%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA098^1 : 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 : n031.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 1.74s 1.41s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 392 ( 9 ~; 0 |; 0 &; 382 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 1 con; 0-6 aty)
% Number of variables : 77 ( 10 ^; 61 !; 6 ?; 77 :)
% 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/ITSET':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > ( X0 > $o ) > X1 > X1 ) ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_4,type,
'const/iterate/support':
!>[X0: $tType,X1: $tType] : ( ( X0 > X0 > X0 ) > ( X1 > X0 ) > ( X1 > $o ) > X1 > $o ) ).
thf(func_def_5,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_6,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_7,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_8,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_10,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_16,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_17,type,
sK2: sK0 > $o ).
thf(func_def_19,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f30,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1 )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1 ) ),
inference(superposition,[status(thm)],[f18,f27]) ).
thf(f27,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4 ) @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ),
inference(forward_demodulation,[status(thm)],[f26,f19]) ).
thf(f19,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1,X3: X0 > $o,X4: X1 > X1 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X4 @ X3 @ X2 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3 ) )
@ ( 'const/sets/ITSET' @ X0 @ X1
@ ^ [Y0: X0] : ( X4 @ ( X2 @ Y0 ) )
@ ( 'const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3 )
@ ( 'const/iterate/neutral' @ X1 @ X4 ) )
@ ( 'const/iterate/neutral' @ X1 @ X4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1,X3: X0 > $o,X4: X1 > X1 > X1] :
( ( 'const/class/COND' @ X1 @ ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3 ) )
@ ( 'const/sets/ITSET' @ X0 @ X1
@ ^ [Y0: X0,Y1: X1] : ( X4 @ ( X2 @ Y0 ) @ Y1 )
@ ( 'const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3 )
@ ( 'const/iterate/neutral' @ X1 @ X4 ) )
@ ( 'const/iterate/neutral' @ X1 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X4 @ X3 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1,X3: X0 > $o,X4: X1 > X1 > X1] :
( ( 'const/class/COND' @ X1 @ ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3 ) )
@ ( 'const/sets/ITSET' @ X0 @ X1
@ ^ [Y0: X0,Y1: X1] : ( X4 @ ( X2 @ Y0 ) @ Y1 )
@ ( 'const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3 )
@ ( 'const/iterate/neutral' @ X1 @ X4 ) )
@ ( 'const/iterate/neutral' @ X1 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X4 @ X3 @ X2 ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1,X3: X0 > $o,X4: X1 > X1 > X1] :
( ( 'const/class/COND' @ X1 @ ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3 ) )
@ ( 'const/sets/ITSET' @ X0 @ X1
@ ^ [X5: X0,X6: X1] : ( X4 @ ( X2 @ X5 ) @ X6 )
@ ( 'const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3 )
@ ( 'const/iterate/neutral' @ X1 @ X4 ) )
@ ( 'const/iterate/neutral' @ X1 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X4 @ X3 @ X2 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X3: X0 > X1,X4: X0 > $o,X5: X1 > X1 > X1] :
( ( 'const/class/COND' @ X1 @ ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X5 @ X3 @ X4 ) )
@ ( 'const/sets/ITSET' @ X0 @ X1
@ ^ [X6: X0,X7: X1] : ( X5 @ ( X3 @ X6 ) @ X7 )
@ ( 'const/iterate/support' @ X1 @ X0 @ X5 @ X3 @ X4 )
@ ( 'const/iterate/neutral' @ X1 @ X5 ) )
@ ( 'const/iterate/neutral' @ X1 @ X5 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X5 @ X4 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.GBhyE2mWwv/DTF2THF_1973.p','thm/iterate/iterate_') ).
thf(f26,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4 ) )
@ ( 'const/sets/ITSET' @ X0 @ X1
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) )
@ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4 )
@ ( 'const/iterate/neutral' @ X1 @ X2 ) )
@ ( 'const/iterate/neutral' @ X1 @ X2 ) ) ),
inference(superposition,[status(thm)],[f19,f15]) ).
thf(f15,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: $tType,X3: X0 > X0 > X0,X4: X1 > X0,X5: X1 > $o] :
( ( 'const/iterate/support' @ X0 @ X1 @ X3 @ X4 @ X5 )
= ( 'const/iterate/support' @ X0 @ X1 @ X3 @ X4 @ ( 'const/iterate/support' @ X0 @ X1 @ X3 @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GBhyE2mWwv/DTF2THF_1973.p','thm/iterate/SUPPORT_SUPPORT_') ).
