%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA109^1 : 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 08:38:54 AM UTC 2026
% Result : Theorem 1.68s 1.45s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 86 ( 7 ~; 0 |; 0 &; 78 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-4 aty)
% Number of variables : 18 ( 0 ^; 14 !; 4 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'type/nums/num': $tType ).
thf(func_def_2,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_5,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
sK0: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_11,type,
sK1: 'type/nums/num' ).
thf(func_def_13,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( sK0 @ sK1 )
!= ( sK0 @ sK1 ) ),
inference(superposition,[status(thm)],[f11,f15]) ).
thf(f15,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X0 ) @ X1 )
= ( X1 @ X0 ) ),
inference(superposition,[status(thm)],[f9,f10]) ).
thf(f10,plain,
! [X0: 'type/nums/num'] :
( ( 'const/iterate/..' @ X0 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/iterate/..' @ X0 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ),
file('/export/starexec/sandbox/tmp/tmp.riI1x17ZHH/DTF2THF_3256.p','thm/iterate/NUMSEG_SING_') ).
thf(f9,plain,
! [X0: $tType,X2: X0,X1: X0 > 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.riI1x17ZHH/DTF2THF_3256.p','thm/iterate/SUM_SING_') ).
thf(f11,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 )
!= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 )
!= ( sK0 @ sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
!= ( X0 @ X1 ) )
=> ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 )
!= ( sK0 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
!= ( X0 @ X1 ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
= ( X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
= ( X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.riI1x17ZHH/DTF2THF_3256.p','thm/iterate/SUM_SING_NUMSEG_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ANA109^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.15 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.35 % Computer : n031.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Tue Feb 24 03:51:32 EST 2026
% 0.19/0.35 % CPUTime :
% 0.19/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.49 ---- Original DTF file ---
% 0.30/0.49 thf(spec,logic,$$dhol).
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 % File : ANA109^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.49 % Domain : Analysis
% 0.30/0.49 % Problem : SUM_SING_NUMSEG
% 0.30/0.49 % Version : Especial.
% 0.30/0.49 % English :
% 0.30/0.49
% 0.30/0.49 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.30/0.49 % Source : [Kal16]
% 0.30/0.49 % Names : SUM_SING_NUMSEG_.p [Kal16]
% 0.30/0.49
% 0.30/0.49 % Status : Theorem
% 0.30/0.49 % Rating : 0.00 v7.1.0
% 0.30/0.49 % Syntax : Number of formulae : 9 ( 3 unt; 6 typ; 0 def)
% 0.30/0.49 % Number of atoms : 9 ( 3 equ; 0 cnn)
% 0.30/0.49 % Maximal formula atoms : 1 ( 3 avg)
% 0.30/0.49 % Number of connectives : 20 ( 0 ~; 0 |; 0 &; 20 @)
% 0.30/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.49 % Maximal formula depth : 4 ( 3 avg)
% 0.30/0.49 % Number of types : 3 ( 2 usr)
% 0.30/0.49 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.30/0.49 % Number of symbols : 5 ( 4 usr; 0 con; 2-4 aty)
% 0.30/0.49 % Number of variables : 9 ( 0 ^; 6 !; 0 ?; 9 :)
% 0.30/0.49 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.49 % SPC : TH1_THM_EQU_NAR
% 0.30/0.49
% 0.30/0.49 % Comments : Exported from core HOL Light.
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 thf('thf_type_type/realax/real',type,
% 0.30/0.49 'type/realax/real': $tType ).
% 0.30/0.49
% 0.30/0.49 thf('thf_type_type/nums/num',type,
% 0.30/0.49 'type/nums/num': $tType ).
% 0.30/0.49
% 0.30/0.49 thf('thf_const_const/sets/INSERT',type,
% 0.30/0.49 'const/sets/INSERT':
% 0.30/0.49 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.30/0.49
% 0.30/0.49 thf('thf_const_const/sets/EMPTY',type,
% 0.30/0.49 'const/sets/EMPTY':
% 0.30/0.49 !>[A: $tType] : ( A > $o ) ).
