' ).
thf(func_def_14,type,
sK1: 'type/nums/num' ).
thf(func_def_16,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK4: 'type/nums/num' ).
thf(f50,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
!= ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) ) ),
inference(superposition,[status(thm)],[f15,f41]) ).
thf(f41,plain,
( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ sK1 ) ) ),
inference(forward_demodulation,[status(thm)],[f40,f14]) ).
thf(f14,plain,
! [X0: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ X0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ X0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= X0 ),
file('/export/starexec/sandbox2/tmp/tmp.VDwRx1rkjm/DTF2THF_31146.p','thm/arith/SUC_SUB1_') ).
thf(f40,plain,
( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ ( 'const/arith/-' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ ( 'const/arith/-' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f17,f16]) ).
thf(f16,plain,
( ( 'const/arith/<=' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( 'const/arith/<=' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
= $true )
& ( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ sK1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12]) ).
thf(f12,plain,
( ? [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= $true )
& ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) )
=> ( ( ( 'const/arith/<=' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
= $true )
& ( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= $true )
& ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= $true )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VDwRx1rkjm/DTF2THF_31146.p','thm/iterate/NUMSEG_REC_') ).
thf(f17,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ X1 )
= $true )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ X1 )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ X1 )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VDwRx1rkjm/DTF2THF_31146.p','thm/iterate/NUMSEG_RREC_') ).
thf(f15,plain,
( ( 'const/iterate/..' @ sK0 @ ( 'const/nums/SUC' @ sK1 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK1 ) @ ( 'const/iterate/..' @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV494^1 : TPTP v9.2.1. Released v7.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:48:09 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEV494^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.46 % Domain : Analysis
% 0.30/0.46 % Problem : NUMSEG_REC
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Kal16]
% 0.30/0.46 % Names : NUMSEG_REC_.p [Kal16]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v7.1.0
% 0.30/0.46 % Syntax : Number of formulae : 12 ( 1 unt; 9 typ; 0 def)
% 0.30/0.46 % Number of atoms : 11 ( 3 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 3 avg)
% 0.30/0.46 % Number of connectives : 32 ( 0 ~; 0 |; 0 &; 30 @)
% 0.30/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 6 ( 5 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 9 ( 8 usr; 1 con; 0-4 aty)
% 0.30/0.46 % Number of variables : 6 ( 0 ^; 5 !; 0 ?; 6 :)
% 0.30/0.46 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : Exported from core HOL Light.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf('thf_type_type/nums/num',type,
% 0.30/0.46 'type/nums/num': $tType ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/sets/INSERT',type,
% 0.30/0.46 'const/sets/INSERT':
% 0.30/0.46 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/nums/SUC',type,
% 0.30/0.46 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/nums/NUMERAL',type,
% 0.30/0.46 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/nums/BIT1',type,
% 0.30/0.46 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/nums/_0',type,
% 0.30/0.46 'const/nums/_0': 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/iterate/..',type,
% 0.30/0.46 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/arith/-',type,
% 0.30/0.46 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 0.30/0.46
% 0.30/0.46 thf('thf_const_const/arith/<=',type,
% 0.30/0.46 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 0.30/0.46
% 0.30/0.46 thf('thm/arith/SUC_SUB1_',axiom,
% 0.30/0.46 ! [A: 'type/nums/num'] :
% 0.30/0.46 ( ( 'const/arith/-' @ ( 'const/nums/SUC' @ A ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 thf('thm/iterate/NUMSEG_RREC_',axiom,
% 0.30/0.46 ! [A: 'type/nums/num',A0: 'type/nums/num'] :
% 0.30/0.46 ( ( 'const/arith/<=' @ A @ A0 )
% 0.30/0.46 => ( ( 'const/sets/INSERT' @ 'type/nums/num' @ A0 @ ( 'const/iterate/..' @ A @ ( 'const/arith/-' @ A0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
% 0.30/0.46 = ( 'const/iterate/..' @ A @ A0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf('thm/iterate/NUMSEG_REC_',conjecture,
% 0.30/0.46 ! [A: 'type/nums/num',A0: 'type/nums/num'] :
% 0.30/0.46 ( ( 'const/arith/<=' @ A @ ( 'const/nums/SUC' @ A0 ) )
% 0.30/0.46 => ( ( 'const/iterate/..' @ A @ ( 'const/nums/SUC' @ A0 ) )
% 0.30/0.46 = ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ A0 ) @ ( 'const/iterate/..' @ A @ A0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.50/1.28 ---- Embedded in THF ---
% 1.50/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.28 %%% Generated on Tue Feb 24 12:48:10 EST 2026
% 1.50/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.28 %%% Logic specification used:
% 1.50/1.28 %%% thf(spec, logic, $$dhol).
