%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA099^1 : 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 : n010.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 08:38:52 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 40 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 462 ( 18 ~; 8 |; 4 &; 421 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 2 con; 0-5 aty)
% Number of variables : 89 ( 21 ^; 60 !; 8 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
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/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_5,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_11,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_12,type,
sK2: sK0 > 'type/realax/real' ).
thf(func_def_13,type,
sK3: sK0 > $o ).
thf(func_def_15,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f28,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK1 @ Y0 ) @ ( sK2 @ Y0 ) ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK1 @ Y0 ) @ ( sK2 @ Y0 ) ) ) ),
inference(superposition,[status(thm)],[f22,f26]) ).
thf(f26,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X0 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X1 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X0 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X1 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f24,f19]) ).
thf(f19,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox2/tmp/tmp.kErxOHTnYu/DTF2THF_5192.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f24,plain,
! [X0: $tType,X2: sK0 > X0,X3: sK0 > X0,X1: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true )
| ( ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3
@ ^ [Y0: sK0] : ( X1 @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) )
= ( X1 @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ X2 ) @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ X3 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $tType,X2: sK0 > X0,X3: sK0 > X0,X1: X0 > X0 > X0] :
( ( $true != $true )
| ( ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3
@ ^ [Y0: sK0] : ( X1 @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) )
= ( X1 @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ X2 ) @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ X3 ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f18,f20]) ).
thf(f20,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK2 ) )
!= ( 'const/iterate/sum' @ sK0 @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK1 @ Y0 ) @ ( sK2 @ Y0 ) ) ) )
& ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f13,f15]) ).
thf(f15,plain,
( ? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
!= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X2 @ Y0 ) ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true ) )
=> ( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK2 ) )
!= ( 'const/iterate/sum' @ sK0 @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK1 @ Y0 ) @ ( sK2 @ Y0 ) ) ) )
& ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
!= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X2 @ Y0 ) ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X3 )
=> ( ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X3 )
=> ( ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X3 )
=> ( ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kErxOHTnYu/DTF2THF_5192.p','thm/iterate/SUM_ADD_') ).
thf(f18,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > X1,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true )
| ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) @ ( X4 @ Y0 ) ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > X1,X4: X0 > X1,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true )
| ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) @ ( X4 @ Y0 ) ) ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ! [X3: X0 > X1,X4: X0 > X1,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X5 )
= $true )
=> ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) @ ( X4 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > X1,X5: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X5 )
=> ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5
@ ^ [X6: X0] : ( X2 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > X1,X5: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X5 )
=> ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5
@ ^ [X6: X0] : ( X2 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kErxOHTnYu/DTF2THF_5192.p','thm/iterate/ITERATE_OP_') ).
thf(f22,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK1 @ Y0 ) @ ( sK2 @ Y0 ) ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ sK1 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f17,f17,f17]) ).
thf(f17,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kErxOHTnYu/DTF2THF_5192.p','thm/iterate/sum_') ).
thf(f21,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK2 ) )
!= ( 'const/iterate/sum' @ sK0 @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK1 @ Y0 ) @ ( sK2 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA099^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n010.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 03:50:03 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.45 ---- Original DTF file ---
% 0.27/0.45 thf(spec,logic,$$dhol).
% 0.27/0.45 %------------------------------------------------------------------------------
% 0.27/0.45 % File : ANA099^1 : TPTP v9.2.1. Released v7.0.0.
% 0.27/0.45 % Domain : Analysis
% 0.27/0.45 % Problem : SUM_ADD
% 0.27/0.45 % Version : Especial.