thf(f18,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1 )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK1 @ sK2 ) @ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f14,f16,f16]) ).
thf(f16,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GBhyE2mWwv/DTF2THF_1973.p','thm/iterate/sum_') ).
thf(f14,plain,
( ( 'const/iterate/sum' @ sK0 @ sK2 @ sK1 )
!= ( 'const/iterate/sum' @ sK0 @ ( 'const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK1 @ sK2 ) @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( 'const/iterate/sum' @ sK0 @ sK2 @ sK1 )
!= ( 'const/iterate/sum' @ sK0 @ ( 'const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK1 @ sK2 ) @ sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).
thf(f12,plain,
( ? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X2 ) @ X1 )
!= ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
=> ( ( 'const/iterate/sum' @ sK0 @ sK2 @ sK1 )
!= ( 'const/iterate/sum' @ sK0 @ ( 'const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK1 @ sK2 ) @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X2 ) @ X1 )
!= ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X2 ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X3: X0 > $o] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X3 ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real',X3: X0 > $o] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X3 ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.GBhyE2mWwv/DTF2THF_1973.p','thm/iterate/SUM_SUPPORT_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ANA098^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.31 % Computer : n031.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Feb 24 03:51:17 EST 2026
% 0.11/0.31 % CPUTime :
% 0.11/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : ANA098^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.40 % Domain : Analysis
% 0.17/0.40 % Problem : SUM_SUPPORT
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English :
% 0.17/0.40
% 0.17/0.40 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Kal16]
% 0.17/0.40 % Names : SUM_SUPPORT_.p [Kal16]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.17/0.40 % Syntax : Number of formulae : 13 ( 4 unt; 9 typ; 1 def)
% 0.17/0.40 % Number of atoms : 11 ( 4 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 1 ( 2 avg)
% 0.17/0.40 % Number of connectives : 63 ( 0 ~; 0 |; 0 &; 63 @)
% 0.17/0.40 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 6 ( 5 avg)
% 0.17/0.40 % Number of types : 2 ( 1 usr)
% 0.17/0.40 % Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 9 ( 8 usr; 0 con; 2-6 aty)
% 0.17/0.40 % Number of variables : 26 ( 2 ^; 14 !; 0 ?; 26 :)
% 0.17/0.40 % ( 10 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.40 % SPC : TH1_THM_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : Exported from core HOL Light.
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf('thf_type_type/realax/real',type,
% 0.17/0.40 'type/realax/real': $tType ).
% 0.17/0.40
% 0.17/0.40 thf('thf_const_const/sets/ITSET',type,
% 0.17/0.40 'const/sets/ITSET':
% 0.17/0.40 !>[A: $tType,A0: $tType] : ( ( A > A0 > A0 ) > ( A > $o ) > A0 > A0 ) ).
% 0.17/0.40
% 0.17/0.40 thf('thf_const_const/sets/FINITE',type,
% 0.17/0.40 'const/sets/FINITE':
% 0.17/0.40 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.17/0.40
% 0.17/0.40 thf('thf_const_const/realax/real_add',type,
% 0.17/0.40 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.17/0.40
% 0.17/0.40 thf('thf_const_const/iterate/support',type,
% 0.17/0.40 'const/iterate/support':
% 0.17/0.40 !>[B: $tType,A: $tType] : ( ( B > B > B ) > ( A > B ) > ( A > $o ) > A > $o ) ).
