%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM658^1 : 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 09:24:08 AM UTC 2026
% Result : Theorem 1.50s 1.23s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 36 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 104 ( 26 ~; 9 |; 1 &; 56 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 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,
more: nat > nat > $o ).
thf(func_def_5,type,
less: nat > nat > $o ).
thf(f32,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f31,f23]) ).
thf(f23,plain,
x != y,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( more @ x @ y )
!= $true )
& ( x != y ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/tmp/tmp.vnSUvsN2ON/DTF2THF_29074.p',n) ).
thf(f31,plain,
x = y,
inference(subsumption_resolution,[status(thm)],[f30,f24]) ).
thf(f24,plain,
( ( more @ x @ y )
!= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f30,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true != $true )
| ( x = y )
| ( ( more @ x @ y )
= $true ) ),
inference(superposition,[status(thm)],[f26,f25]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X0 @ X1 )
= $true )
| ( ( more @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( ( more @ X0 @ X1 )
= $true )
| ( ( less @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: nat,X0: nat] :
( ( ( less @ X0 @ X1 )
= $true )
| ( ( more @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: nat,X0: nat] :
( ( X0 != X1 )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( ( less @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( ( less @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vnSUvsN2ON/DTF2THF_29074.p',satz10a) ).
thf(f26,plain,
( ( less @ x @ y )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( less @ x @ y )
!= $true ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( less @ x @ y )
!= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( less @ x @ y ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( less @ x @ y ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
less @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.vnSUvsN2ON/DTF2THF_29074.p',satz10j) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM658^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n021.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 11:09:39 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
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : NUM658^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Number Theory
% 0.18/0.45 % Problem : Landau theorem 10j
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : less x y
% 0.18/0.45
% 0.18/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.18/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.18/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : satz10j [Lan30]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % : Without extensionality : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 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
% 0.18/0.45 % Syntax : Number of formulae : 9 ( 1 unt; 5 typ; 0 def)
% 0.18/0.45 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 3 ( 1 avg)
% 0.18/0.45 % Number of connectives : 18 ( 6 ~; 0 |; 0 &; 8 @)
% 0.18/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 8 ( 6 avg)
% 0.18/0.45 % Number of types : 2 ( 1 usr)
% 0.18/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments :
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(nat_type,type,
% 0.18/0.45 nat: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(x,type,
% 0.18/0.45 x: nat ).
% 0.18/0.45
% 0.18/0.45 thf(y,type,
% 0.18/0.45 y: nat ).
% 0.18/0.45
% 0.18/0.45 thf(more,type,
% 0.18/0.45 more: nat > nat > $o ).
% 0.18/0.45
% 0.18/0.45 thf(n,axiom,
% 0.18/0.45 ~ ( ~ ( more @ x @ y )
% 0.18/0.45 => ( x = y ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(less,type,
% 0.18/0.45 less: nat > nat > $o ).
% 0.18/0.45
% 0.18/0.45 thf(satz10a,axiom,
% 0.18/0.45 ! [Xx: nat,Xy: nat] :
% 0.18/0.45 ( ( Xx != Xy )
% 0.18/0.45 => ( ~ ( more @ Xx @ Xy )
% 0.18/0.45 => ( less @ Xx @ Xy ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(et,axiom,
% 0.18/0.45 ! [Xa: $o] :
% 0.18/0.45 ( ~ ~ Xa
% 0.18/0.45 => Xa ) ).
% 0.18/0.45
% 0.18/0.45 thf(satz10j,conjecture,
% 0.18/0.45 less @ x @ y ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.50/1.20 ---- Embedded in THF ---
% 1.50/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.20 %%% Generated on Tue Feb 24 11:09:39 EST 2026
% 1.50/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.20 %%% Logic specification used:
% 1.50/1.20 %%% thf(spec, logic, $$dhol).
% 1.50/1.20
% 1.50/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vnSUvsN2ON/DTF2DTF29074.p
% See solution above
% 1.50/1.20 ------------------------
% 1.50/1.21 ---- Cleaned THF ---
% 1.50/1.21 thf(nat_type,type,
% 1.50/1.21 nat: $tType ).
% 1.50/1.21
% 1.50/1.21 thf(x,type,
% 1.50/1.21 x: nat ).