% 1.50/1.28
% 1.50/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.VDwRx1rkjm/DTF2DTF31146.p
% See solution above
% 1.50/1.28 ------------------------
% 1.50/1.29 ---- Cleaned THF ---
% 1.50/1.29 thf('thf_type_type/nums/num',type,
% 1.50/1.29 'type/nums/num': $tType ).
% 1.50/1.29
% 1.50/1.29 thf('thf_const_const/sets/INSERT',type,
% 1.50/1.29 'const/sets/INSERT':
% 1.50/1.29 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 1.50/1.29
% 1.50/1.29 thf('thf_const_const/nums/SUC',type,
% 1.50/1.29 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 1.50/1.29
% 1.50/1.29 thf('thf_const_const/nums/NUMERAL',type,
% 1.50/1.29 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.50/1.29
% 1.50/1.29 thf('thf_const_const/nums/BIT1',type,
% 1.50/1.29 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 1.50/1.29
% 1.50/1.29 thf('thf_const_const/nums/_0',type,
% 1.50/1.29 'const/nums/_0': 'type/nums/num' ).
% 1.50/1.29
% 1.50/1.29 thf('thf_const_const/iterate/..',type,
% 1.50/1.29 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 1.50/1.29
% 1.50/1.29 thf('thf_const_const/arith/-',type,
% 1.50/1.29 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 1.50/1.29
% 1.50/1.29 thf('thf_const_const/arith/<=',type,
% 1.50/1.29 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 1.50/1.29
% 1.50/1.29 thf('thm/arith/SUC_SUB1_',axiom,
% 1.50/1.29 ! [A: 'type/nums/num'] :
% 1.50/1.29 ( ( 'const/arith/-' @ ( 'const/nums/SUC' @ A ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
% 1.50/1.29 = A ) ).
% 1.50/1.29
% 1.50/1.29 thf('thm/iterate/NUMSEG_RREC_',axiom,
% 1.50/1.29 ! [A: 'type/nums/num',A0: 'type/nums/num'] :
% 1.50/1.29 ( ( 'const/arith/<=' @ A @ A0 )
% 1.50/1.29 => ( ( 'const/sets/INSERT' @ 'type/nums/num' @ A0 @ ( 'const/iterate/..' @ A @ ( 'const/arith/-' @ A0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
% 1.50/1.29 = ( 'const/iterate/..' @ A @ A0 ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf('thm/iterate/NUMSEG_REC_',conjecture,
% 1.50/1.29 ! [A: 'type/nums/num',A0: 'type/nums/num'] :
% 1.50/1.29 ( ( 'const/arith/<=' @ A @ ( 'const/nums/SUC' @ A0 ) )
% 1.50/1.29 => ( ( 'const/iterate/..' @ A @ ( 'const/nums/SUC' @ A0 ) )
% 1.50/1.29 = ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ A0 ) @ ( 'const/iterate/..' @ A @ A0 ) ) ) ) ).
% 1.50/1.29 ------------------------
% 1.68/1.30 % (31422)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_31146 for (2999ds/275Mi)
% 1.68/1.30 % (31419)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_31146 for (2999ds/27Mi)
% 1.68/1.30 % (31422)Refutation not found, incomplete strategy
% 1.68/1.30 % (31422)------------------------------
% 1.68/1.30 % (31422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.30 % (31422)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.30
% 1.68/1.30
% 1.68/1.30 % (31422)Memory used [KB]: 5500
% 1.68/1.30 % (31422)Time elapsed: 0.002 s
% 1.68/1.30 % (31422)Instructions burned: 2 (million)
% 1.68/1.30 % (31422)------------------------------
% 1.68/1.30 % (31422)------------------------------
% 1.68/1.31 % (31419)First to succeed.
% 1.68/1.31 % (31419)Refutation found. Thanks to Tanya!
% 1.68/1.31 % SZS status Theorem for DTF2THF_31146
% 1.68/1.31 % SZS output start Proof for DTF2THF_31146
% 1.68/1.31 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.68/1.31 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.68/1.31 thf(func_def_1, type, 'const/sets/INSERT': !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 1.68/1.31 thf(func_def_2, type, 'const/nums/SUC': 'type/nums/num' > 'type/nums/num').