% 0.17/0.40
% 0.17/0.40 thf('thf_const_const/iterate/sum',type,
% 0.17/0.40 'const/iterate/sum':
% 0.17/0.40 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.17/0.40
% 0.17/0.40 thf('thf_const_const/iterate/neutral',type,
% 0.17/0.40 'const/iterate/neutral':
% 0.17/0.40 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 0.17/0.40
% 0.17/0.40 thf('thf_const_const/iterate/iterate',type,
% 0.17/0.40 'const/iterate/iterate':
% 0.17/0.40 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 0.17/0.40
% 0.17/0.40 thf('thf_const_const/class/COND',type,
% 0.17/0.40 'const/class/COND':
% 0.17/0.40 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.17/0.40
% 0.17/0.40 thf('thm/iterate/iterate_',axiom,
% 0.17/0.40 ! [A: $tType,A0: $tType,A1: A > A0,A2: A > $o,A3: A0 > A0 > A0] :
% 0.17/0.40 ( ( 'const/iterate/iterate' @ A @ A0 @ A3 @ A2 @ A1 )
% 0.17/0.40 = ( 'const/class/COND' @ A0 @ ( 'const/sets/FINITE' @ A @ ( 'const/iterate/support' @ A0 @ A @ A3 @ A1 @ A2 ) )
% 0.17/0.40 @ ( 'const/sets/ITSET' @ A @ A0
% 0.17/0.40 @ ^ [A4: A,A5: A0] : ( A3 @ ( A1 @ A4 ) @ A5 )
% 0.17/0.40 @ ( 'const/iterate/support' @ A0 @ A @ A3 @ A1 @ A2 )
% 0.17/0.40 @ ( 'const/iterate/neutral' @ A0 @ A3 ) )
% 0.17/0.40 @ ( 'const/iterate/neutral' @ A0 @ A3 ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf('thm/iterate/sum_',definition,
% 0.17/0.40 ! [A: $tType] :
% 0.17/0.40 ( ( 'const/iterate/sum' @ A )
% 0.17/0.40 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 0.17/0.40
% 0.17/0.40 thf('thm/iterate/SUPPORT_SUPPORT_',axiom,
% 0.17/0.40 ! [A: $tType,A0: $tType,A1: A > A > A,A2: A0 > A,A3: A0 > $o] :
% 0.17/0.40 ( ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ A3 ) )
% 0.17/0.40 = ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ A3 ) ) ).
% 0.17/0.40
% 0.17/0.40 thf('thm/iterate/SUM_SUPPORT_',conjecture,
% 0.17/0.40 ! [A: $tType,A0: A > 'type/realax/real',A1: A > $o] :
% 0.17/0.40 ( ( 'const/iterate/sum' @ A @ ( 'const/iterate/support' @ 'type/realax/real' @ A @ 'const/realax/real_add' @ A0 @ A1 ) @ A0 )
% 0.17/0.40 = ( 'const/iterate/sum' @ A @ A1 @ A0 ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.57/1.37 ---- Embedded in THF ---
% 1.57/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.37 %%% Generated on Tue Feb 24 03:51:18 EST 2026
% 1.57/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.37 %%% Logic specification used:
% 1.57/1.37 %%% thf(spec, logic, $$dhol).
% 1.57/1.37
% 1.57/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.GBhyE2mWwv/DTF2DTF1973.p
% See solution above
% 1.57/1.37 ------------------------
% 1.57/1.38 ---- Cleaned THF ---
% 1.57/1.38 thf('thf_type_type/realax/real',type,
% 1.57/1.38 'type/realax/real': $tType ).
% 1.57/1.38
% 1.57/1.38 thf('thf_const_const/sets/ITSET',type,
% 1.57/1.38 'const/sets/ITSET':
% 1.57/1.38 !>[A: $tType,A0: $tType] : ( ( A > A0 > A0 ) > ( A > $o ) > A0 > A0 ) ).
% 1.57/1.38
% 1.57/1.38 thf('thf_const_const/sets/FINITE',type,
% 1.57/1.38 'const/sets/FINITE':
% 1.57/1.38 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.57/1.38
% 1.57/1.38 thf('thf_const_const/realax/real_add',type,
% 1.57/1.38 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.57/1.38
% 1.57/1.38 thf('thf_const_const/iterate/support',type,
% 1.57/1.38 'const/iterate/support':
% 1.57/1.38 !>[B: $tType,A: $tType] : ( ( B > B > B ) > ( A > B ) > ( A > $o ) > A > $o ) ).
% 1.57/1.38
% 1.57/1.38 thf('thf_const_const/iterate/sum',type,
% 1.57/1.38 'const/iterate/sum':
% 1.57/1.38 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.57/1.38
% 1.57/1.38 thf('thf_const_const/iterate/neutral',type,
% 1.57/1.38 'const/iterate/neutral':
% 1.57/1.38 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 1.57/1.38
% 1.57/1.38 thf('thf_const_const/iterate/iterate',type,
% 1.57/1.38 'const/iterate/iterate':
% 1.57/1.38 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 1.57/1.38
% 1.57/1.38 thf('thf_const_const/class/COND',type,
% 1.57/1.38 'const/class/COND':
% 1.57/1.38 !>[A: $tType] : ( $o > A > A > A ) ).