% 0.30/0.49
% 0.30/0.49 thf('thf_const_const/iterate/sum',type,
% 0.30/0.49 'const/iterate/sum':
% 0.30/0.49 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.30/0.49
% 0.30/0.49 thf('thf_const_const/iterate/..',type,
% 0.30/0.49 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.30/0.49
% 0.30/0.49 thf('thm/iterate/SUM_SING_',axiom,
% 0.30/0.49 ! [A: $tType,A0: A > 'type/realax/real',A1: A] :
% 0.30/0.49 ( ( 'const/iterate/sum' @ A @ ( 'const/sets/INSERT' @ A @ A1 @ ( 'const/sets/EMPTY' @ A ) ) @ A0 )
% 0.30/0.49 = ( A0 @ A1 ) ) ).
% 0.30/0.49
% 0.30/0.49 thf('thm/iterate/NUMSEG_SING_',axiom,
% 0.30/0.49 ! [A: 'type/nums/num'] :
% 0.30/0.49 ( ( 'const/iterate/..' @ A @ A )
% 0.30/0.49 = ( 'const/sets/INSERT' @ 'type/nums/num' @ A @ ( 'const/sets/EMPTY' @ 'type/nums/num' ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf('thm/iterate/SUM_SING_NUMSEG_',conjecture,
% 0.30/0.49 ! [A: 'type/nums/num' > 'type/realax/real',A0: 'type/nums/num'] :
% 0.30/0.49 ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A0 ) @ A )
% 0.30/0.49 = ( A @ A0 ) ) ).
% 0.30/0.49
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 ------------------------
% 1.68/1.42 ---- Embedded in THF ---
% 1.68/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.42 %%% Generated on Tue Feb 24 03:51:33 EST 2026
% 1.68/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.42 %%% Logic specification used:
% 1.68/1.42 %%% thf(spec, logic, $$dhol).
% 1.68/1.42
% 1.68/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.riI1x17ZHH/DTF2DTF3256.p
% See solution above
% 1.68/1.42 ------------------------
% 1.68/1.43 ---- Cleaned THF ---
% 1.68/1.43 thf('thf_type_type/realax/real',type,
% 1.68/1.43 'type/realax/real': $tType ).
% 1.68/1.43
% 1.68/1.43 thf('thf_type_type/nums/num',type,
% 1.68/1.43 'type/nums/num': $tType ).
% 1.68/1.43
% 1.68/1.43 thf('thf_const_const/sets/INSERT',type,
% 1.68/1.43 'const/sets/INSERT':
% 1.68/1.43 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 1.68/1.43
% 1.68/1.43 thf('thf_const_const/sets/EMPTY',type,
% 1.68/1.43 'const/sets/EMPTY':
% 1.68/1.43 !>[A: $tType] : ( A > $o ) ).
% 1.68/1.43
% 1.68/1.43 thf('thf_const_const/iterate/sum',type,
% 1.68/1.43 'const/iterate/sum':
% 1.68/1.43 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.68/1.43
% 1.68/1.43 thf('thf_const_const/iterate/..',type,
% 1.68/1.43 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 1.68/1.43
% 1.68/1.43 thf('thm/iterate/SUM_SING_',axiom,
% 1.68/1.43 ! [A: $tType,A0: A > 'type/realax/real',A1: A] :
% 1.68/1.43 ( ( 'const/iterate/sum' @ A @ ( 'const/sets/INSERT' @ A @ A1 @ ( 'const/sets/EMPTY' @ A ) ) @ A0 )
% 1.68/1.43 = ( A0 @ A1 ) ) ).
% 1.68/1.43
% 1.68/1.43 thf('thm/iterate/NUMSEG_SING_',axiom,
% 1.68/1.43 ! [A: 'type/nums/num'] :
% 1.68/1.43 ( ( 'const/iterate/..' @ A @ A )
% 1.68/1.43 = ( 'const/sets/INSERT' @ 'type/nums/num' @ A @ ( 'const/sets/EMPTY' @ 'type/nums/num' ) ) ) ).
% 1.68/1.43
% 1.68/1.43 thf('thm/iterate/SUM_SING_NUMSEG_',conjecture,
% 1.68/1.43 ! [A: 'type/nums/num' > 'type/realax/real',A0: 'type/nums/num'] :
% 1.68/1.43 ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A0 ) @ A )
% 1.68/1.43 = ( A @ A0 ) ) ).
