%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM699^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n021.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 09:24:20 AM UTC 2026
% Result : Theorem 1.46s 1.26s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 89 ( 11 ~; 4 |; 0 &; 71 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
x: nat ).
thf(func_def_2,type,
y: nat ).
thf(func_def_3,type,
less: nat > nat > $o ).
thf(func_def_5,type,
lessis: nat > nat > $o ).
thf(func_def_6,type,
suc: nat > nat ).
thf(func_def_7,type,
pl: nat > nat > nat ).
thf(func_def_8,type,
n_1: nat ).
thf(f22,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f21,f17]) ).
thf(f17,plain,
( ( less @ y @ x )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( less @ y @ x )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
less @ y @ x,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
less @ y @ x,
file('/export/starexec/sandbox2/tmp/tmp.AWkN8qrU3P/DTF2THF_5132.p',l) ).
thf(f21,plain,
( ( less @ y @ x )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( less @ y @ x )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f15,f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ ( suc @ X0 ) @ X1 )
= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f16,f18]) ).
thf(f18,plain,
! [X0: nat] :
( ( pl @ X0 @ n_1 )
= ( suc @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: nat] :
( ( pl @ X0 @ n_1 )
= ( suc @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.AWkN8qrU3P/DTF2THF_5132.p',satz4a) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ ( pl @ X0 @ n_1 ) @ X1 ) )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ ( pl @ X0 @ n_1 ) @ X1 ) )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: nat,X0: nat] :
( ( ( less @ X0 @ X1 )
= $true )
=> ( $true
= ( lessis @ ( pl @ X0 @ n_1 ) @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( less @ X0 @ X1 )
=> ( lessis @ ( pl @ X0 @ n_1 ) @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( less @ X1 @ X0 )
=> ( lessis @ ( pl @ X1 @ n_1 ) @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.AWkN8qrU3P/DTF2THF_5132.p',satz25b) ).
thf(f15,plain,
( ( lessis @ ( suc @ y ) @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( lessis @ ( suc @ y ) @ x )
!= $true ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( lessis @ ( suc @ y ) @ x )
!= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( lessis @ ( suc @ y ) @ x ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( lessis @ ( suc @ y ) @ x ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
lessis @ ( suc @ y ) @ x,
file('/export/starexec/sandbox2/tmp/tmp.AWkN8qrU3P/DTF2THF_5132.p',satz25c) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM699^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:11:24 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : NUM699^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Number Theory
% 0.19/0.46 % Problem : Landau theorem 25c
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : lessis (suc y) x
% 0.19/0.46
% 0.19/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : satz25c [Lan30]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % : Without extensionality : Theorem
% 0.19/0.46 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.19/0.46 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 0 def)
% 0.19/0.46 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.19/0.46 % Number of connectives : 15 ( 0 ~; 0 |; 0 &; 14 @)
% 0.19/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 8 ( 4 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(nat_type,type,
% 0.19/0.46 nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(x,type,
% 0.19/0.46 x: nat ).
% 0.19/0.46
% 0.19/0.46 thf(y,type,
% 0.19/0.46 y: nat ).
% 0.19/0.46
% 0.19/0.46 thf(less,type,
% 0.19/0.46 less: nat > nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(l,axiom,
% 0.19/0.46 less @ y @ x ).
% 0.19/0.46
% 0.19/0.46 thf(lessis,type,
% 0.19/0.46 lessis: nat > nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(suc,type,
% 0.19/0.46 suc: nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(pl,type,
% 0.19/0.46 pl: nat > nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(n_1,type,
% 0.19/0.46 n_1: nat ).
% 0.19/0.46
% 0.19/0.46 thf(satz25b,axiom,
% 0.19/0.46 ! [Xx: nat,Xy: nat] :
% 0.19/0.46 ( ( less @ Xy @ Xx )
% 0.19/0.46 => ( lessis @ ( pl @ Xy @ n_1 ) @ Xx ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz4a,axiom,
% 0.19/0.46 ! [Xx: nat] :
% 0.19/0.46 ( ( pl @ Xx @ n_1 )
% 0.19/0.46 = ( suc @ Xx ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz25c,conjecture,
% 0.19/0.46 lessis @ ( suc @ y ) @ x ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.46/1.23 ---- Embedded in THF ---
% 1.46/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.23 %%% Generated on Tue Feb 24 11:11:24 EST 2026
% 1.46/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.23 %%% Logic specification used:
% 1.46/1.23 %%% thf(spec, logic, $$dhol).
% 1.46/1.23
% 1.46/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.AWkN8qrU3P/DTF2DTF5132.p
% See solution above
% 1.46/1.23 ------------------------
% 1.46/1.24 ---- Cleaned THF ---
% 1.46/1.24 thf(nat_type,type,
% 1.46/1.24 nat: $tType ).
