%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV507^1 : 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 : n007.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 09:41:24 AM UTC 2026
% Result : Theorem 1.92s 1.55s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 344 ( 14 ~; 6 |; 5 &; 312 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 3 con; 0-5 aty)
% Number of variables : 60 ( 0 ^; 56 !; 4 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
'type/realax/real': $tType ).
thf(type_def_8,type,
sK0: $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/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_3,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_7,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_8,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_9,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_10,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_11,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_12,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_13,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_14,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_16,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_19,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_21,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f28,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(superposition,[status(thm)],[f23,f26]) ).
thf(f26,plain,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(forward_demodulation,[status(thm)],[f25,f20]) ).
thf(f20,plain,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/NEUTRAL_REAL_ADD_') ).
thf(f25,plain,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f21,f17]) ).
thf(f17,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f21,plain,
! [X0: $tType,X2: $tType,X3: X2 > X2 > X2,X7: X0 > X2] :
( ( ( 'const/iterate/monoidal' @ X2 @ X3 )
!= $true )
| ( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true ) )
& ! [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) )
| ( ( 'const/iterate/monoidal' @ X2 @ X3 )
!= $true ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ! [X5: X1 > X2,X6: X1,X7: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X6 @ X7 ) @ X5 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X7 )
!= $true ) )
& ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) ) )
| ( ( 'const/iterate/monoidal' @ X2 @ X3 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ( 'const/iterate/monoidal' @ X2 @ X3 )
= $true )
=> ( ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) )
& ! [X5: X1 > X2,X6: X1,X7: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X7 )
= $true )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X6 @ X7 ) @ X5 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) )
& ! [X5: X1 > X2,X6: X1,X7: X1 > $o] :
( ( 'const/sets/FINITE' @ X1 @ X7 )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X6 @ X7 ) @ X5 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) )
& ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( 'const/sets/FINITE' @ X1 @ X6 )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/ITERATE_CLAUSES_') ).
thf(f23,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f19,f18]) ).
thf(f18,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/sum_') ).
thf(f19,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/SUM_CLAUSES_0') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV507^1 : 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
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:47:38 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEV507^1 : TPTP v9.2.1. Released v7.0.0.
% 0.20/0.45 % Domain : Analysis
% 0.20/0.45 % Problem : SUM_CLAUSES_
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Kal16]
% 0.20/0.45 % Names : SUM_CLAUSES_0.p [Kal16]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.20/0.45 % Syntax : Number of formulae : 20 ( 4 unt; 15 typ; 1 def)
% 0.20/0.45 % Number of atoms : 12 ( 5 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 4 ( 2 avg)
% 0.20/0.45 % Number of connectives : 59 ( 0 ~; 0 |; 1 &; 56 @)
% 0.20/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 13 ( 4 avg)
% 0.20/0.45 % Number of types : 3 ( 2 usr)
% 0.20/0.45 % Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 14 ( 13 usr; 1 con; 0-5 aty)
% 0.20/0.45 % Number of variables : 21 ( 0 ^; 11 !; 0 ?; 21 :)
% 0.20/0.45 % ( 10 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.45 % SPC : TH1_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : Exported from core HOL Light.
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf('thf_type_type/realax/real',type,
% 0.20/0.45 'type/realax/real': $tType ).