% 0.27/0.45 % English :
% 0.27/0.45
% 0.27/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.27/0.45 % Source : [Kal16]
% 0.27/0.45 % Names : SUM_ADD_.p [Kal16]
% 0.27/0.45
% 0.27/0.45 % Status : Theorem
% 0.27/0.45 % Rating : 0.00 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.27/0.45 % Syntax : Number of formulae : 10 ( 2 unt; 6 typ; 1 def)
% 0.27/0.45 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.27/0.45 % Maximal formula atoms : 3 ( 1 avg)
% 0.27/0.45 % Number of connectives : 51 ( 0 ~; 0 |; 0 &; 48 @)
% 0.27/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.27/0.45 % Maximal formula depth : 11 ( 6 avg)
% 0.27/0.45 % Number of types : 2 ( 1 usr)
% 0.27/0.45 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.27/0.45 % Number of symbols : 6 ( 5 usr; 0 con; 2-5 aty)
% 0.27/0.45 % Number of variables : 18 ( 2 ^; 11 !; 0 ?; 18 :)
% 0.27/0.45 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.27/0.45 % SPC : TH1_THM_EQU_NAR
% 0.27/0.45
% 0.27/0.45 % Comments : Exported from core HOL Light.
% 0.27/0.45 %------------------------------------------------------------------------------
% 0.27/0.45 thf('thf_type_type/realax/real',type,
% 0.27/0.45 'type/realax/real': $tType ).
% 0.27/0.45
% 0.27/0.45 thf('thf_const_const/sets/FINITE',type,
% 0.27/0.45 'const/sets/FINITE':
% 0.27/0.45 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.27/0.45
% 0.27/0.45 thf('thf_const_const/realax/real_add',type,
% 0.27/0.45 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.27/0.45
% 0.27/0.45 thf('thf_const_const/iterate/sum',type,
% 0.27/0.45 'const/iterate/sum':
% 0.27/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.27/0.45
% 0.27/0.45 thf('thf_const_const/iterate/monoidal',type,
% 0.27/0.45 'const/iterate/monoidal':
% 0.27/0.45 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.27/0.45
% 0.27/0.45 thf('thf_const_const/iterate/iterate',type,
% 0.27/0.45 'const/iterate/iterate':
% 0.27/0.45 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 0.27/0.45
% 0.27/0.45 thf('thm/iterate/sum_',definition,
% 0.27/0.45 ! [A: $tType] :
% 0.27/0.45 ( ( 'const/iterate/sum' @ A )
% 0.27/0.45 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 0.27/0.45
% 0.27/0.45 thf('thm/iterate/ITERATE_OP_',axiom,
% 0.27/0.45 ! [A: $tType,A0: $tType,A1: A0 > A0 > A0] :
% 0.27/0.45 ( ( 'const/iterate/monoidal' @ A0 @ A1 )
% 0.27/0.45 => ! [A2: A > A0,A3: A > A0,A4: A > $o] :
% 0.27/0.45 ( ( 'const/sets/FINITE' @ A @ A4 )
% 0.27/0.45 => ( ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A4
% 0.27/0.45 @ ^ [A5: A] : ( A1 @ ( A2 @ A5 ) @ ( A3 @ A5 ) ) )
% 0.27/0.45 = ( A1 @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A4 @ A2 ) @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A4 @ A3 ) ) ) ) ) ).
% 0.27/0.45
% 0.27/0.45 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 0.27/0.45 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 0.27/0.45
% 0.27/0.45 thf('thm/iterate/SUM_ADD_',conjecture,
% 0.27/0.45 ! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
% 0.27/0.45 ( ( 'const/sets/FINITE' @ A @ A2 )
% 0.27/0.45 => ( ( 'const/iterate/sum' @ A @ A2
% 0.27/0.45 @ ^ [A3: A] : ( 'const/realax/real_add' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) )
% 0.27/0.45 = ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ) ).
% 0.27/0.45
% 0.27/0.45 %------------------------------------------------------------------------------
% 0.27/0.45 ------------------------
% 1.48/1.26 ---- Embedded in THF ---
% 1.48/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.26 %%% Generated on Tue Feb 24 03:50:04 EST 2026
% 1.48/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.26 %%% Logic specification used:
% 1.48/1.26 %%% thf(spec, logic, $$dhol).
% 1.48/1.26
% 1.48/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.kErxOHTnYu/DTF2DTF5192.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.27 ---- Cleaned THF ---
% 1.48/1.27 thf('thf_type_type/realax/real',type,
% 1.48/1.27 'type/realax/real': $tType ).
