%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA112^1 : 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 : n023.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 08:38:54 AM UTC 2026
% Result : Theorem 1.77s 1.50s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 117 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 415 ( 20 ~; 9 |; 3 &; 379 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 115 ( 47 ^; 58 !; 10 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'type/nums/num': $tType ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_4,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_11,type,
sK0: 'type/nums/num' ).
thf(func_def_12,type,
sK1: 'type/nums/num' ).
thf(func_def_13,type,
sK2: 'type/nums/num' ).
thf(func_def_14,type,
sK3: 'type/nums/num' ).
thf(func_def_15,type,
sK4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real' ).
thf(func_def_17,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f23,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f22,f17]) ).
thf(f17,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num',X2: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.APPhIGbirl/DTF2THF_21635.p','thm/iterate/FINITE_NUMSEG_') ).
thf(f22,plain,
( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f21,f17]) ).
thf(f21,plain,
( ( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 ) )
!= $true )
| ( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 ) )
!= $true )
| ( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) )
!= $true )
| ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ ( sK4 @ Y0 ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ ( sK4 @ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f18,f19]) ).
thf(f19,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( ( 'const/iterate/sum' @ X1 @ X4
@ ^ [Y0: X1] :
( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y1: X0] : ( X2 @ Y1 @ Y0 ) ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/iterate/sum' @ X1 @ X4 @ ( X2 @ Y0 ) ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true )
| ( ( 'const/iterate/sum' @ X1 @ X4
@ ^ [Y0: X1] :
( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y1: X0] : ( X2 @ Y1 @ Y0 ) ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/iterate/sum' @ X1 @ X4 @ ( X2 @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( ( 'const/iterate/sum' @ X1 @ X4
@ ^ [Y0: X1] :
( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y1: X0] : ( X2 @ Y1 @ Y0 ) ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/iterate/sum' @ X1 @ X4 @ ( X2 @ Y0 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/sets/FINITE' @ X1 @ X4 )
= $true ) )
=> ( ( 'const/iterate/sum' @ X1 @ X4
@ ^ [Y0: X1] :
( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y1: X0] : ( X2 @ Y1 @ Y0 ) ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/iterate/sum' @ X1 @ X4 @ ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X5: X0] : ( 'const/iterate/sum' @ X1 @ X4 @ ( X2 @ X5 ) ) )
= ( 'const/iterate/sum' @ X1 @ X4
@ ^ [X6: X1] :
( 'const/iterate/sum' @ X0 @ X3
@ ^ [X7: X0] : ( X2 @ X7 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X5: X0] : ( 'const/iterate/sum' @ X1 @ X4 @ ( X2 @ X5 ) ) )
= ( 'const/iterate/sum' @ X1 @ X4
@ ^ [X5: X1] :
( 'const/iterate/sum' @ X0 @ X3
@ ^ [X6: X0] : ( X2 @ X6 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.APPhIGbirl/DTF2THF_21635.p','thm/iterate/SUM_SWAP_') ).
thf(f18,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ ( sK4 @ Y0 ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] :
( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 )
@ ^ [Y1: 'type/nums/num'] : ( sK4 @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ ( sK4 @ Y0 ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] :
( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 )
@ ^ [Y1: 'type/nums/num'] : ( sK4 @ Y1 @ Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f12,f15]) ).
thf(f15,plain,
( ? [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] :
( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y1: 'type/nums/num'] : ( X4 @ Y1 @ Y0 ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ ( X4 @ Y0 ) ) ) )
=> ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ ( sK4 @ Y0 ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] :
( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK0 @ sK1 )
@ ^ [Y1: 'type/nums/num'] : ( sK4 @ Y1 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] :
( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y1: 'type/nums/num'] : ( X4 @ Y1 @ Y0 ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ ( X4 @ Y0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] :
( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y1: 'type/nums/num'] : ( X4 @ Y1 @ Y0 ) ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ ( X4 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X5: 'type/nums/num'] :
( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [X6: 'type/nums/num'] : ( X4 @ X6 @ X5 ) ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [X7: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ ( X4 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num',X5: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X4 )
@ ^ [X6: 'type/nums/num'] :
( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X2 )
@ ^ [X7: 'type/nums/num'] : ( X5 @ X7 @ X6 ) ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X2 )
@ ^ [X6: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X4 ) @ ( X5 @ X6 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num',X5: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X4 )
@ ^ [X6: 'type/nums/num'] :
( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X2 )
@ ^ [X7: 'type/nums/num'] : ( X5 @ X7 @ X6 ) ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X2 )
@ ^ [X6: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X4 ) @ ( X5 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.APPhIGbirl/DTF2THF_21635.p','thm/iterate/SUM_SWAP_NUMSEG_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA112^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 03:51:19 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.25/0.48 ---- Original DTF file ---
% 0.25/0.48 thf(spec,logic,$$dhol).