% 1.57/1.38
% 1.57/1.38 thf('thm/iterate/iterate_',axiom,
% 1.57/1.38 ! [A: $tType,A0: $tType,A1: A > A0,A2: A > $o,A3: A0 > A0 > A0] :
% 1.57/1.38 ( ( 'const/iterate/iterate' @ A @ A0 @ A3 @ A2 @ A1 )
% 1.57/1.38 = ( 'const/class/COND' @ A0 @ ( 'const/sets/FINITE' @ A @ ( 'const/iterate/support' @ A0 @ A @ A3 @ A1 @ A2 ) )
% 1.57/1.38 @ ( 'const/sets/ITSET' @ A @ A0
% 1.57/1.38 @ ^ [A4: A,A5: A0] : ( A3 @ ( A1 @ A4 ) @ A5 )
% 1.57/1.38 @ ( 'const/iterate/support' @ A0 @ A @ A3 @ A1 @ A2 )
% 1.57/1.38 @ ( 'const/iterate/neutral' @ A0 @ A3 ) )
% 1.57/1.38 @ ( 'const/iterate/neutral' @ A0 @ A3 ) ) ) ).
% 1.57/1.38
% 1.57/1.38 thf('thm/iterate/sum_',definition,
% 1.57/1.38 ! [A: $tType] :
% 1.57/1.38 ( ( 'const/iterate/sum' @ A )
% 1.57/1.38 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 1.57/1.38
% 1.57/1.38 thf('thm/iterate/SUPPORT_SUPPORT_',axiom,
% 1.57/1.38 ! [A: $tType,A0: $tType,A1: A > A > A,A2: A0 > A,A3: A0 > $o] :
% 1.57/1.38 ( ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ A3 ) )
% 1.57/1.38 = ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ A3 ) ) ).
% 1.57/1.38
% 1.57/1.38 thf('thm/iterate/SUM_SUPPORT_',conjecture,
% 1.57/1.38 ! [A: $tType,A0: A > 'type/realax/real',A1: A > $o] :
% 1.57/1.38 ( ( 'const/iterate/sum' @ A @ ( 'const/iterate/support' @ 'type/realax/real' @ A @ 'const/realax/real_add' @ A0 @ A1 ) @ A0 )
% 1.57/1.38 = ( 'const/iterate/sum' @ A @ A1 @ A0 ) ) ).
% 1.57/1.38 ------------------------
% 1.74/1.40 % (2077)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_1973 for (2999ds/2Mi)
% 1.74/1.40 % (2079)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1973 for (2999ds/18Mi)
% 1.74/1.40 % (2076)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1973 for (2999ds/2Mi)
% 1.74/1.40 % (2074)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_1973 for (2999ds/4Mi)
% 1.74/1.40 % (2075)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_1973 for (2999ds/27Mi)
% 1.74/1.40 % (2078)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_1973 for (2999ds/275Mi)
% 1.74/1.40 % (2076)Instruction limit reached!
% 1.74/1.40 % (2076)------------------------------
% 1.74/1.40 % (2076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.40 % (2076)Termination reason: Unknown
% 1.74/1.40 % (2076)Termination phase: Preprocessing 3
% 1.74/1.40
% 1.74/1.40 % (2076)Memory used [KB]: 895
% 1.74/1.40 % (2076)Time elapsed: 0.003 s
% 1.74/1.40 % (2076)Instructions burned: 2 (million)
% 1.74/1.40 % (2076)------------------------------
% 1.74/1.40 % (2076)------------------------------
% 1.74/1.40 % (2077)Instruction limit reached!
% 1.74/1.40 % (2077)------------------------------
% 1.74/1.40 % (2077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.40 % (2077)Termination reason: Unknown
% 1.74/1.40 % (2077)Termination phase: shuffling
% 1.74/1.40
% 1.74/1.40 % (2077)Memory used [KB]: 895
% 1.74/1.40 % (2077)Time elapsed: 0.003 s
% 1.74/1.40 % (2077)Instructions burned: 2 (million)
% 1.74/1.40 % (2077)------------------------------
% 1.74/1.40 % (2077)------------------------------
% 1.74/1.40 % (2078)Refutation not found, incomplete strategy
% 1.74/1.40 % (2078)------------------------------
% 1.74/1.40 % (2078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.40 % (2078)Termination reason: Refutation not found, incomplete strategy
% 1.74/1.40
% 1.74/1.40
% 1.74/1.40 % (2078)Memory used [KB]: 5500
% 1.74/1.40 % (2078)Time elapsed: 0.003 s
% 1.74/1.40 % (2078)Instructions burned: 2 (million)
% 1.74/1.40 % (2078)------------------------------
% 1.74/1.40 % (2078)------------------------------
% 1.74/1.40 % (2074)Instruction limit reached!