% 0.20/0.45
% 0.20/0.45 thf('thf_type_type/nums/num',type,
% 0.20/0.45 'type/nums/num': $tType ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/sets/INSERT',type,
% 0.20/0.45 'const/sets/INSERT':
% 0.20/0.45 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/sets/IN',type,
% 0.20/0.45 'const/sets/IN':
% 0.20/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/sets/FINITE',type,
% 0.20/0.45 'const/sets/FINITE':
% 0.20/0.45 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/sets/EMPTY',type,
% 0.20/0.45 'const/sets/EMPTY':
% 0.20/0.45 !>[A: $tType] : ( A > $o ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/realax/real_of_num',type,
% 0.20/0.45 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/realax/real_add',type,
% 0.20/0.45 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/nums/NUMERAL',type,
% 0.20/0.45 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/nums/_0',type,
% 0.20/0.45 'const/nums/_0': 'type/nums/num' ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/iterate/sum',type,
% 0.20/0.45 'const/iterate/sum':
% 0.20/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/iterate/neutral',type,
% 0.20/0.45 'const/iterate/neutral':
% 0.20/0.45 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/iterate/monoidal',type,
% 0.20/0.45 'const/iterate/monoidal':
% 0.20/0.45 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/iterate/iterate',type,
% 0.20/0.45 'const/iterate/iterate':
% 0.20/0.45 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/class/COND',type,
% 0.20/0.45 'const/class/COND':
% 0.20/0.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.20/0.45
% 0.20/0.45 thf('thm/iterate/ITERATE_CLAUSES_',axiom,
% 0.20/0.45 ! [A: $tType,A0: $tType,A1: $tType,A2: A1 > A1 > A1] :
% 0.20/0.45 ( ( 'const/iterate/monoidal' @ A1 @ A2 )
% 0.20/0.45 => ( ! [A3: A > A1] :
% 0.20/0.45 ( ( 'const/iterate/iterate' @ A @ A1 @ A2 @ ( 'const/sets/EMPTY' @ A ) @ A3 )
% 0.20/0.45 = ( 'const/iterate/neutral' @ A1 @ A2 ) )
% 0.20/0.45 & ! [A3: A0 > A1,A4: A0,A5: A0 > $o] :
% 0.20/0.45 ( ( 'const/sets/FINITE' @ A0 @ A5 )
% 0.20/0.45 => ( ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ ( 'const/sets/INSERT' @ A0 @ A4 @ A5 ) @ A3 )
% 0.20/0.45 = ( 'const/class/COND' @ A1 @ ( 'const/sets/IN' @ A0 @ A4 @ A5 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) @ ( A2 @ ( A3 @ A4 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 0.20/0.45 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 0.20/0.45
% 0.20/0.45 thf('thm/iterate/sum_',definition,
% 0.20/0.45 ! [A: $tType] :
% 0.20/0.45 ( ( 'const/iterate/sum' @ A )
% 0.20/0.45 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 0.20/0.45
% 0.20/0.45 thf('thm/iterate/NEUTRAL_REAL_ADD_',axiom,
% 0.20/0.45 ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
% 0.20/0.45 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf('thm/iterate/SUM_CLAUSES_0',conjecture,
% 0.20/0.45 ! [A: $tType,A0: A > 'type/realax/real'] :
% 0.20/0.45 ( ( 'const/iterate/sum' @ A @ ( 'const/sets/EMPTY' @ A ) @ A0 )
% 0.20/0.45 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.92/1.51 ---- Embedded in THF ---
% 1.92/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.92/1.51 %%% Generated on Tue Feb 24 12:47:39 EST 2026
% 1.92/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 1.92/1.51 %%% Logic specification used:
% 1.92/1.51 %%% thf(spec, logic, $$dhol).
% 1.92/1.51
% 1.92/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2DTF28752.p
% See solution above
% 1.92/1.51 ------------------------
% 1.92/1.52 ---- Cleaned THF ---
% 1.92/1.52 thf('thf_type_type/realax/real',type,
% 1.92/1.52 'type/realax/real': $tType ).
% 1.92/1.52
% 1.92/1.52 thf('thf_type_type/nums/num',type,
% 1.92/1.52 'type/nums/num': $tType ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/sets/INSERT',type,
% 1.92/1.52 'const/sets/INSERT':
% 1.92/1.52 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/sets/IN',type,
% 1.92/1.52 'const/sets/IN':
% 1.92/1.52 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/sets/FINITE',type,
% 1.92/1.52 'const/sets/FINITE':
% 1.92/1.52 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/sets/EMPTY',type,
% 1.92/1.52 'const/sets/EMPTY':
% 1.92/1.52 !>[A: $tType] : ( A > $o ) ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/realax/real_of_num',type,
% 1.92/1.52 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/realax/real_add',type,
% 1.92/1.52 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/nums/NUMERAL',type,
% 1.92/1.52 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/nums/_0',type,
% 1.92/1.52 'const/nums/_0': 'type/nums/num' ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/iterate/sum',type,
% 1.92/1.52 'const/iterate/sum':
% 1.92/1.52 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/iterate/neutral',type,
% 1.92/1.52 'const/iterate/neutral':
% 1.92/1.52 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/iterate/monoidal',type,
% 1.92/1.52 'const/iterate/monoidal':
% 1.92/1.52 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/iterate/iterate',type,
% 1.92/1.52 'const/iterate/iterate':
% 1.92/1.52 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 1.92/1.52
% 1.92/1.52 thf('thf_const_const/class/COND',type,
% 1.92/1.52 'const/class/COND':
% 1.92/1.52 !>[A: $tType] : ( $o > A > A > A ) ).
