%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM694^1 : 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 : n002.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 09:24:19 AM UTC 2026
% Result : Theorem 1.38s 1.20s
% Output : Refutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 65 ( 10 ~; 4 |; 0 &; 48 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% 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,
lessis: nat > nat > $o ).
thf(func_def_3,type,
n_1: nat ).
thf(func_def_4,type,
moreis: nat > nat > $o ).
thf(func_def_6,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f21,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
$true != $true,
inference(superposition,[status(thm)],[f16,f19]) ).
thf(f19,plain,
! [X0: nat] :
( $true
= ( lessis @ n_1 @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat] :
( ( $true != $true )
| ( $true
= ( lessis @ n_1 @ X0 ) ) ),
inference(superposition,[status(thm)],[f15,f17]) ).
thf(f17,plain,
! [X0: nat] :
( ( moreis @ X0 @ n_1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat] :
( ( moreis @ X0 @ n_1 )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat] : ( moreis @ X0 @ n_1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: nat] : ( moreis @ X0 @ n_1 ),
file('/export/starexec/sandbox2/tmp/tmp.jck4jdvAFc/DTF2THF_8456.p',satz24) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( moreis @ X1 @ X0 ) )
| ( ( lessis @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( moreis @ X1 @ X0 ) )
| ( ( lessis @ X0 @ X1 )
= $true ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: nat,X0: nat] :
( ( ( moreis @ X0 @ X1 )
!= $true )
| ( ( lessis @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X1: nat,X0: nat] :
( ( ( moreis @ X0 @ X1 )
= $true )
=> ( ( lessis @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: nat,X1: nat] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: nat,X1: nat] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.jck4jdvAFc/DTF2THF_8456.p',satz13) ).
thf(f16,plain,
( ( lessis @ n_1 @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( lessis @ n_1 @ x )
!= $true ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( lessis @ n_1 @ x )
!= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( lessis @ n_1 @ x ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( lessis @ n_1 @ x ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
lessis @ n_1 @ x,
file('/export/starexec/sandbox2/tmp/tmp.jck4jdvAFc/DTF2THF_8456.p',satz24a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM694^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n002.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 11:11:33 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.25/0.48 ---- Original DTF file ---
% 0.25/0.49 thf(spec,logic,$$dhol).
% 0.25/0.49 %------------------------------------------------------------------------------
% 0.25/0.49 % File : NUM694^1 : TPTP v9.2.1. Released v3.7.0.
% 0.25/0.49 % Domain : Number Theory
% 0.25/0.49 % Problem : Landau theorem 24a
% 0.25/0.49 % Version : Especial.
% 0.25/0.49 % English : lessis n_1 x
% 0.25/0.49
% 0.25/0.49 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.25/0.49 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.25/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.25/0.49 % Source : [Bro09]
% 0.25/0.49 % Names : satz24a [Lan30]
% 0.25/0.49
% 0.25/0.49 % Status : Theorem
% 0.25/0.49 % : Without extensionality : Theorem
% 0.25/0.49 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.25/0.49 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 0 def)
% 0.25/0.49 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.25/0.49 % Maximal formula atoms : 2 ( 1 avg)
% 0.25/0.49 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 8 @)
% 0.25/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.25/0.49 % Maximal formula depth : 6 ( 4 avg)
% 0.25/0.49 % Number of types : 2 ( 1 usr)
% 0.25/0.49 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.25/0.49 % Number of symbols : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.25/0.49 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.25/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.25/0.49
% 0.25/0.49 % Comments :
% 0.25/0.49 %------------------------------------------------------------------------------
% 0.25/0.49 thf(nat_type,type,
% 0.25/0.49 nat: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(x,type,
% 0.25/0.49 x: nat ).
% 0.25/0.49
% 0.25/0.49 thf(lessis,type,
% 0.25/0.49 lessis: nat > nat > $o ).
% 0.25/0.49
% 0.25/0.49 thf(n_1,type,
% 0.25/0.49 n_1: nat ).
% 0.25/0.49
% 0.25/0.49 thf(moreis,type,
% 0.25/0.49 moreis: nat > nat > $o ).
% 0.25/0.49
% 0.25/0.49 thf(satz13,axiom,
% 0.25/0.49 ! [Xx: nat,Xy: nat] :
% 0.25/0.49 ( ( moreis @ Xx @ Xy )
% 0.25/0.49 => ( lessis @ Xy @ Xx ) ) ).