% 1.74/1.40 % (2074)------------------------------
% 1.74/1.40 % (2074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.40 % (2074)Termination reason: Unknown
% 1.74/1.40 % (2074)Termination phase: Saturation
% 1.74/1.40
% 1.74/1.40 % (2074)Memory used [KB]: 5500
% 1.74/1.40 % (2074)Time elapsed: 0.005 s
% 1.74/1.40 % (2074)Instructions burned: 5 (million)
% 1.74/1.40 % (2074)------------------------------
% 1.74/1.40 % (2074)------------------------------
% 1.74/1.40 % (2073)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1973 for (2999ds/183Mi)
% 1.74/1.41 % (2075)First to succeed.
% 1.74/1.41 % (2075)Refutation found. Thanks to Tanya!
% 1.74/1.41 % SZS status Theorem for DTF2THF_1973
% 1.74/1.41 % SZS output start Proof for DTF2THF_1973
% 1.74/1.41 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.74/1.41 thf(type_def_7, type, sK0: $tType).
% 1.74/1.41 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.74/1.41 thf(func_def_1, type, 'const/sets/ITSET': !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > (X0 > $o) > X1 > X1)).
% 1.74/1.41 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.74/1.41 thf(func_def_3, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.74/1.41 thf(func_def_4, type, 'const/iterate/support': !>[X0: $tType, X1: $tType]:((X0 > X0 > X0) > (X1 > X0) > (X1 > $o) > X1 > $o)).
% 1.74/1.41 thf(func_def_5, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.74/1.41 thf(func_def_6, type, 'const/iterate/neutral': !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.74/1.41 thf(func_def_7, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 1.74/1.41 thf(func_def_8, type, 'const/class/COND': !>[X0: $tType]:($o > X0 > X0 > X0)).
% 1.74/1.41 thf(func_def_10, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.74/1.41 thf(func_def_16, type, sK1: sK0 > 'type/realax/real').
% 1.74/1.41 thf(func_def_17, type, sK2: sK0 > $o).
% 1.74/1.41 thf(func_def_19, type, ph4: !>[X0: $tType]:(X0)).
% 1.74/1.41 thf(f30,plain,(
% 1.74/1.41 $false),
% 1.74/1.41 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.74/1.41 thf(f29,plain,(
% 1.74/1.41 (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1) != ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1))),
% 1.74/1.41 inference(superposition,[status(thm)],[f18,f27])).
% 1.74/1.41 thf(f27,plain,(
% 1.74/1.41 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X3 : X0 > X1,X4 : X0 > $o] : ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4) @ X3) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3))) )),
% 1.74/1.41 inference(forward_demodulation,[status(thm)],[f26,f19])).
% 1.74/1.41 thf(f19,plain,(
% 1.74/1.41 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1,X3 : X0 > $o,X4 : X1 > X1 > X1] : ((('const/iterate/iterate' @ X0 @ X1 @ X4 @ X3 @ X2) = ('const/class/COND' @ X1 @ ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3)) @ ('const/sets/ITSET' @ X0 @ X1 @ (^[Y0 : X0]: (X4 @ (X2 @ Y0))) @ ('const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3) @ ('const/iterate/neutral' @ X1 @ X4)) @ ('const/iterate/neutral' @ X1 @ X4)))) )),
% 1.74/1.41 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.74/1.41 thf(f17,plain,(
% 1.74/1.41 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1,X3 : X0 > $o,X4 : X1 > X1 > X1] : ((('const/class/COND' @ X1 @ ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3)) @ ('const/sets/ITSET' @ X0 @ X1 @ (^[Y0 : X0]: ((^[Y1 : X1]: (X4 @ (X2 @ Y0) @ Y1)))) @ ('const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3) @ ('const/iterate/neutral' @ X1 @ X4)) @ ('const/iterate/neutral' @ X1 @ X4)) = ('const/iterate/iterate' @ X0 @ X1 @ X4 @ X3 @ X2))) )),
% 1.74/1.41 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.41 thf(f8,plain,(
% 1.74/1.41 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1,X3 : X0 > $o,X4 : X1 > X1 > X1] : (('const/class/COND' @ X1 @ ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3)) @ ('const/sets/ITSET' @ X0 @ X1 @ (^[Y0 : X0]: ((^[Y1 : X1]: (X4 @ (X2 @ Y0) @ Y1)))) @ ('const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3) @ ('const/iterate/neutral' @ X1 @ X4)) @ ('const/iterate/neutral' @ X1 @ X4)) = ('const/iterate/iterate' @ X0 @ X1 @ X4 @ X3 @ X2))),
% 1.74/1.41 inference(fool_elimination,[status(thm)],[f7])).