% 1.92/1.52
% 1.92/1.52 thf('thm/iterate/ITERATE_CLAUSES_',axiom,
% 1.92/1.52 ! [A: $tType,A0: $tType,A1: $tType,A2: A1 > A1 > A1] :
% 1.92/1.52 ( ( 'const/iterate/monoidal' @ A1 @ A2 )
% 1.92/1.52 => ( ! [A3: A > A1] :
% 1.92/1.52 ( ( 'const/iterate/iterate' @ A @ A1 @ A2 @ ( 'const/sets/EMPTY' @ A ) @ A3 )
% 1.92/1.52 = ( 'const/iterate/neutral' @ A1 @ A2 ) )
% 1.92/1.52 & ! [A3: A0 > A1,A4: A0,A5: A0 > $o] :
% 1.92/1.52 ( ( 'const/sets/FINITE' @ A0 @ A5 )
% 1.92/1.52 => ( ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ ( 'const/sets/INSERT' @ A0 @ A4 @ A5 ) @ A3 )
% 1.92/1.52 = ( 'const/class/COND' @ A1 @ ( 'const/sets/IN' @ A0 @ A4 @ A5 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) @ ( A2 @ ( A3 @ A4 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) ) ) ) ) ) ) ).
% 1.92/1.52
% 1.92/1.52 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 1.92/1.52 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 1.92/1.52
% 1.92/1.52 thf('thm/iterate/sum_',definition,
% 1.92/1.52 ! [A: $tType] :
% 1.92/1.52 ( ( 'const/iterate/sum' @ A )
% 1.92/1.52 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 1.92/1.52
% 1.92/1.52 thf('thm/iterate/NEUTRAL_REAL_ADD_',axiom,
% 1.92/1.52 ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
% 1.92/1.52 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 1.92/1.52
% 1.92/1.52 thf('thm/iterate/SUM_CLAUSES_0',conjecture,
% 1.92/1.52 ! [A: $tType,A0: A > 'type/realax/real'] :
% 1.92/1.52 ( ( 'const/iterate/sum' @ A @ ( 'const/sets/EMPTY' @ A ) @ A0 )
% 1.92/1.52 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 1.92/1.52 ------------------------
% 1.92/1.54 % (28853)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_28752 for (2999ds/2Mi)
% 1.92/1.54 % (28851)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_28752 for (2999ds/27Mi)
% 1.92/1.54 % (28849)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28752 for (2999ds/183Mi)
% 1.92/1.54 % (28855)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28752 for (2999ds/18Mi)
% 1.92/1.54 % (28852)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28752 for (2999ds/2Mi)
% 1.92/1.54 % (28850)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_28752 for (2999ds/4Mi)
% 1.92/1.54 % (28854)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_28752 for (2999ds/275Mi)
% 1.92/1.54 % (28852)Instruction limit reached!
% 1.92/1.54 % (28852)------------------------------
% 1.92/1.54 % (28852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.54 % (28852)Termination reason: Unknown
% 1.92/1.54 % (28852)Termination phase: Property scanning
% 1.92/1.54
% 1.92/1.54 % (28853)Instruction limit reached!