% 1.68/1.43 ------------------------
% 1.68/1.45 % (3354)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3256 for (2999ds/183Mi)
% 1.68/1.45 % (3355)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_3256 for (2999ds/4Mi)
% 1.68/1.45 % (3356)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_3256 for (2999ds/27Mi)
% 1.68/1.45 % (3357)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3256 for (2999ds/2Mi)
% 1.68/1.45 % (3358)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_3256 for (2999ds/2Mi)
% 1.68/1.45 % (3359)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_3256 for (2999ds/275Mi)
% 1.68/1.45 % (3360)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3256 for (2999ds/18Mi)
% 1.68/1.45 % (3359)Refutation not found, incomplete strategy
% 1.68/1.45 % (3359)------------------------------
% 1.68/1.45 % (3359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.45 % (3357)Instruction limit reached!
% 1.68/1.45 % (3357)------------------------------
% 1.68/1.45 % (3357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.45 % (3357)Termination reason: Unknown
% 1.68/1.45 % (3357)Termination phase: Saturation
% 1.68/1.45
% 1.68/1.45 % (3357)Memory used [KB]: 5500
% 1.68/1.45 % (3357)Time elapsed: 0.003 s
% 1.68/1.45 % (3357)Instructions burned: 2 (million)
% 1.68/1.45 % (3357)------------------------------
% 1.68/1.45 % (3357)------------------------------
% 1.68/1.45 % (3359)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.45
% 1.68/1.45 % (3358)Instruction limit reached!
% 1.68/1.45 % (3358)------------------------------
% 1.68/1.45 % (3358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.45 % (3358)Termination reason: Unknown
% 1.68/1.45 % (3358)Termination phase: Saturation
% 1.68/1.45
% 1.68/1.45 % (3358)Memory used [KB]: 5500
% 1.68/1.45 % (3358)Time elapsed: 0.003 s
% 1.68/1.45 % (3358)Instructions burned: 2 (million)
% 1.68/1.45 % (3358)------------------------------
% 1.68/1.45 % (3358)------------------------------
% 1.68/1.45
% 1.68/1.45 % (3359)Memory used [KB]: 5500
% 1.68/1.45 % (3359)Time elapsed: 0.003 s
% 1.68/1.45 % (3359)Instructions burned: 1 (million)
% 1.68/1.45 % (3359)------------------------------
% 1.68/1.45 % (3359)------------------------------
% 1.68/1.45 % (3355)Instruction limit reached!
% 1.68/1.45 % (3355)------------------------------
% 1.68/1.45 % (3355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.45 % (3355)Termination reason: Unknown
% 1.68/1.45 % (3355)Termination phase: Saturation
% 1.68/1.45
% 1.68/1.45 % (3355)Memory used [KB]: 5500
% 1.68/1.45 % (3355)Time elapsed: 0.004 s
% 1.68/1.45 % (3355)Instructions burned: 4 (million)
% 1.68/1.45 % (3355)------------------------------
% 1.68/1.45 % (3355)------------------------------
% 1.68/1.45 % (3356)First to succeed.
% 1.68/1.45 % (3356)Refutation found. Thanks to Tanya!
% 1.68/1.45 % SZS status Theorem for DTF2THF_3256
% 1.68/1.45 % SZS output start Proof for DTF2THF_3256
% 1.68/1.45 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.68/1.45 thf(type_def_7, type, 'type/nums/num': $tType).
% 1.68/1.45 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.68/1.45 thf(func_def_1, type, 'type/nums/num': $tType).
% 1.68/1.45 thf(func_def_2, type, 'const/sets/INSERT': !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 1.68/1.45 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.68/1.45 thf(func_def_4, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.68/1.45 thf(func_def_5, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 1.68/1.45 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.68/1.45 thf(func_def_10, type, sK0: 'type/nums/num' > 'type/realax/real').
% 1.68/1.45 thf(func_def_11, type, sK1: 'type/nums/num').
% 1.68/1.45 thf(func_def_13, type, ph3: !>[X0: $tType]:(X0)).