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 % File : ANA112^1 : TPTP v9.2.1. Released v7.0.0.
% 0.25/0.48 % Domain : Analysis
% 0.25/0.48 % Problem : SUM_SWAP_NUMSEG
% 0.25/0.48 % Version : Especial.
% 0.25/0.48 % English :
% 0.25/0.48
% 0.25/0.48 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.25/0.48 % Source : [Kal16]
% 0.25/0.48 % Names : SUM_SWAP_NUMSEG_.p [Kal16]
% 0.25/0.48
% 0.25/0.48 % Status : Theorem
% 0.25/0.48 % Rating : 0.00 v7.1.0
% 0.25/0.48 % Syntax : Number of formulae : 8 ( 1 unt; 5 typ; 0 def)
% 0.25/0.48 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.25/0.48 % Maximal formula atoms : 3 ( 3 avg)
% 0.25/0.48 % Number of connectives : 48 ( 0 ~; 0 |; 1 &; 46 @)
% 0.25/0.48 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.25/0.48 % Maximal formula depth : 10 ( 7 avg)
% 0.25/0.48 % Number of types : 3 ( 2 usr)
% 0.25/0.48 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.25/0.48 % Number of symbols : 4 ( 3 usr; 0 con; 2-3 aty)
% 0.25/0.48 % Number of variables : 20 ( 6 ^; 12 !; 0 ?; 20 :)
% 0.25/0.48 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.25/0.48 % SPC : TH1_THM_EQU_NAR
% 0.25/0.48
% 0.25/0.48 % Comments : Exported from core HOL Light.
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 thf('thf_type_type/realax/real',type,
% 0.25/0.48 'type/realax/real': $tType ).
% 0.25/0.48
% 0.25/0.48 thf('thf_type_type/nums/num',type,
% 0.25/0.48 'type/nums/num': $tType ).
% 0.25/0.48
% 0.25/0.48 thf('thf_const_const/sets/FINITE',type,
% 0.25/0.48 'const/sets/FINITE':
% 0.25/0.48 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.25/0.48
% 0.25/0.48 thf('thf_const_const/iterate/sum',type,
% 0.25/0.48 'const/iterate/sum':
% 0.25/0.48 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.25/0.48
% 0.25/0.48 thf('thf_const_const/iterate/..',type,
% 0.25/0.48 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.25/0.48
% 0.25/0.48 thf('thm/iterate/SUM_SWAP_',axiom,
% 0.25/0.48 ! [A: $tType,B: $tType,A0: A > B > 'type/realax/real',A1: A > $o,A2: B > $o] :
% 0.25/0.48 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.25/0.48 & ( 'const/sets/FINITE' @ B @ A2 ) )
% 0.25/0.48 => ( ( 'const/iterate/sum' @ A @ A1
% 0.25/0.48 @ ^ [A3: A] : ( 'const/iterate/sum' @ B @ A2 @ ( A0 @ A3 ) ) )
% 0.25/0.48 = ( 'const/iterate/sum' @ B @ A2
% 0.25/0.48 @ ^ [A3: B] :
% 0.25/0.48 ( 'const/iterate/sum' @ A @ A1
% 0.25/0.48 @ ^ [A4: A] : ( A0 @ A4 @ A3 ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf('thm/iterate/FINITE_NUMSEG_',axiom,
% 0.25/0.48 ! [A: 'type/nums/num',A0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 ) ) ).