% 1.50/1.21
% 1.50/1.21 thf(y,type,
% 1.50/1.21 y: nat ).
% 1.50/1.21
% 1.50/1.21 thf(more,type,
% 1.50/1.21 more: nat > nat > $o ).
% 1.50/1.21
% 1.50/1.21 thf(n,axiom,
% 1.50/1.21 ~ ( ~ ( more @ x @ y )
% 1.50/1.21 => ( x = y ) ) ).
% 1.50/1.21
% 1.50/1.21 thf(less,type,
% 1.50/1.21 less: nat > nat > $o ).
% 1.50/1.21
% 1.50/1.21 thf(satz10a,axiom,
% 1.50/1.21 ! [Xx: nat,Xy: nat] :
% 1.50/1.21 ( ( Xx != Xy )
% 1.50/1.21 => ( ~ ( more @ Xx @ Xy )
% 1.50/1.21 => ( less @ Xx @ Xy ) ) ) ).
% 1.50/1.21
% 1.50/1.21 thf(et,axiom,
% 1.50/1.21 ! [Xa: $o] :
% 1.50/1.21 ( ~ ~ Xa
% 1.50/1.21 => Xa ) ).
% 1.50/1.21
% 1.50/1.21 thf(satz10j,conjecture,
% 1.50/1.21 less @ x @ y ).
% 1.50/1.22 ------------------------
% 1.50/1.23 % (29236)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29074 for (2999ds/2Mi)
% 1.50/1.23 % (29235)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_29074 for (2999ds/27Mi)
% 1.50/1.23 % (29236)First to succeed.
% 1.50/1.23 % (29234)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_29074 for (2999ds/4Mi)
% 1.50/1.23 % (29235)Also succeeded, but the first one will report.
% 1.50/1.23 % (29234)Also succeeded, but the first one will report.
% 1.50/1.23 % (29236)Refutation found. Thanks to Tanya!
% 1.50/1.23 % SZS status Theorem for DTF2THF_29074
% 1.50/1.23 % SZS output start Proof for DTF2THF_29074
% 1.50/1.23 thf(type_def_5, type, nat: $tType).
% 1.50/1.23 thf(func_def_0, type, nat: $tType).
% 1.50/1.23 thf(func_def_1, type, x: nat).
% 1.50/1.23 thf(func_def_2, type, y: nat).
% 1.50/1.23 thf(func_def_3, type, more: nat > nat > $o).
% 1.50/1.23 thf(func_def_5, type, less: nat > nat > $o).
% 1.50/1.23 thf(f32,plain,(
% 1.50/1.23 $false),
% 1.50/1.23 inference(subsumption_resolution,[status(thm)],[f31,f23])).
% 1.50/1.23 thf(f23,plain,(
% 1.50/1.23 (x != y)),
% 1.50/1.23 inference(cnf_transformation,[status(thm)],[f22])).
% 1.50/1.23 thf(f22,plain,(
% 1.50/1.23 ((more @ x @ y) != $true) & (x != y)),
% 1.50/1.23 inference(ennf_transformation,[status(thm)],[f17])).
% 1.50/1.23 thf(f17,plain,(
% 1.50/1.23 ~(((more @ x @ y) != $true) => (x = y))),
% 1.50/1.23 inference(flattening,[status(thm)],[f12])).
% 1.50/1.23 thf(f12,plain,(
% 1.50/1.23 ~(~((more @ x @ y) = $true) => (x = y))),
% 1.50/1.23 inference(fool_elimination,[status(thm)],[f11])).
% 1.50/1.23 thf(f11,plain,(
% 1.50/1.23 ~(~(more @ x @ y) => (x = y))),
% 1.50/1.23 inference(rectify,[status(thm)],[f1])).
% 1.50/1.23 thf(f1,axiom,(
% 1.50/1.23 ~(~(more @ x @ y) => (x = y))),
% 1.50/1.23 file('/export/starexec/sandbox2/tmp/tmp.vnSUvsN2ON/DTF2THF_29074.p',n)).
% 1.50/1.23 thf(f31,plain,(
% 1.50/1.23 (x = y)),
% 1.50/1.23 inference(subsumption_resolution,[status(thm)],[f30,f24])).