% 0.25/0.49
% 0.25/0.49 thf(satz24,axiom,
% 0.25/0.49 ! [Xx: nat] : ( moreis @ Xx @ n_1 ) ).
% 0.25/0.49
% 0.25/0.49 thf(satz24a,conjecture,
% 0.25/0.49 lessis @ n_1 @ x ).
% 0.25/0.49
% 0.25/0.49 %------------------------------------------------------------------------------
% 0.25/0.49 ------------------------
% 1.33/1.17 ---- Embedded in THF ---
% 1.33/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.33/1.17 %%% Generated on Tue Feb 24 11:11:34 EST 2026
% 1.33/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.33/1.17 %%% Logic specification used:
% 1.33/1.17 %%% thf(spec, logic, $$dhol).
% 1.33/1.17
% 1.33/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jck4jdvAFc/DTF2DTF8456.p
% See solution above
% 1.33/1.17 ------------------------
% 1.33/1.18 ---- Cleaned THF ---
% 1.33/1.18 thf(nat_type,type,
% 1.33/1.18 nat: $tType ).
% 1.33/1.18
% 1.33/1.18 thf(x,type,
% 1.33/1.18 x: nat ).
% 1.33/1.18
% 1.33/1.18 thf(lessis,type,
% 1.33/1.18 lessis: nat > nat > $o ).
% 1.33/1.18
% 1.33/1.18 thf(n_1,type,
% 1.33/1.18 n_1: nat ).
% 1.33/1.18
% 1.33/1.18 thf(moreis,type,
% 1.33/1.18 moreis: nat > nat > $o ).
% 1.33/1.18
% 1.33/1.18 thf(satz13,axiom,
% 1.33/1.18 ! [Xx: nat,Xy: nat] :
% 1.33/1.18 ( ( moreis @ Xx @ Xy )
% 1.33/1.18 => ( lessis @ Xy @ Xx ) ) ).
% 1.33/1.18
% 1.33/1.18 thf(satz24,axiom,
% 1.33/1.18 ! [Xx: nat] : ( moreis @ Xx @ n_1 ) ).
% 1.33/1.18
% 1.33/1.18 thf(satz24a,conjecture,
% 1.33/1.18 lessis @ n_1 @ x ).
% 1.33/1.18 ------------------------
% 1.33/1.20 % (8556)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_8456 for (3000ds/27Mi)
% 1.38/1.20 % (8556)First to succeed.
% 1.38/1.20 % (8556)Refutation found. Thanks to Tanya!
% 1.38/1.20 % SZS status Theorem for DTF2THF_8456
% 1.38/1.20 % SZS output start Proof for DTF2THF_8456
% 1.38/1.20 thf(type_def_5, type, nat: $tType).
% 1.38/1.20 thf(func_def_0, type, nat: $tType).
% 1.38/1.20 thf(func_def_1, type, x: nat).
% 1.38/1.20 thf(func_def_2, type, lessis: nat > nat > $o).
% 1.38/1.20 thf(func_def_3, type, n_1: nat).
% 1.38/1.20 thf(func_def_4, type, moreis: nat > nat > $o).
% 1.38/1.20 thf(func_def_6, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.38/1.20 thf(f21,plain,(
% 1.38/1.20 $false),
% 1.38/1.20 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.38/1.20 thf(f20,plain,(
% 1.38/1.20 ($true != $true)),
% 1.38/1.20 inference(superposition,[status(thm)],[f16,f19])).
% 1.38/1.20 thf(f19,plain,(
% 1.38/1.20 ( ! [X0 : nat] : (($true = (lessis @ n_1 @ X0))) )),
% 1.38/1.20 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.38/1.20 thf(f18,plain,(
% 1.38/1.20 ( ! [X0 : nat] : (($true != $true) | ($true = (lessis @ n_1 @ X0))) )),
% 1.38/1.20 inference(superposition,[status(thm)],[f15,f17])).
% 1.38/1.20 thf(f17,plain,(
% 1.38/1.20 ( ! [X0 : nat] : (((moreis @ X0 @ n_1) = $true)) )),
% 1.38/1.20 inference(cnf_transformation,[status(thm)],[f11])).
% 1.38/1.20 thf(f11,plain,(
% 1.38/1.20 ! [X0 : nat] : ((moreis @ X0 @ n_1) = $true)),
% 1.38/1.20 inference(fool_elimination,[status(thm)],[f10])).