% 1.92/1.54 % (28853)------------------------------
% 1.92/1.54 % (28853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.54 % (28853)Termination reason: Unknown
% 1.92/1.54 % (28853)Termination phase: shuffling
% 1.92/1.54
% 1.92/1.54 % (28853)Memory used [KB]: 1023
% 1.92/1.54 % (28853)Time elapsed: 0.003 s
% 1.92/1.54 % (28853)Instructions burned: 2 (million)
% 1.92/1.54 % (28853)------------------------------
% 1.92/1.54 % (28853)------------------------------
% 1.92/1.54 % (28852)Memory used [KB]: 1023
% 1.92/1.54 % (28852)Time elapsed: 0.003 s
% 1.92/1.54 % (28852)Instructions burned: 2 (million)
% 1.92/1.54 % (28852)------------------------------
% 1.92/1.54 % (28852)------------------------------
% 1.92/1.54 % (28854)Refutation not found, incomplete strategy
% 1.92/1.54 % (28854)------------------------------
% 1.92/1.54 % (28854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.54 % (28854)Termination reason: Refutation not found, incomplete strategy
% 1.92/1.54
% 1.92/1.54
% 1.92/1.54 % (28854)Memory used [KB]: 5500
% 1.92/1.54 % (28854)Time elapsed: 0.002 s
% 1.92/1.54 % (28854)Instructions burned: 2 (million)
% 1.92/1.54 % (28854)------------------------------
% 1.92/1.54 % (28854)------------------------------
% 1.92/1.54 % (28850)Instruction limit reached!
% 1.92/1.54 % (28850)------------------------------
% 1.92/1.54 % (28850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.54 % (28850)Termination reason: Unknown
% 1.92/1.54 % (28850)Termination phase: Saturation
% 1.92/1.54
% 1.92/1.54 % (28850)Memory used [KB]: 5500
% 1.92/1.55 % (28850)Time elapsed: 0.004 s
% 1.92/1.55 % (28850)Instructions burned: 5 (million)
% 1.92/1.55 % (28850)------------------------------
% 1.92/1.55 % (28850)------------------------------
% 1.92/1.55 % (28851)First to succeed.
% 1.92/1.55 % (28849)Also succeeded, but the first one will report.
% 1.92/1.55 % (28855)Also succeeded, but the first one will report.
% 1.92/1.55 % (28851)Refutation found. Thanks to Tanya!
% 1.92/1.55 % SZS status Theorem for DTF2THF_28752
% 1.92/1.55 % SZS output start Proof for DTF2THF_28752
% 1.92/1.55 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.92/1.55 thf(type_def_7, type, 'type/realax/real': $tType).
% 1.92/1.55 thf(type_def_8, type, sK0: $tType).
% 1.92/1.55 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.92/1.55 thf(func_def_1, type, 'type/nums/num': $tType).
% 1.92/1.55 thf(func_def_2, type, 'const/sets/INSERT': !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 1.92/1.55 thf(func_def_3, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.92/1.55 thf(func_def_4, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.92/1.55 thf(func_def_5, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.92/1.55 thf(func_def_6, type, 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real').
% 1.92/1.55 thf(func_def_7, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.92/1.55 thf(func_def_8, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.92/1.55 thf(func_def_9, type, 'const/nums/_0': 'type/nums/num').
% 1.92/1.55 thf(func_def_10, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.92/1.55 thf(func_def_11, type, 'const/iterate/neutral': !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.92/1.55 thf(func_def_12, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 1.92/1.55 thf(func_def_13, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 1.92/1.55 thf(func_def_14, type, 'const/class/COND': !>[X0: $tType]:($o > X0 > X0 > X0)).
% 1.92/1.55 thf(func_def_16, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.92/1.55 thf(func_def_19, type, sK1: sK0 > 'type/realax/real').
% 1.92/1.55 thf(func_def_21, type, ph3: !>[X0: $tType]:(X0)).
% 1.92/1.55 thf(f28,plain,(
% 1.92/1.55 $false),
% 1.92/1.55 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.92/1.55 thf(f27,plain,(
% 1.92/1.55 (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.92/1.55 inference(superposition,[status(thm)],[f23,f26])).
% 1.92/1.55 thf(f26,plain,(
% 1.92/1.55 ( ! [X0 : $tType,X1 : X0 > 'type/realax/real'] : ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1))) )),
% 1.92/1.55 inference(forward_demodulation,[status(thm)],[f25,f20])).
% 1.92/1.55 thf(f20,plain,(
% 1.92/1.55 (('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') = ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.92/1.55 inference(cnf_transformation,[status(thm)],[f4])).
% 1.92/1.55 thf(f4,axiom,(
% 1.92/1.55 (('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') = ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.92/1.55 file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/NEUTRAL_REAL_ADD_')).