% 1.48/1.27
% 1.48/1.27 thf('thf_const_const/sets/FINITE',type,
% 1.48/1.27 'const/sets/FINITE':
% 1.48/1.27 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.48/1.27
% 1.48/1.27 thf('thf_const_const/realax/real_add',type,
% 1.48/1.27 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.48/1.27
% 1.48/1.27 thf('thf_const_const/iterate/sum',type,
% 1.48/1.27 'const/iterate/sum':
% 1.48/1.27 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.48/1.27
% 1.48/1.27 thf('thf_const_const/iterate/monoidal',type,
% 1.48/1.27 'const/iterate/monoidal':
% 1.48/1.27 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 1.48/1.27
% 1.48/1.27 thf('thf_const_const/iterate/iterate',type,
% 1.48/1.27 'const/iterate/iterate':
% 1.48/1.27 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 1.48/1.27
% 1.48/1.27 thf('thm/iterate/sum_',definition,
% 1.48/1.27 ! [A: $tType] :
% 1.48/1.27 ( ( 'const/iterate/sum' @ A )
% 1.48/1.27 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 1.48/1.27
% 1.48/1.27 thf('thm/iterate/ITERATE_OP_',axiom,
% 1.48/1.27 ! [A: $tType,A0: $tType,A1: A0 > A0 > A0] :
% 1.48/1.27 ( ( 'const/iterate/monoidal' @ A0 @ A1 )
% 1.48/1.27 => ! [A2: A > A0,A3: A > A0,A4: A > $o] :
% 1.48/1.27 ( ( 'const/sets/FINITE' @ A @ A4 )
% 1.48/1.27 => ( ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A4
% 1.48/1.27 @ ^ [A5: A] : ( A1 @ ( A2 @ A5 ) @ ( A3 @ A5 ) ) )
% 1.48/1.27 = ( A1 @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A4 @ A2 ) @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A4 @ A3 ) ) ) ) ) ).
% 1.48/1.27
% 1.48/1.27 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 1.48/1.27 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 1.48/1.27
% 1.48/1.27 thf('thm/iterate/SUM_ADD_',conjecture,
% 1.48/1.27 ! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
% 1.48/1.27 ( ( 'const/sets/FINITE' @ A @ A2 )
% 1.48/1.27 => ( ( 'const/iterate/sum' @ A @ A2
% 1.48/1.27 @ ^ [A3: A] : ( 'const/realax/real_add' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) )
% 1.48/1.27 = ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ) ).
% 1.48/1.28 ------------------------
% 1.48/1.29 % (5401)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5192 for (2999ds/18Mi)
% 1.48/1.29 % (5398)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5192 for (2999ds/2Mi)
% 1.48/1.29 % (5398)Instruction limit reached!
% 1.48/1.29 % (5398)------------------------------
% 1.48/1.29 % (5398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (5398)Termination reason: Unknown
% 1.48/1.29 % (5398)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (5398)Memory used [KB]: 5500
% 1.48/1.29 % (5398)Time elapsed: 0.002 s
% 1.48/1.29 % (5398)Instructions burned: 3 (million)
% 1.48/1.29 % (5398)------------------------------
% 1.48/1.29 % (5398)------------------------------
% 1.48/1.29 % (5401)First to succeed.
% 1.48/1.29 % (5401)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_5192
% 1.48/1.29 % SZS output start Proof for DTF2THF_5192
% 1.48/1.29 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.48/1.29 thf(type_def_7, type, sK0: $tType).
% 1.48/1.29 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.48/1.29 thf(func_def_1, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.48/1.29 thf(func_def_2, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.48/1.29 thf(func_def_3, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.48/1.29 thf(func_def_4, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 1.48/1.29 thf(func_def_5, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 1.48/1.29 thf(func_def_11, type, sK1: sK0 > 'type/realax/real').
% 1.48/1.29 thf(func_def_12, type, sK2: sK0 > 'type/realax/real').