% 1.38/1.20 thf(f10,plain,(
% 1.38/1.20 ! [X0 : nat] : (moreis @ X0 @ n_1)),
% 1.38/1.20 inference(rectify,[status(thm)],[f2])).
% 1.38/1.20 thf(f2,axiom,(
% 1.38/1.20 ! [X0 : nat] : (moreis @ X0 @ n_1)),
% 1.38/1.20 file('/export/starexec/sandbox2/tmp/tmp.jck4jdvAFc/DTF2THF_8456.p',satz24)).
% 1.38/1.20 thf(f15,plain,(
% 1.38/1.20 ( ! [X0 : nat,X1 : nat] : (($true != (moreis @ X1 @ X0)) | ((lessis @ X0 @ X1) = $true)) )),
% 1.38/1.20 inference(cnf_transformation,[status(thm)],[f14])).
% 1.38/1.20 thf(f14,plain,(
% 1.38/1.20 ! [X0 : nat,X1 : nat] : (($true != (moreis @ X1 @ X0)) | ((lessis @ X0 @ X1) = $true))),
% 1.38/1.20 inference(rectify,[status(thm)],[f13])).
% 1.38/1.20 thf(f13,plain,(
% 1.38/1.20 ! [X1 : nat,X0 : nat] : (((moreis @ X0 @ X1) != $true) | ((lessis @ X1 @ X0) = $true))),
% 1.38/1.20 inference(ennf_transformation,[status(thm)],[f7])).
% 1.38/1.20 thf(f7,plain,(
% 1.38/1.20 ! [X1 : nat,X0 : nat] : (((moreis @ X0 @ X1) = $true) => ((lessis @ X1 @ X0) = $true))),
% 1.38/1.20 inference(fool_elimination,[status(thm)],[f6])).
% 1.38/1.20 thf(f6,plain,(
% 1.38/1.20 ! [X0 : nat,X1 : nat] : ((moreis @ X0 @ X1) => (lessis @ X1 @ X0))),
% 1.38/1.20 inference(rectify,[status(thm)],[f1])).
% 1.38/1.20 thf(f1,axiom,(
% 1.38/1.20 ! [X0 : nat,X1 : nat] : ((moreis @ X0 @ X1) => (lessis @ X1 @ X0))),
% 1.38/1.20 file('/export/starexec/sandbox2/tmp/tmp.jck4jdvAFc/DTF2THF_8456.p',satz13)).
% 1.38/1.20 thf(f16,plain,(
% 1.38/1.20 ((lessis @ n_1 @ x) != $true)),
% 1.38/1.20 inference(cnf_transformation,[status(thm)],[f12])).
% 1.38/1.20 thf(f12,plain,(
% 1.38/1.20 ((lessis @ n_1 @ x) != $true)),
% 1.38/1.20 inference(flattening,[status(thm)],[f9])).
% 1.38/1.20 thf(f9,plain,(
% 1.38/1.20 ~((lessis @ n_1 @ x) = $true)),
% 1.38/1.20 inference(fool_elimination,[status(thm)],[f8])).
% 1.38/1.20 thf(f8,plain,(
% 1.38/1.20 ~(lessis @ n_1 @ x)),
% 1.38/1.20 inference(rectify,[status(thm)],[f4])).
% 1.38/1.20 thf(f4,negated_conjecture,(
% 1.38/1.20 ~(lessis @ n_1 @ x)),
% 1.38/1.20 inference(negated_conjecture,[status(cth)],[f3])).
% 1.38/1.20 thf(f3,conjecture,(
% 1.38/1.20 (lessis @ n_1 @ x)),
% 1.38/1.20 file('/export/starexec/sandbox2/tmp/tmp.jck4jdvAFc/DTF2THF_8456.p',satz24a)).
% 1.38/1.20 % SZS output end Proof for DTF2THF_8456
% 1.38/1.20 % (8556)------------------------------
% 1.38/1.20 % (8556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.20 % (8556)Termination reason: Refutation
% 1.38/1.20
% 1.38/1.20 % (8556)Memory used [KB]: 5500
% 1.38/1.20 % (8556)Time elapsed: 0.003 s
% 1.38/1.20 % (8556)Instructions burned: 1 (million)
% 1.38/1.20 % (8556)------------------------------
% 1.38/1.20 % (8556)------------------------------
% 1.38/1.20 % (8553)Success in time 0.012 s
%------------------------------------------------------------------------------