% 1.50/1.23 thf(f24,plain,(
% 1.50/1.23 ((more @ x @ y) != $true)),
% 1.50/1.23 inference(cnf_transformation,[status(thm)],[f22])).
% 1.50/1.23 thf(f30,plain,(
% 1.50/1.23 ((more @ x @ y) = $true) | (x = y)),
% 1.50/1.23 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.50/1.23 thf(f29,plain,(
% 1.50/1.23 ($true != $true) | (x = y) | ((more @ x @ y) = $true)),
% 1.50/1.23 inference(superposition,[status(thm)],[f26,f25])).
% 1.50/1.23 thf(f25,plain,(
% 1.50/1.23 ( ! [X0 : nat,X1 : nat] : (((less @ X0 @ X1) = $true) | ((more @ X0 @ X1) = $true) | (X0 = X1)) )),
% 1.50/1.23 inference(cnf_transformation,[status(thm)],[f21])).
% 1.50/1.23 thf(f21,plain,(
% 1.50/1.23 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ((more @ X0 @ X1) = $true) | ((less @ X0 @ X1) = $true))),
% 1.50/1.23 inference(flattening,[status(thm)],[f20])).
% 1.50/1.23 thf(f20,plain,(
% 1.50/1.23 ! [X1 : nat,X0 : nat] : ((((less @ X0 @ X1) = $true) | ((more @ X0 @ X1) = $true)) | (X0 = X1))),
% 1.50/1.23 inference(ennf_transformation,[status(thm)],[f16])).
% 1.50/1.23 thf(f16,plain,(
% 1.50/1.23 ! [X1 : nat,X0 : nat] : ((X0 != X1) => (((more @ X0 @ X1) != $true) => ((less @ X0 @ X1) = $true)))),
% 1.50/1.23 inference(flattening,[status(thm)],[f10])).
% 1.50/1.23 thf(f10,plain,(
% 1.50/1.23 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~((more @ X0 @ X1) = $true) => ((less @ X0 @ X1) = $true)))),
% 1.50/1.23 inference(fool_elimination,[status(thm)],[f9])).
% 1.50/1.23 thf(f9,plain,(
% 1.50/1.23 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 1.50/1.23 inference(rectify,[status(thm)],[f2])).
% 1.50/1.23 thf(f2,axiom,(
% 1.50/1.23 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 1.50/1.23 file('/export/starexec/sandbox2/tmp/tmp.vnSUvsN2ON/DTF2THF_29074.p',satz10a)).
% 1.50/1.23 thf(f26,plain,(
% 1.50/1.23 ((less @ x @ y) != $true)),
% 1.50/1.23 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.23 thf(f18,plain,(
% 1.50/1.23 ((less @ x @ y) != $true)),
% 1.50/1.23 inference(flattening,[status(thm)],[f14])).
% 1.50/1.23 thf(f14,plain,(
% 1.50/1.23 ~((less @ x @ y) = $true)),
% 1.50/1.23 inference(fool_elimination,[status(thm)],[f13])).
% 1.50/1.23 thf(f13,plain,(
% 1.50/1.23 ~(less @ x @ y)),
% 1.50/1.23 inference(rectify,[status(thm)],[f5])).
% 1.50/1.23 thf(f5,negated_conjecture,(
% 1.50/1.23 ~(less @ x @ y)),
% 1.50/1.23 inference(negated_conjecture,[status(cth)],[f4])).
% 1.50/1.23 thf(f4,conjecture,(
% 1.50/1.23 (less @ x @ y)),
% 1.50/1.23 file('/export/starexec/sandbox2/tmp/tmp.vnSUvsN2ON/DTF2THF_29074.p',satz10j)).
% 1.50/1.23 % SZS output end Proof for DTF2THF_29074
% 1.50/1.23 % (29236)------------------------------
% 1.50/1.23 % (29236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (29236)Termination reason: Refutation
% 1.50/1.23
% 1.50/1.23 % (29236)Memory used [KB]: 5500
% 1.50/1.23 % (29236)Time elapsed: 0.003 s
% 1.50/1.23 % (29236)Instructions burned: 1 (million)
% 1.50/1.23 % (29236)------------------------------
% 1.50/1.23 % (29236)------------------------------
% 1.50/1.23 % (29231)Success in time 0.014 s
%------------------------------------------------------------------------------