% 1.48/1.29 thf(func_def_13, type, sK3: sK0 > $o).
% 1.48/1.29 thf(func_def_15, type, ph5: !>[X0: $tType]:(X0)).
% 1.48/1.29 thf(f28,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.48/1.29 thf(f27,plain,(
% 1.48/1.29 (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_add' @ (sK1 @ Y0) @ (sK2 @ Y0)))) != ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_add' @ (sK1 @ Y0) @ (sK2 @ Y0)))))),
% 1.48/1.29 inference(superposition,[status(thm)],[f22,f26])).
% 1.48/1.29 thf(f26,plain,(
% 1.48/1.29 ( ! [X0 : sK0 > 'type/realax/real',X1 : sK0 > 'type/realax/real'] : ((('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X0) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X1)) = ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_add' @ (X0 @ Y0) @ (X1 @ Y0)))))) )),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.48/1.29 thf(f25,plain,(
% 1.48/1.29 ( ! [X0 : sK0 > 'type/realax/real',X1 : sK0 > 'type/realax/real'] : (($true != $true) | (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X0) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X1)) = ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_add' @ (X0 @ Y0) @ (X1 @ Y0)))))) )),
% 1.48/1.29 inference(superposition,[status(thm)],[f24,f19])).
% 1.48/1.29 thf(f19,plain,(
% 1.48/1.29 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 1.48/1.29 inference(rectify,[status(thm)],[f3])).
% 1.48/1.29 thf(f3,axiom,(
% 1.48/1.29 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.kErxOHTnYu/DTF2THF_5192.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 1.48/1.29 thf(f24,plain,(
% 1.48/1.29 ( ! [X0 : $tType,X2 : sK0 > X0,X3 : sK0 > X0,X1 : X0 > X0 > X0] : ((('const/iterate/monoidal' @ X0 @ X1) != $true) | (('const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ (^[Y0 : sK0]: (X1 @ (X2 @ Y0) @ (X3 @ Y0)))) = (X1 @ ('const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ X2) @ ('const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ X3)))) )),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.48/1.29 thf(f23,plain,(
% 1.48/1.29 ( ! [X0 : $tType,X2 : sK0 > X0,X3 : sK0 > X0,X1 : X0 > X0 > X0] : (($true != $true) | (('const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ (^[Y0 : sK0]: (X1 @ (X2 @ Y0) @ (X3 @ Y0)))) = (X1 @ ('const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ X2) @ ('const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK3 @ X3))) | (('const/iterate/monoidal' @ X0 @ X1) != $true)) )),
% 1.48/1.29 inference(superposition,[status(thm)],[f18,f20])).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 (('const/sets/FINITE' @ sK0 @ sK3) = $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f16])).
% 1.48/1.29 thf(f16,plain,(
% 1.48/1.29 (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK2)) != ('const/iterate/sum' @ sK0 @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_add' @ (sK1 @ Y0) @ (sK2 @ Y0))))) & (('const/sets/FINITE' @ sK0 @ sK3) = $true)),
% 1.48/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f13,f15])).
% 1.48/1.29 thf(f15,plain,(
% 1.48/1.29 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) != ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/realax/real_add' @ (X1 @ Y0) @ (X2 @ Y0))))) & (('const/sets/FINITE' @ X0 @ X3) = $true)) => ((('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK2)) != ('const/iterate/sum' @ sK0 @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_add' @ (sK1 @ Y0) @ (sK2 @ Y0))))) & (('const/sets/FINITE' @ sK0 @ sK3) = $true))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f13,plain,(
% 1.48/1.29 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) != ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/realax/real_add' @ (X1 @ Y0) @ (X2 @ Y0))))) & (('const/sets/FINITE' @ X0 @ X3) = $true))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f12])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X3) = $true) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = ('const/iterate/sum' @ X0 @ X3 @ (^[Y0 : X0]: ('const/realax/real_add' @ (X1 @ Y0) @ (X2 @ Y0))))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f11])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X3) => (('const/iterate/sum' @ X0 @ X3 @ (^[X4 : X0] : ('const/realax/real_add' @ (X1 @ X4) @ (X2 @ X4)))) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f5])).