% 1.74/1.41 thf(f7,plain,(
% 1.74/1.41 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1,X3 : X0 > $o,X4 : X1 > X1 > X1] : (('const/class/COND' @ X1 @ ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3)) @ ('const/sets/ITSET' @ X0 @ X1 @ (^[X5 : X0, X6 : X1] : (X4 @ (X2 @ X5) @ X6)) @ ('const/iterate/support' @ X1 @ X0 @ X4 @ X2 @ X3) @ ('const/iterate/neutral' @ X1 @ X4)) @ ('const/iterate/neutral' @ X1 @ X4)) = ('const/iterate/iterate' @ X0 @ X1 @ X4 @ X3 @ X2))),
% 1.74/1.41 inference(rectify,[status(thm)],[f1])).
% 1.74/1.41 thf(f1,axiom,(
% 1.74/1.41 ! [X0 : $tType,X1 : $tType,X3 : X0 > X1,X4 : X0 > $o,X5 : X1 > X1 > X1] : (('const/class/COND' @ X1 @ ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X5 @ X3 @ X4)) @ ('const/sets/ITSET' @ X0 @ X1 @ (^[X6 : X0, X7 : X1] : (X5 @ (X3 @ X6) @ X7)) @ ('const/iterate/support' @ X1 @ X0 @ X5 @ X3 @ X4) @ ('const/iterate/neutral' @ X1 @ X5)) @ ('const/iterate/neutral' @ X1 @ X5)) = ('const/iterate/iterate' @ X0 @ X1 @ X5 @ X4 @ X3))),
% 1.74/1.41 file('/export/starexec/sandbox/tmp/tmp.GBhyE2mWwv/DTF2THF_1973.p','thm/iterate/iterate_')).
% 1.74/1.41 thf(f26,plain,(
% 1.74/1.41 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X3 : X0 > X1,X4 : X0 > $o] : ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4) @ X3) = ('const/class/COND' @ X1 @ ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4)) @ ('const/sets/ITSET' @ X0 @ X1 @ (^[Y0 : X0]: (X2 @ (X3 @ Y0))) @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X4) @ ('const/iterate/neutral' @ X1 @ X2)) @ ('const/iterate/neutral' @ X1 @ X2)))) )),
% 1.74/1.41 inference(superposition,[status(thm)],[f19,f15])).
% 1.74/1.41 thf(f15,plain,(
% 1.74/1.41 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X0 > X0,X3 : X1 > X0,X4 : X1 > $o] : ((('const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ ('const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4)) = ('const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4))) )),
% 1.74/1.41 inference(cnf_transformation,[status(thm)],[f10])).
% 1.74/1.41 thf(f10,plain,(
% 1.74/1.41 ! [X0 : $tType,X1 : $tType,X2 : X0 > X0 > X0,X3 : X1 > X0,X4 : X1 > $o] : (('const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ ('const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4)) = ('const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4))),
% 1.74/1.41 inference(rectify,[status(thm)],[f3])).
% 1.74/1.41 thf(f3,axiom,(
% 1.74/1.41 ! [X0 : $tType,X1 : $tType,X3 : X0 > X0 > X0,X4 : X1 > X0,X5 : X1 > $o] : (('const/iterate/support' @ X0 @ X1 @ X3 @ X4 @ X5) = ('const/iterate/support' @ X0 @ X1 @ X3 @ X4 @ ('const/iterate/support' @ X0 @ X1 @ X3 @ X4 @ X5)))),
% 1.74/1.41 file('/export/starexec/sandbox/tmp/tmp.GBhyE2mWwv/DTF2THF_1973.p','thm/iterate/SUPPORT_SUPPORT_')).