% 1.68/1.31 thf(func_def_3, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.68/1.31 thf(func_def_4, type, 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num').
% 1.68/1.31 thf(func_def_5, type, 'const/nums/_0': 'type/nums/num').
% 1.68/1.31 thf(func_def_6, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 1.68/1.31 thf(func_def_7, type, 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num').
% 1.68/1.31 thf(func_def_8, type, 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o).
% 1.68/1.31 thf(func_def_10, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.68/1.31 thf(func_def_13, type, sK0: 'type/nums/num').
% 1.68/1.31 thf(func_def_14, type, sK1: 'type/nums/num').
% 1.68/1.31 thf(func_def_16, type, ph3: !>[X0: $tType]:(X0)).
% 1.68/1.31 thf(func_def_17, type, sK4: 'type/nums/num').
% 1.68/1.31 thf(f50,plain,(
% 1.68/1.31 $false),
% 1.68/1.31 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.68/1.31 thf(f47,plain,(
% 1.68/1.31 (('const/iterate/..' @ sK0 @ ('const/nums/SUC' @ sK1)) != ('const/iterate/..' @ sK0 @ ('const/nums/SUC' @ sK1)))),
% 1.68/1.31 inference(superposition,[status(thm)],[f15,f41])).
% 1.68/1.31 thf(f41,plain,(
% 1.68/1.31 (('const/iterate/..' @ sK0 @ ('const/nums/SUC' @ sK1)) = ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ sK1) @ ('const/iterate/..' @ sK0 @ sK1)))),
% 1.68/1.31 inference(forward_demodulation,[status(thm)],[f40,f14])).
% 1.68/1.31 thf(f14,plain,(
% 1.68/1.31 ( ! [X0 : 'type/nums/num'] : ((('const/arith/-' @ ('const/nums/SUC' @ X0) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = X0)) )),
% 1.68/1.31 inference(cnf_transformation,[status(thm)],[f1])).
% 1.68/1.31 thf(f1,axiom,(
% 1.68/1.31 ! [X0 : 'type/nums/num'] : (('const/arith/-' @ ('const/nums/SUC' @ X0) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = X0)),
% 1.68/1.31 file('/export/starexec/sandbox2/tmp/tmp.VDwRx1rkjm/DTF2THF_31146.p','thm/arith/SUC_SUB1_')).
% 1.68/1.31 thf(f40,plain,(
% 1.68/1.31 (('const/iterate/..' @ sK0 @ ('const/nums/SUC' @ sK1)) = ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ sK1) @ ('const/iterate/..' @ sK0 @ ('const/arith/-' @ ('const/nums/SUC' @ sK1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),
% 1.68/1.31 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.68/1.31 thf(f39,plain,(
% 1.68/1.31 (('const/iterate/..' @ sK0 @ ('const/nums/SUC' @ sK1)) = ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ sK1) @ ('const/iterate/..' @ sK0 @ ('const/arith/-' @ ('const/nums/SUC' @ sK1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) | ($true != $true)),
% 1.68/1.31 inference(superposition,[status(thm)],[f17,f16])).
% 1.68/1.31 thf(f16,plain,(
% 1.68/1.31 (('const/arith/<=' @ sK0 @ ('const/nums/SUC' @ sK1)) = $true)),
% 1.68/1.31 inference(cnf_transformation,[status(thm)],[f13])).
% 1.68/1.31 thf(f13,plain,(
% 1.68/1.31 (('const/arith/<=' @ sK0 @ ('const/nums/SUC' @ sK1)) = $true) & (('const/iterate/..' @ sK0 @ ('const/nums/SUC' @ sK1)) != ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ sK1) @ ('const/iterate/..' @ sK0 @ sK1)))),
% 1.68/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12])).
% 1.68/1.31 thf(f12,plain,(
% 1.68/1.31 ? [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X0 @ ('const/nums/SUC' @ X1)) = $true) & (('const/iterate/..' @ X0 @ ('const/nums/SUC' @ X1)) != ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ X1) @ ('const/iterate/..' @ X0 @ X1)))) => ((('const/arith/<=' @ sK0 @ ('const/nums/SUC' @ sK1)) = $true) & (('const/iterate/..' @ sK0 @ ('const/nums/SUC' @ sK1)) != ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ sK1) @ ('const/iterate/..' @ sK0 @ sK1))))),
% 1.68/1.31 introduced(definition,[],[choice_axiom])).