% 1.92/1.55 thf(f25,plain,(
% 1.92/1.55 ( ! [X0 : $tType,X1 : X0 > 'type/realax/real'] : ((('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1))) )),
% 1.92/1.55 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.92/1.55 thf(f24,plain,(
% 1.92/1.55 ( ! [X0 : $tType,X1 : X0 > 'type/realax/real'] : (($true != $true) | (('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1))) )),
% 1.92/1.55 inference(superposition,[status(thm)],[f21,f17])).
% 1.92/1.55 thf(f17,plain,(
% 1.92/1.55 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 1.92/1.55 inference(cnf_transformation,[status(thm)],[f9])).
% 1.92/1.55 thf(f9,plain,(
% 1.92/1.55 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 1.92/1.55 inference(fool_elimination,[status(thm)],[f8])).
% 1.92/1.55 thf(f8,plain,(
% 1.92/1.55 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 1.92/1.55 inference(rectify,[status(thm)],[f2])).
% 1.92/1.55 thf(f2,axiom,(
% 1.92/1.55 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 1.92/1.55 file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 1.92/1.55 thf(f21,plain,(
% 1.92/1.55 ( ! [X0 : $tType,X2 : $tType,X3 : X2 > X2 > X2,X7 : X0 > X2] : ((('const/iterate/monoidal' @ X2 @ X3) != $true) | (('const/iterate/neutral' @ X2 @ X3) = ('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7))) )),
% 1.92/1.55 inference(cnf_transformation,[status(thm)],[f16])).
% 1.92/1.55 thf(f16,plain,(
% 1.92/1.55 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X2 > X2] : ((! [X4 : X1 > X2,X5 : X1,X6 : X1 > $o] : ((('const/iterate/iterate' @ X1 @ X2 @ X3 @ ('const/sets/INSERT' @ X1 @ X5 @ X6) @ X4) = ('const/class/COND' @ X2 @ ('const/sets/IN' @ X1 @ X5 @ X6) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4) @ (X3 @ (X4 @ X5) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4)))) | (('const/sets/FINITE' @ X1 @ X6) != $true)) & ! [X7 : X0 > X2] : (('const/iterate/neutral' @ X2 @ X3) = ('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7))) | (('const/iterate/monoidal' @ X2 @ X3) != $true))),
% 1.92/1.55 inference(rectify,[status(thm)],[f12])).
% 1.92/1.55 thf(f12,plain,(
% 1.92/1.55 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X2 > X2] : ((! [X5 : X1 > X2,X6 : X1,X7 : X1 > $o] : ((('const/iterate/iterate' @ X1 @ X2 @ X3 @ ('const/sets/INSERT' @ X1 @ X6 @ X7) @ X5) = ('const/class/COND' @ X2 @ ('const/sets/IN' @ X1 @ X6 @ X7) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5) @ (X3 @ (X5 @ X6) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5)))) | (('const/sets/FINITE' @ X1 @ X7) != $true)) & ! [X4 : X0 > X2] : (('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4) = ('const/iterate/neutral' @ X2 @ X3))) | (('const/iterate/monoidal' @ X2 @ X3) != $true))),
% 1.92/1.55 inference(ennf_transformation,[status(thm)],[f11])).
% 1.92/1.55 thf(f11,plain,(
% 1.92/1.55 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X2 > X2] : ((('const/iterate/monoidal' @ X2 @ X3) = $true) => (! [X4 : X0 > X2] : (('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4) = ('const/iterate/neutral' @ X2 @ X3)) & ! [X5 : X1 > X2,X6 : X1,X7 : X1 > $o] : ((('const/sets/FINITE' @ X1 @ X7) = $true) => (('const/iterate/iterate' @ X1 @ X2 @ X3 @ ('const/sets/INSERT' @ X1 @ X6 @ X7) @ X5) = ('const/class/COND' @ X2 @ ('const/sets/IN' @ X1 @ X6 @ X7) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5) @ (X3 @ (X5 @ X6) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5)))))))),
% 1.92/1.55 inference(fool_elimination,[status(thm)],[f10])).