% 0.25/0.48
% 0.25/0.48 thf('thm/iterate/SUM_SWAP_NUMSEG_',conjecture,
% 0.25/0.48 ! [A: 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num',A2: 'type/nums/num',A3: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
% 0.25/0.48 ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 )
% 0.25/0.48 @ ^ [A4: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A1 @ A2 ) @ ( A3 @ A4 ) ) )
% 0.25/0.48 = ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A1 @ A2 )
% 0.25/0.48 @ ^ [A4: 'type/nums/num'] :
% 0.25/0.48 ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 )
% 0.25/0.48 @ ^ [A5: 'type/nums/num'] : ( A3 @ A5 @ A4 ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.49 ------------------------
% 1.62/1.47 ---- Embedded in THF ---
% 1.62/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.47 %%% Generated on Tue Feb 24 03:51:20 EST 2026
% 1.62/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.47 %%% Logic specification used:
% 1.62/1.47 %%% thf(spec, logic, $$dhol).
% 1.62/1.47
% 1.62/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.APPhIGbirl/DTF2DTF21635.p
% See solution above
% 1.62/1.47 ------------------------
% 1.62/1.48 ---- Cleaned THF ---
% 1.62/1.48 thf('thf_type_type/realax/real',type,
% 1.62/1.48 'type/realax/real': $tType ).
% 1.62/1.48
% 1.62/1.48 thf('thf_type_type/nums/num',type,
% 1.62/1.48 'type/nums/num': $tType ).
% 1.62/1.48
% 1.62/1.48 thf('thf_const_const/sets/FINITE',type,
% 1.62/1.48 'const/sets/FINITE':
% 1.62/1.48 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.62/1.48
% 1.62/1.48 thf('thf_const_const/iterate/sum',type,
% 1.62/1.48 'const/iterate/sum':
% 1.62/1.48 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.62/1.48
% 1.62/1.48 thf('thf_const_const/iterate/..',type,
% 1.62/1.48 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 1.62/1.48
% 1.62/1.48 thf('thm/iterate/SUM_SWAP_',axiom,
% 1.62/1.48 ! [A: $tType,B: $tType,A0: A > B > 'type/realax/real',A1: A > $o,A2: B > $o] :
% 1.62/1.48 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.62/1.48 & ( 'const/sets/FINITE' @ B @ A2 ) )
% 1.62/1.48 => ( ( 'const/iterate/sum' @ A @ A1
% 1.62/1.48 @ ^ [A3: A] : ( 'const/iterate/sum' @ B @ A2 @ ( A0 @ A3 ) ) )
% 1.62/1.48 = ( 'const/iterate/sum' @ B @ A2
% 1.62/1.48 @ ^ [A3: B] :
% 1.62/1.48 ( 'const/iterate/sum' @ A @ A1
% 1.62/1.48 @ ^ [A4: A] : ( A0 @ A4 @ A3 ) ) ) ) ) ).
% 1.62/1.48
% 1.62/1.48 thf('thm/iterate/FINITE_NUMSEG_',axiom,
% 1.62/1.48 ! [A: 'type/nums/num',A0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 ) ) ).
% 1.62/1.48
% 1.62/1.48 thf('thm/iterate/SUM_SWAP_NUMSEG_',conjecture,
% 1.62/1.48 ! [A: 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num',A2: 'type/nums/num',A3: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
% 1.62/1.48 ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 )
% 1.62/1.48 @ ^ [A4: 'type/nums/num'] : ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A1 @ A2 ) @ ( A3 @ A4 ) ) )
% 1.62/1.48 = ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A1 @ A2 )
% 1.62/1.48 @ ^ [A4: 'type/nums/num'] :
% 1.62/1.48 ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 )
% 1.62/1.48 @ ^ [A5: 'type/nums/num'] : ( A3 @ A5 @ A4 ) ) ) ) ).
% 1.62/1.48 ------------------------
% 1.77/1.50 % (21795)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_21635 for (2999ds/275Mi)
% 1.77/1.50 % (21794)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_21635 for (2999ds/2Mi)
% 1.77/1.50 % (21791)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_21635 for (2999ds/4Mi)
% 1.77/1.50 % (21790)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21635 for (2999ds/183Mi)
% 1.77/1.50 % (21793)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21635 for (2999ds/2Mi)
% 1.77/1.50 % (21792)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_21635 for (2999ds/27Mi)
% 1.77/1.50 % (21796)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21635 for (2999ds/18Mi)
% 1.77/1.50 % (21793)Instruction limit reached!
% 1.77/1.50 % (21793)------------------------------
% 1.77/1.50 % (21793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.50 % (21793)Termination reason: Unknown
% 1.77/1.50 % (21793)Termination phase: Saturation
% 1.77/1.50 % (21794)Instruction limit reached!