% 1.68/1.31 thf(f10,plain,(
% 1.68/1.31 ? [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X0 @ ('const/nums/SUC' @ X1)) = $true) & (('const/iterate/..' @ X0 @ ('const/nums/SUC' @ X1)) != ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ X1) @ ('const/iterate/..' @ X0 @ X1))))),
% 1.68/1.31 inference(ennf_transformation,[status(thm)],[f9])).
% 1.68/1.31 thf(f9,plain,(
% 1.68/1.31 ~! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X0 @ ('const/nums/SUC' @ X1)) = $true) => (('const/iterate/..' @ X0 @ ('const/nums/SUC' @ X1)) = ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ X1) @ ('const/iterate/..' @ X0 @ X1))))),
% 1.68/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.68/1.31 thf(f8,plain,(
% 1.68/1.31 ~! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/arith/<=' @ X0 @ ('const/nums/SUC' @ X1)) => (('const/iterate/..' @ X0 @ ('const/nums/SUC' @ X1)) = ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ X1) @ ('const/iterate/..' @ X0 @ X1))))),
% 1.68/1.31 inference(rectify,[status(thm)],[f4])).
% 1.68/1.31 thf(f4,negated_conjecture,(
% 1.68/1.31 ~! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/arith/<=' @ X0 @ ('const/nums/SUC' @ X1)) => (('const/iterate/..' @ X0 @ ('const/nums/SUC' @ X1)) = ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ X1) @ ('const/iterate/..' @ X0 @ X1))))),
% 1.68/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.68/1.31 thf(f3,conjecture,(
% 1.68/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/arith/<=' @ X0 @ ('const/nums/SUC' @ X1)) => (('const/iterate/..' @ X0 @ ('const/nums/SUC' @ X1)) = ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ X1) @ ('const/iterate/..' @ X0 @ X1))))),
% 1.68/1.31 file('/export/starexec/sandbox2/tmp/tmp.VDwRx1rkjm/DTF2THF_31146.p','thm/iterate/NUMSEG_REC_')).
% 1.68/1.31 thf(f17,plain,(
% 1.68/1.31 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X0 @ X1) != $true) | (('const/sets/INSERT' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) = ('const/iterate/..' @ X0 @ X1))) )),
% 1.68/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.31 thf(f11,plain,(
% 1.68/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X0 @ X1) != $true) | (('const/sets/INSERT' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) = ('const/iterate/..' @ X0 @ X1)))),
% 1.68/1.31 inference(ennf_transformation,[status(thm)],[f7])).
% 1.68/1.31 thf(f7,plain,(
% 1.68/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X0 @ X1) = $true) => (('const/sets/INSERT' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) = ('const/iterate/..' @ X0 @ X1)))),
% 1.68/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.68/1.31 thf(f6,plain,(
% 1.68/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/arith/<=' @ X0 @ X1) => (('const/sets/INSERT' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) = ('const/iterate/..' @ X0 @ X1)))),
% 1.68/1.31 inference(rectify,[status(thm)],[f2])).
% 1.68/1.31 thf(f2,axiom,(
% 1.68/1.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/arith/<=' @ X0 @ X1) => (('const/sets/INSERT' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ ('const/arith/-' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) = ('const/iterate/..' @ X0 @ X1)))),
% 1.68/1.31 file('/export/starexec/sandbox2/tmp/tmp.VDwRx1rkjm/DTF2THF_31146.p','thm/iterate/NUMSEG_RREC_')).
% 1.68/1.31 thf(f15,plain,(
% 1.68/1.31 (('const/iterate/..' @ sK0 @ ('const/nums/SUC' @ sK1)) != ('const/sets/INSERT' @ 'type/nums/num' @ ('const/nums/SUC' @ sK1) @ ('const/iterate/..' @ sK0 @ sK1)))),
% 1.68/1.31 inference(cnf_transformation,[status(thm)],[f13])).
% 1.68/1.31 % SZS output end Proof for DTF2THF_31146
% 1.68/1.31 % (31419)------------------------------
% 1.68/1.31 % (31419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.31 % (31419)Termination reason: Refutation
% 1.68/1.31
% 1.68/1.31 % (31419)Memory used [KB]: 5500
% 1.68/1.31 % (31419)Time elapsed: 0.003 s
% 1.68/1.31 % (31419)Instructions burned: 4 (million)
% 1.68/1.31 % (31419)------------------------------
% 1.68/1.31 % (31419)------------------------------
% 1.68/1.31 % (31416)Success in time 0.014 s
%------------------------------------------------------------------------------