% 1.46/1.24
% 1.46/1.24 thf(x,type,
% 1.46/1.24 x: nat ).
% 1.46/1.24
% 1.46/1.24 thf(y,type,
% 1.46/1.24 y: nat ).
% 1.46/1.24
% 1.46/1.24 thf(less,type,
% 1.46/1.24 less: nat > nat > $o ).
% 1.46/1.24
% 1.46/1.24 thf(l,axiom,
% 1.46/1.24 less @ y @ x ).
% 1.46/1.24
% 1.46/1.24 thf(lessis,type,
% 1.46/1.24 lessis: nat > nat > $o ).
% 1.46/1.24
% 1.46/1.24 thf(suc,type,
% 1.46/1.24 suc: nat > nat ).
% 1.46/1.24
% 1.46/1.24 thf(pl,type,
% 1.46/1.24 pl: nat > nat > nat ).
% 1.46/1.24
% 1.46/1.24 thf(n_1,type,
% 1.46/1.24 n_1: nat ).
% 1.46/1.24
% 1.46/1.24 thf(satz25b,axiom,
% 1.46/1.24 ! [Xx: nat,Xy: nat] :
% 1.46/1.24 ( ( less @ Xy @ Xx )
% 1.46/1.24 => ( lessis @ ( pl @ Xy @ n_1 ) @ Xx ) ) ).
% 1.46/1.24
% 1.46/1.24 thf(satz4a,axiom,
% 1.46/1.24 ! [Xx: nat] :
% 1.46/1.24 ( ( pl @ Xx @ n_1 )
% 1.46/1.24 = ( suc @ Xx ) ) ).
% 1.46/1.24
% 1.46/1.24 thf(satz25c,conjecture,
% 1.46/1.24 lessis @ ( suc @ y ) @ x ).
% 1.46/1.24 ------------------------
% 1.46/1.25 % (5232)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5132 for (2999ds/183Mi)
% 1.46/1.25 % (5235)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5132 for (2999ds/2Mi)
% 1.46/1.25 % (5235)Instruction limit reached!
% 1.46/1.25 % (5235)------------------------------
% 1.46/1.25 % (5235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (5235)Termination reason: Unknown
% 1.46/1.25 % (5235)Termination phase: Saturation
% 1.46/1.25
% 1.46/1.25 % (5235)Memory used [KB]: 5500
% 1.46/1.25 % (5235)Time elapsed: 0.002 s
% 1.46/1.25 % (5235)Instructions burned: 2 (million)
% 1.46/1.25 % (5235)------------------------------
% 1.46/1.25 % (5235)------------------------------
% 1.46/1.25 % (5232)First to succeed.
% 1.46/1.26 % (5232)Refutation found. Thanks to Tanya!
% 1.46/1.26 % SZS status Theorem for DTF2THF_5132
% 1.46/1.26 % SZS output start Proof for DTF2THF_5132
% 1.46/1.26 thf(type_def_5, type, nat: $tType).
% 1.46/1.26 thf(func_def_0, type, nat: $tType).
% 1.46/1.26 thf(func_def_1, type, x: nat).
% 1.46/1.26 thf(func_def_2, type, y: nat).
% 1.46/1.26 thf(func_def_3, type, less: nat > nat > $o).
% 1.46/1.26 thf(func_def_5, type, lessis: nat > nat > $o).
% 1.46/1.26 thf(func_def_6, type, suc: nat > nat).
% 1.46/1.26 thf(func_def_7, type, pl: nat > nat > nat).
% 1.46/1.26 thf(func_def_8, type, n_1: nat).
% 1.46/1.26 thf(f22,plain,(
% 1.46/1.26 $false),
% 1.46/1.26 inference(subsumption_resolution,[status(thm)],[f21,f17])).
% 1.46/1.26 thf(f17,plain,(
% 1.46/1.26 ((less @ y @ x) = $true)),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.46/1.26 thf(f8,plain,(
% 1.46/1.26 ((less @ y @ x) = $true)),
% 1.46/1.26 inference(fool_elimination,[status(thm)],[f7])).
% 1.46/1.26 thf(f7,plain,(
% 1.46/1.26 (less @ y @ x)),
% 1.46/1.26 inference(rectify,[status(thm)],[f1])).
% 1.46/1.26 thf(f1,axiom,(
% 1.46/1.26 (less @ y @ x)),
% 1.46/1.26 file('/export/starexec/sandbox2/tmp/tmp.AWkN8qrU3P/DTF2THF_5132.p',l)).