% 1.77/1.50 % (21794)------------------------------
% 1.77/1.50 % (21794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.50
% 1.77/1.50 % (21793)Memory used [KB]: 895
% 1.77/1.50 % (21793)Time elapsed: 0.003 s
% 1.77/1.50 % (21793)Instructions burned: 2 (million)
% 1.77/1.50 % (21793)------------------------------
% 1.77/1.50 % (21793)------------------------------
% 1.77/1.50 % (21794)Termination reason: Unknown
% 1.77/1.50 % (21794)Termination phase: Property scanning
% 1.77/1.50
% 1.77/1.50 % (21794)Memory used [KB]: 1023
% 1.77/1.50 % (21794)Time elapsed: 0.003 s
% 1.77/1.50 % (21794)Instructions burned: 3 (million)
% 1.77/1.50 % (21794)------------------------------
% 1.77/1.50 % (21794)------------------------------
% 1.77/1.50 % (21791)Instruction limit reached!
% 1.77/1.50 % (21791)------------------------------
% 1.77/1.50 % (21791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.50 % (21791)Termination reason: Unknown
% 1.77/1.50 % (21791)Termination phase: Saturation
% 1.77/1.50
% 1.77/1.50 % (21795)First to succeed.
% 1.77/1.50 % (21791)Memory used [KB]: 5500
% 1.77/1.50 % (21791)Time elapsed: 0.004 s
% 1.77/1.50 % (21791)Instructions burned: 4 (million)
% 1.77/1.50 % (21791)------------------------------
% 1.77/1.50 % (21791)------------------------------
% 1.77/1.50 % (21792)Also succeeded, but the first one will report.
% 1.77/1.50 % (21795)Refutation found. Thanks to Tanya!
% 1.77/1.50 % SZS status Theorem for DTF2THF_21635
% 1.77/1.50 % SZS output start Proof for DTF2THF_21635
% 1.77/1.50 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.77/1.50 thf(type_def_7, type, 'type/nums/num': $tType).
% 1.77/1.50 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.77/1.50 thf(func_def_1, type, 'type/nums/num': $tType).
% 1.77/1.50 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.77/1.50 thf(func_def_3, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.77/1.50 thf(func_def_4, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 1.77/1.50 thf(func_def_11, type, sK0: 'type/nums/num').
% 1.77/1.50 thf(func_def_12, type, sK1: 'type/nums/num').
% 1.77/1.50 thf(func_def_13, type, sK2: 'type/nums/num').
% 1.77/1.50 thf(func_def_14, type, sK3: 'type/nums/num').
% 1.77/1.50 thf(func_def_15, type, sK4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real').
% 1.77/1.50 thf(func_def_17, type, ph6: !>[X0: $tType]:(X0)).
% 1.77/1.50 thf(f23,plain,(
% 1.77/1.50 $false),
% 1.77/1.50 inference(subsumption_resolution,[status(thm)],[f22,f17])).
% 1.77/1.50 thf(f17,plain,(
% 1.77/1.50 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1)) = $true)) )),
% 1.77/1.50 inference(cnf_transformation,[status(thm)],[f11])).
% 1.77/1.50 thf(f11,plain,(
% 1.77/1.50 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1)) = $true)),
% 1.77/1.50 inference(fool_elimination,[status(thm)],[f10])).
% 1.77/1.50 thf(f10,plain,(
% 1.77/1.50 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 1.77/1.50 inference(rectify,[status(thm)],[f2])).
% 1.77/1.50 thf(f2,axiom,(
% 1.77/1.50 ! [X0 : 'type/nums/num',X2 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2))),
% 1.77/1.50 file('/export/starexec/sandbox/tmp/tmp.APPhIGbirl/DTF2THF_21635.p','thm/iterate/FINITE_NUMSEG_')).
% 1.77/1.50 thf(f22,plain,(
% 1.77/1.50 (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3)) != $true)),
% 1.77/1.50 inference(subsumption_resolution,[status(thm)],[f21,f17])).
% 1.77/1.50 thf(f21,plain,(
% 1.77/1.50 (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1)) != $true) | (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3)) != $true)),
% 1.77/1.50 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.77/1.50 thf(f20,plain,(
% 1.77/1.50 (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1)) != $true) | (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3)) != $true) | (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ (sK4 @ Y0)))) != ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ (sK4 @ Y0)))))),
% 1.77/1.50 inference(superposition,[status(thm)],[f18,f19])).