% 1.48/1.29 thf(f5,negated_conjecture,(
% 1.48/1.29 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X3) => (('const/iterate/sum' @ X0 @ X3 @ (^[X4 : X0] : ('const/realax/real_add' @ (X1 @ X4) @ (X2 @ X4)))) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f4])).
% 1.48/1.29 thf(f4,conjecture,(
% 1.48/1.29 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X3) => (('const/iterate/sum' @ X0 @ X3 @ (^[X4 : X0] : ('const/realax/real_add' @ (X1 @ X4) @ (X2 @ X4)))) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.kErxOHTnYu/DTF2THF_5192.p','thm/iterate/SUM_ADD_')).
% 1.48/1.29 thf(f18,plain,(
% 1.48/1.29 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X3 : X0 > X1,X4 : X0 > X1,X5 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X5) != $true) | ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4)) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ (^[Y0 : X0]: (X2 @ (X3 @ Y0) @ (X4 @ Y0))))) | (('const/iterate/monoidal' @ X1 @ X2) != $true)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.29 thf(f14,plain,(
% 1.48/1.29 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (! [X3 : X0 > X1,X4 : X0 > X1,X5 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X5) != $true) | ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4)) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ (^[Y0 : X0]: (X2 @ (X3 @ Y0) @ (X4 @ Y0)))))) | (('const/iterate/monoidal' @ X1 @ X2) != $true))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f10])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : ((('const/iterate/monoidal' @ X1 @ X2) = $true) => ! [X3 : X0 > X1,X4 : X0 > X1,X5 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X5) = $true) => ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4)) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ (^[Y0 : X0]: (X2 @ (X3 @ Y0) @ (X4 @ Y0)))))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f9])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (('const/iterate/monoidal' @ X1 @ X2) => ! [X3 : X0 > X1,X4 : X0 > X1,X5 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X5) => ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4)) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ (^[X6 : X0] : (X2 @ (X3 @ X6) @ (X4 @ X6)))))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f2])).
% 1.48/1.29 thf(f2,axiom,(
% 1.48/1.29 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (('const/iterate/monoidal' @ X1 @ X2) => ! [X3 : X0 > X1,X4 : X0 > X1,X5 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X5) => ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4)) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ (^[X6 : X0] : (X2 @ (X3 @ X6) @ (X4 @ X6)))))))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.kErxOHTnYu/DTF2THF_5192.p','thm/iterate/ITERATE_OP_')).
% 1.48/1.29 thf(f22,plain,(
% 1.48/1.29 (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_add' @ (sK1 @ Y0) @ (sK2 @ Y0)))) != ('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ sK1) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ sK2)))),
% 1.48/1.29 inference(definition_unfolding,[status(thm)],[f21,f17,f17,f17])).
% 1.48/1.29 thf(f17,plain,(
% 1.48/1.29 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f1])).
% 1.48/1.29 thf(f1,axiom,(
% 1.48/1.29 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.kErxOHTnYu/DTF2THF_5192.p','thm/iterate/sum_')).
% 1.48/1.29 thf(f21,plain,(
% 1.48/1.29 (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK2)) != ('const/iterate/sum' @ sK0 @ sK3 @ (^[Y0 : sK0]: ('const/realax/real_add' @ (sK1 @ Y0) @ (sK2 @ Y0)))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f16])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_5192
% 1.48/1.29 % (5401)------------------------------
% 1.48/1.29 % (5401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (5401)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (5401)Memory used [KB]: 5500
% 1.48/1.29 % (5401)Time elapsed: 0.004 s
% 1.48/1.29 % (5401)Instructions burned: 4 (million)
% 1.48/1.29 % (5401)------------------------------
% 1.48/1.29 % (5401)------------------------------
% 1.48/1.29 % (5394)Success in time 0.014 s
%------------------------------------------------------------------------------