% 1.68/1.45 thf(f22,plain,(
% 1.68/1.45 $false),
% 1.68/1.45 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.68/1.45 thf(f21,plain,(
% 1.68/1.45 ((sK0 @ sK1) != (sK0 @ sK1))),
% 1.68/1.45 inference(superposition,[status(thm)],[f11,f15])).
% 1.68/1.45 thf(f15,plain,(
% 1.68/1.45 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num' > 'type/realax/real'] : ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X0) @ X1) = (X1 @ X0))) )),
% 1.68/1.45 inference(superposition,[status(thm)],[f9,f10])).
% 1.68/1.45 thf(f10,plain,(
% 1.68/1.45 ( ! [X0 : 'type/nums/num'] : ((('const/iterate/..' @ X0 @ X0) = ('const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num'))) )),
% 1.68/1.45 inference(cnf_transformation,[status(thm)],[f2])).
% 1.68/1.45 thf(f2,axiom,(
% 1.68/1.45 ! [X0 : 'type/nums/num'] : (('const/iterate/..' @ X0 @ X0) = ('const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num'))),
% 1.68/1.45 file('/export/starexec/sandbox/tmp/tmp.riI1x17ZHH/DTF2THF_3256.p','thm/iterate/NUMSEG_SING_')).
% 1.68/1.45 thf(f9,plain,(
% 1.68/1.45 ( ! [X0 : $tType,X2 : X0,X1 : X0 > 'type/realax/real'] : ((('const/iterate/sum' @ X0 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0) @ X1) = (X1 @ X2))) )),
% 1.68/1.45 inference(cnf_transformation,[status(thm)],[f1])).
% 1.68/1.45 thf(f1,axiom,(
% 1.68/1.45 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0] : (('const/iterate/sum' @ X0 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0) @ X1) = (X1 @ X2))),
% 1.68/1.45 file('/export/starexec/sandbox/tmp/tmp.riI1x17ZHH/DTF2THF_3256.p','thm/iterate/SUM_SING_')).
% 1.68/1.45 thf(f11,plain,(
% 1.68/1.45 (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK1) @ sK0) != (sK0 @ sK1))),
% 1.68/1.45 inference(cnf_transformation,[status(thm)],[f8])).
% 1.68/1.45 thf(f8,plain,(
% 1.68/1.45 (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK1) @ sK0) != (sK0 @ sK1))),
% 1.68/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.68/1.45 thf(f7,plain,(
% 1.68/1.45 ? [X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/nums/num'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X1) @ X0) != (X0 @ X1)) => (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK1) @ sK0) != (sK0 @ sK1))),
% 1.68/1.45 introduced(definition,[],[choice_axiom])).
% 1.68/1.45 thf(f6,plain,(
% 1.68/1.45 ? [X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/nums/num'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X1) @ X0) != (X0 @ X1))),
% 1.68/1.45 inference(ennf_transformation,[status(thm)],[f4])).
% 1.68/1.45 thf(f4,negated_conjecture,(
% 1.68/1.45 ~! [X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/nums/num'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X1) @ X0) = (X0 @ X1))),
% 1.68/1.45 inference(negated_conjecture,[status(cth)],[f3])).
% 1.68/1.45 thf(f3,conjecture,(
% 1.68/1.45 ! [X0 : 'type/nums/num' > 'type/realax/real',X1 : 'type/nums/num'] : (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X1) @ X0) = (X0 @ X1))),
% 1.68/1.45 file('/export/starexec/sandbox/tmp/tmp.riI1x17ZHH/DTF2THF_3256.p','thm/iterate/SUM_SING_NUMSEG_')).
% 1.68/1.45 % SZS output end Proof for DTF2THF_3256
% 1.68/1.45 % (3356)------------------------------
% 1.68/1.45 % (3356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.45 % (3356)Termination reason: Refutation
% 1.68/1.45
% 1.68/1.45 % (3356)Memory used [KB]: 5500
% 1.68/1.45 % (3356)Time elapsed: 0.005 s
% 1.68/1.45 % (3356)Instructions burned: 4 (million)
% 1.68/1.45 % (3356)------------------------------
% 1.68/1.45 % (3356)------------------------------
% 1.68/1.45 % (3353)Success in time 0.019 s
%------------------------------------------------------------------------------