% 1.77/1.50 thf(f19,plain,(
% 1.77/1.50 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > 'type/realax/real',X3 : X0 > $o,X4 : X1 > $o] : ((('const/iterate/sum' @ X1 @ X4 @ (^[Y0 : X1]: ('const/iterate/sum' @ X0 @ X3 @ (^[Y1 : X0]: (X2 @ Y1 @ Y0))))) = ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/iterate/sum' @ X1 @ X4 @ (X2 @ Y0))))) | (('const/sets/FINITE' @ X1 @ X4) != $true) | (('const/sets/FINITE' @ X0 @ X3) != $true)) )),
% 1.77/1.50 inference(cnf_transformation,[status(thm)],[f14])).
% 1.77/1.50 thf(f14,plain,(
% 1.77/1.50 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > 'type/realax/real',X3 : X0 > $o,X4 : X1 > $o] : ((('const/sets/FINITE' @ X0 @ X3) != $true) | (('const/sets/FINITE' @ X1 @ X4) != $true) | (('const/iterate/sum' @ X1 @ X4 @ (^[Y0 : X1]: ('const/iterate/sum' @ X0 @ X3 @ (^[Y1 : X0]: (X2 @ Y1 @ Y0))))) = ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/iterate/sum' @ X1 @ X4 @ (X2 @ Y0))))))),
% 1.77/1.50 inference(flattening,[status(thm)],[f13])).
% 1.77/1.50 thf(f13,plain,(
% 1.77/1.50 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > 'type/realax/real',X3 : X0 > $o,X4 : X1 > $o] : ((('const/iterate/sum' @ X1 @ X4 @ (^[Y0 : X1]: ('const/iterate/sum' @ X0 @ X3 @ (^[Y1 : X0]: (X2 @ Y1 @ Y0))))) = ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/iterate/sum' @ X1 @ X4 @ (X2 @ Y0))))) | ((('const/sets/FINITE' @ X0 @ X3) != $true) | (('const/sets/FINITE' @ X1 @ X4) != $true)))),
% 1.77/1.50 inference(ennf_transformation,[status(thm)],[f7])).
% 1.77/1.50 thf(f7,plain,(
% 1.77/1.50 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > 'type/realax/real',X3 : X0 > $o,X4 : X1 > $o] : (((('const/sets/FINITE' @ X0 @ X3) = $true) & (('const/sets/FINITE' @ X1 @ X4) = $true)) => (('const/iterate/sum' @ X1 @ X4 @ (^[Y0 : X1]: ('const/iterate/sum' @ X0 @ X3 @ (^[Y1 : X0]: (X2 @ Y1 @ Y0))))) = ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/iterate/sum' @ X1 @ X4 @ (X2 @ Y0))))))),
% 1.77/1.50 inference(fool_elimination,[status(thm)],[f6])).
% 1.77/1.50 thf(f6,plain,(
% 1.77/1.50 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > 'type/realax/real',X3 : X0 > $o,X4 : X1 > $o] : ((('const/sets/FINITE' @ X1 @ X4) & ('const/sets/FINITE' @ X0 @ X3)) => (('const/iterate/sum' @ X0 @ X3 @ (^[X5 : X0] : ('const/iterate/sum' @ X1 @ X4 @ (X2 @ X5)))) = ('const/iterate/sum' @ X1 @ X4 @ (^[X6 : X1] : ('const/iterate/sum' @ X0 @ X3 @ (^[X7 : X0] : (X2 @ X7 @ X6)))))))),
% 1.77/1.50 inference(rectify,[status(thm)],[f1])).
% 1.77/1.50 thf(f1,axiom,(
% 1.77/1.50 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > 'type/realax/real',X3 : X0 > $o,X4 : X1 > $o] : ((('const/sets/FINITE' @ X1 @ X4) & ('const/sets/FINITE' @ X0 @ X3)) => (('const/iterate/sum' @ X0 @ X3 @ (^[X5 : X0] : ('const/iterate/sum' @ X1 @ X4 @ (X2 @ X5)))) = ('const/iterate/sum' @ X1 @ X4 @ (^[X5 : X1] : ('const/iterate/sum' @ X0 @ X3 @ (^[X6 : X0] : (X2 @ X6 @ X5)))))))),
% 1.77/1.50 file('/export/starexec/sandbox/tmp/tmp.APPhIGbirl/DTF2THF_21635.p','thm/iterate/SUM_SWAP_')).