% 1.46/1.26 thf(f21,plain,(
% 1.46/1.26 ((less @ y @ x) != $true)),
% 1.46/1.26 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.46/1.26 thf(f20,plain,(
% 1.46/1.26 ((less @ y @ x) != $true) | ($true != $true)),
% 1.46/1.26 inference(superposition,[status(thm)],[f15,f19])).
% 1.46/1.26 thf(f19,plain,(
% 1.46/1.26 ( ! [X0 : nat,X1 : nat] : (((lessis @ (suc @ X0) @ X1) = $true) | ((less @ X0 @ X1) != $true)) )),
% 1.46/1.26 inference(superposition,[status(thm)],[f16,f18])).
% 1.46/1.26 thf(f18,plain,(
% 1.46/1.26 ( ! [X0 : nat] : (((pl @ X0 @ n_1) = (suc @ X0))) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f3])).
% 1.46/1.26 thf(f3,axiom,(
% 1.46/1.26 ! [X0 : nat] : ((pl @ X0 @ n_1) = (suc @ X0))),
% 1.46/1.26 file('/export/starexec/sandbox2/tmp/tmp.AWkN8qrU3P/DTF2THF_5132.p',satz4a)).
% 1.46/1.26 thf(f16,plain,(
% 1.46/1.26 ( ! [X0 : nat,X1 : nat] : (($true = (lessis @ (pl @ X0 @ n_1) @ X1)) | ((less @ X0 @ X1) != $true)) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.46/1.26 thf(f14,plain,(
% 1.46/1.26 ! [X0 : nat,X1 : nat] : (($true = (lessis @ (pl @ X0 @ n_1) @ X1)) | ((less @ X0 @ X1) != $true))),
% 1.46/1.26 inference(ennf_transformation,[status(thm)],[f10])).
% 1.46/1.26 thf(f10,plain,(
% 1.46/1.26 ! [X1 : nat,X0 : nat] : (((less @ X0 @ X1) = $true) => ($true = (lessis @ (pl @ X0 @ n_1) @ X1)))),
% 1.46/1.26 inference(fool_elimination,[status(thm)],[f9])).
% 1.46/1.26 thf(f9,plain,(
% 1.46/1.26 ! [X0 : nat,X1 : nat] : ((less @ X0 @ X1) => (lessis @ (pl @ X0 @ n_1) @ X1))),
% 1.46/1.26 inference(rectify,[status(thm)],[f2])).
% 1.46/1.26 thf(f2,axiom,(
% 1.46/1.26 ! [X1 : nat,X0 : nat] : ((less @ X1 @ X0) => (lessis @ (pl @ X1 @ n_1) @ X0))),
% 1.46/1.26 file('/export/starexec/sandbox2/tmp/tmp.AWkN8qrU3P/DTF2THF_5132.p',satz25b)).
% 1.46/1.26 thf(f15,plain,(
% 1.46/1.26 ((lessis @ (suc @ y) @ x) != $true)),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.46/1.26 thf(f13,plain,(
% 1.46/1.26 ((lessis @ (suc @ y) @ x) != $true)),
% 1.46/1.26 inference(flattening,[status(thm)],[f12])).
% 1.46/1.26 thf(f12,plain,(
% 1.46/1.26 ~((lessis @ (suc @ y) @ x) = $true)),
% 1.46/1.26 inference(fool_elimination,[status(thm)],[f11])).
% 1.46/1.26 thf(f11,plain,(
% 1.46/1.26 ~(lessis @ (suc @ y) @ x)),
% 1.46/1.26 inference(rectify,[status(thm)],[f5])).
% 1.46/1.26 thf(f5,negated_conjecture,(
% 1.46/1.26 ~(lessis @ (suc @ y) @ x)),
% 1.46/1.26 inference(negated_conjecture,[status(cth)],[f4])).
% 1.46/1.26 thf(f4,conjecture,(
% 1.46/1.26 (lessis @ (suc @ y) @ x)),
% 1.46/1.26 file('/export/starexec/sandbox2/tmp/tmp.AWkN8qrU3P/DTF2THF_5132.p',satz25c)).
% 1.46/1.26 % SZS output end Proof for DTF2THF_5132
% 1.46/1.26 % (5232)------------------------------
% 1.46/1.26 % (5232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (5232)Termination reason: Refutation
% 1.46/1.26
% 1.46/1.26 % (5232)Memory used [KB]: 5500
% 1.46/1.26 % (5232)Time elapsed: 0.002 s
% 1.46/1.26 % (5232)Instructions burned: 2 (million)
% 1.46/1.26 % (5232)------------------------------
% 1.46/1.26 % (5232)------------------------------
% 1.46/1.26 % (5228)Success in time 0.005 s
%------------------------------------------------------------------------------