% 1.74/1.41 thf(f18,plain,(
% 1.74/1.41 (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1) != ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK1 @ sK2) @ sK1))),
% 1.74/1.41 inference(definition_unfolding,[status(thm)],[f14,f16,f16])).
% 1.74/1.41 thf(f16,plain,(
% 1.74/1.41 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))) )),
% 1.74/1.41 inference(cnf_transformation,[status(thm)],[f2])).
% 1.74/1.41 thf(f2,axiom,(
% 1.74/1.41 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))),
% 1.74/1.41 file('/export/starexec/sandbox/tmp/tmp.GBhyE2mWwv/DTF2THF_1973.p','thm/iterate/sum_')).
% 1.74/1.41 thf(f14,plain,(
% 1.74/1.41 (('const/iterate/sum' @ sK0 @ sK2 @ sK1) != ('const/iterate/sum' @ sK0 @ ('const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK1 @ sK2) @ sK1))),
% 1.74/1.41 inference(cnf_transformation,[status(thm)],[f13])).
% 1.74/1.41 thf(f13,plain,(
% 1.74/1.41 (('const/iterate/sum' @ sK0 @ sK2 @ sK1) != ('const/iterate/sum' @ sK0 @ ('const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK1 @ sK2) @ sK1))),
% 1.74/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12])).
% 1.74/1.41 thf(f12,plain,(
% 1.74/1.41 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o] : (('const/iterate/sum' @ X0 @ ('const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X2) @ X1) != ('const/iterate/sum' @ X0 @ X2 @ X1)) => (('const/iterate/sum' @ sK0 @ sK2 @ sK1) != ('const/iterate/sum' @ sK0 @ ('const/iterate/support' @ 'type/realax/real' @ sK0 @ 'const/realax/real_add' @ sK1 @ sK2) @ sK1))),
% 1.74/1.41 introduced(definition,[],[choice_axiom])).
% 1.74/1.41 thf(f11,plain,(
% 1.74/1.41 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o] : (('const/iterate/sum' @ X0 @ ('const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X2) @ X1) != ('const/iterate/sum' @ X0 @ X2 @ X1))),
% 1.74/1.41 inference(ennf_transformation,[status(thm)],[f9])).
% 1.74/1.41 thf(f9,plain,(
% 1.74/1.41 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o] : (('const/iterate/sum' @ X0 @ ('const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X2) @ X1) = ('const/iterate/sum' @ X0 @ X2 @ X1))),
% 1.74/1.41 inference(rectify,[status(thm)],[f5])).
% 1.74/1.41 thf(f5,negated_conjecture,(
% 1.74/1.41 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X3 : X0 > $o] : (('const/iterate/sum' @ X0 @ ('const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X3) @ X1) = ('const/iterate/sum' @ X0 @ X3 @ X1))),
% 1.74/1.41 inference(negated_conjecture,[status(cth)],[f4])).
% 1.74/1.41 thf(f4,conjecture,(
% 1.74/1.41 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X3 : X0 > $o] : (('const/iterate/sum' @ X0 @ ('const/iterate/support' @ 'type/realax/real' @ X0 @ 'const/realax/real_add' @ X1 @ X3) @ X1) = ('const/iterate/sum' @ X0 @ X3 @ X1))),
% 1.74/1.41 file('/export/starexec/sandbox/tmp/tmp.GBhyE2mWwv/DTF2THF_1973.p','thm/iterate/SUM_SUPPORT_')).
% 1.74/1.41 % SZS output end Proof for DTF2THF_1973
% 1.74/1.41 % (2075)------------------------------
% 1.74/1.41 % (2075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.41 % (2075)Termination reason: Refutation
% 1.74/1.41
% 1.74/1.41 % (2075)Memory used [KB]: 5628
% 1.74/1.41 % (2075)Time elapsed: 0.009 s
% 1.74/1.41 % (2075)Instructions burned: 13 (million)
% 1.74/1.41 % (2075)------------------------------
% 1.74/1.41 % (2075)------------------------------
% 1.74/1.41 % (2072)Success in time 0.023 s
%------------------------------------------------------------------------------