% 1.77/1.50 thf(f18,plain,(
% 1.77/1.50 (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ (sK4 @ Y0)))) != ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ (^[Y1 : 'type/nums/num']: (sK4 @ Y1 @ Y0))))))),
% 1.77/1.50 inference(cnf_transformation,[status(thm)],[f16])).
% 1.77/1.50 thf(f16,plain,(
% 1.77/1.50 (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ (sK4 @ Y0)))) != ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ (^[Y1 : 'type/nums/num']: (sK4 @ Y1 @ Y0))))))),
% 1.77/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f12,f15])).
% 1.77/1.50 thf(f15,plain,(
% 1.77/1.50 ? [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num',X3 : 'type/nums/num',X4 : 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[Y1 : 'type/nums/num']: (X4 @ Y1 @ Y0))))) != ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (X4 @ Y0))))) => (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ (sK4 @ Y0)))) != ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ (^[Y1 : 'type/nums/num']: (sK4 @ Y1 @ Y0))))))),
% 1.77/1.50 introduced(definition,[],[choice_axiom])).
% 1.77/1.50 thf(f12,plain,(
% 1.77/1.50 ? [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num',X3 : 'type/nums/num',X4 : 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[Y1 : 'type/nums/num']: (X4 @ Y1 @ Y0))))) != ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (X4 @ Y0)))))),
% 1.77/1.50 inference(ennf_transformation,[status(thm)],[f9])).
% 1.77/1.50 thf(f9,plain,(
% 1.77/1.50 ~! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num',X3 : 'type/nums/num',X4 : 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[Y1 : 'type/nums/num']: (X4 @ Y1 @ Y0))))) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[Y0 : 'type/nums/num']: ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (X4 @ Y0)))))),
% 1.77/1.50 inference(fool_elimination,[status(thm)],[f8])).
% 1.77/1.50 thf(f8,plain,(
% 1.77/1.50 ~! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num',X3 : 'type/nums/num',X4 : 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (^[X5 : 'type/nums/num'] : ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[X6 : 'type/nums/num'] : (X4 @ X6 @ X5))))) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[X7 : 'type/nums/num'] : ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X3) @ (X4 @ X7)))))),
% 1.77/1.50 inference(rectify,[status(thm)],[f4])).
% 1.77/1.50 thf(f4,negated_conjecture,(
% 1.77/1.50 ~! [X0 : 'type/nums/num',X2 : 'type/nums/num',X3 : 'type/nums/num',X4 : 'type/nums/num',X5 : 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X3 @ X4) @ (^[X6 : 'type/nums/num'] : ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ (^[X7 : 'type/nums/num'] : (X5 @ X7 @ X6))))) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ (^[X6 : 'type/nums/num'] : ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X3 @ X4) @ (X5 @ X6)))))),
% 1.77/1.50 inference(negated_conjecture,[status(cth)],[f3])).
% 1.77/1.50 thf(f3,conjecture,(
% 1.77/1.50 ! [X0 : 'type/nums/num',X2 : 'type/nums/num',X3 : 'type/nums/num',X4 : 'type/nums/num',X5 : 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X3 @ X4) @ (^[X6 : 'type/nums/num'] : ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ (^[X7 : 'type/nums/num'] : (X5 @ X7 @ X6))))) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ (^[X6 : 'type/nums/num'] : ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X3 @ X4) @ (X5 @ X6)))))),
% 1.77/1.50 file('/export/starexec/sandbox/tmp/tmp.APPhIGbirl/DTF2THF_21635.p','thm/iterate/SUM_SWAP_NUMSEG_')).
% 1.77/1.50 % SZS output end Proof for DTF2THF_21635
% 1.77/1.50 % (21795)------------------------------
% 1.77/1.50 % (21795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.50 % (21795)Termination reason: Refutation
% 1.77/1.50
% 1.77/1.50 % (21795)Memory used [KB]: 5500
% 1.77/1.50 % (21795)Time elapsed: 0.005 s
% 1.77/1.50 % (21795)Instructions burned: 2 (million)
% 1.77/1.50 % (21795)------------------------------
% 1.77/1.50 % (21795)------------------------------
% 1.77/1.50 % (21789)Success in time 0.02 s
%------------------------------------------------------------------------------