% 1.92/1.55 thf(f10,plain,(
% 1.92/1.55 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X2 > X2] : (('const/iterate/monoidal' @ X2 @ X3) => (! [X4 : X0 > X2] : (('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4) = ('const/iterate/neutral' @ X2 @ X3)) & ! [X5 : X1 > X2,X6 : X1,X7 : X1 > $o] : (('const/sets/FINITE' @ X1 @ X7) => (('const/iterate/iterate' @ X1 @ X2 @ X3 @ ('const/sets/INSERT' @ X1 @ X6 @ X7) @ X5) = ('const/class/COND' @ X2 @ ('const/sets/IN' @ X1 @ X6 @ X7) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5) @ (X3 @ (X5 @ X6) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5)))))))),
% 1.92/1.55 inference(rectify,[status(thm)],[f1])).
% 1.92/1.55 thf(f1,axiom,(
% 1.92/1.55 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X2 > X2] : (('const/iterate/monoidal' @ X2 @ X3) => (! [X4 : X0 > X2] : (('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4) = ('const/iterate/neutral' @ X2 @ X3)) & ! [X4 : X1 > X2,X5 : X1,X6 : X1 > $o] : (('const/sets/FINITE' @ X1 @ X6) => (('const/iterate/iterate' @ X1 @ X2 @ X3 @ ('const/sets/INSERT' @ X1 @ X5 @ X6) @ X4) = ('const/class/COND' @ X2 @ ('const/sets/IN' @ X1 @ X5 @ X6) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4) @ (X3 @ (X4 @ X5) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4)))))))),
% 1.92/1.55 file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/ITERATE_CLAUSES_')).
% 1.92/1.55 thf(f23,plain,(
% 1.92/1.55 (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ sK0 @ sK1))),
% 1.92/1.55 inference(definition_unfolding,[status(thm)],[f19,f18])).
% 1.92/1.55 thf(f18,plain,(
% 1.92/1.55 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))) )),
% 1.92/1.55 inference(cnf_transformation,[status(thm)],[f3])).
% 1.92/1.55 thf(f3,axiom,(
% 1.92/1.55 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))),
% 1.92/1.55 file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/sum_')).
% 1.92/1.55 thf(f19,plain,(
% 1.92/1.55 (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1))),
% 1.92/1.55 inference(cnf_transformation,[status(thm)],[f15])).
% 1.92/1.55 thf(f15,plain,(
% 1.92/1.55 (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1))),
% 1.92/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 1.92/1.55 thf(f14,plain,(
% 1.92/1.55 ? [X0 : $tType,X1 : X0 > 'type/realax/real'] : (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1)) => (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1))),
% 1.92/1.55 introduced(definition,[],[choice_axiom])).
% 1.92/1.55 thf(f13,plain,(
% 1.92/1.55 ? [X0 : $tType,X1 : X0 > 'type/realax/real'] : (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != ('const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1))),
% 1.92/1.55 inference(ennf_transformation,[status(thm)],[f6])).
% 1.92/1.55 thf(f6,negated_conjecture,(
% 1.92/1.55 ~! [X0 : $tType,X1 : X0 > 'type/realax/real'] : (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1))),
% 1.92/1.55 inference(negated_conjecture,[status(cth)],[f5])).
% 1.92/1.55 thf(f5,conjecture,(
% 1.92/1.55 ! [X0 : $tType,X1 : X0 > 'type/realax/real'] : (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1))),
% 1.92/1.55 file('/export/starexec/sandbox/tmp/tmp.r0yJNU5mOs/DTF2THF_28752.p','thm/iterate/SUM_CLAUSES_0')).
% 1.92/1.55 % SZS output end Proof for DTF2THF_28752
% 1.92/1.55 % (28851)------------------------------
% 1.92/1.55 % (28851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.55 % (28851)Termination reason: Refutation
% 1.92/1.55
% 1.92/1.55 % (28851)Memory used [KB]: 5500
% 1.92/1.55 % (28851)Time elapsed: 0.005 s
% 1.92/1.55 % (28851)Instructions burned: 4 (million)
% 1.92/1.55 % (28851)------------------------------
% 1.92/1.55 % (28851)------------------------------
% 1.92/1.55 % (28848)Success in time 0.011 s
%------------------------------------------------------------------------------