%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM736^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 09:24:27 AM UTC 2026
% Result : Theorem 1.51s 1.26s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 160 ( 9 ~; 4 |; 0 &; 144 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(func_def_0,type,
frac: $tType ).
thf(func_def_1,type,
x: frac ).
thf(func_def_2,type,
y: frac ).
thf(func_def_3,type,
nat: $tType ).
thf(func_def_4,type,
more: nat > nat > $o ).
thf(func_def_5,type,
ts: nat > nat > nat ).
thf(func_def_6,type,
num: frac > nat ).
thf(func_def_7,type,
den: frac > nat ).
thf(func_def_9,type,
less: nat > nat > $o ).
thf(f20,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f19,f16]) ).
thf(f16,plain,
( ( less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) )
!= $true ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.DGvrMWLiUU/DTF2THF_30001.p',satz42) ).
thf(f19,plain,
( ( less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f17,f15]) ).
thf(f15,plain,
( ( more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.DGvrMWLiUU/DTF2THF_30001.p',m) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
= $true ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: nat,X0: nat] :
( ( $true
!= ( more @ X1 @ X0 ) )
| ( $true
= ( less @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( more @ X1 @ X0 ) )
=> ( $true
= ( less @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( more @ X1 @ X0 )
=> ( less @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.DGvrMWLiUU/DTF2THF_30001.p',satz11) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM736^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n026.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % 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 11:12:40 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : NUM736^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Number Theory
% 0.31/0.46 % Problem : Landau theorem 42
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : less (ts (num y) (den x)) (ts (num x) (den y))
% 0.31/0.46
% 0.31/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.31/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.31/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : satz42 [Lan30]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % : Without extensionality : Theorem
% 0.31/0.46 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 12 ( 2 unt; 9 typ; 0 def)
% 0.31/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.31/0.46 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 24 @)
% 0.31/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.31/0.46 % Number of types : 3 ( 2 usr)
% 0.31/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 7 ( 7 usr; 2 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments :
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(frac_type,type,
% 0.31/0.46 frac: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(x,type,
% 0.31/0.46 x: frac ).
% 0.31/0.46
% 0.31/0.46 thf(y,type,
% 0.31/0.46 y: frac ).
% 0.31/0.46
% 0.31/0.46 thf(nat_type,type,
% 0.31/0.46 nat: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(more,type,
% 0.31/0.46 more: nat > nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(ts,type,
% 0.31/0.46 ts: nat > nat > nat ).
% 0.31/0.46
% 0.31/0.46 thf(num,type,
% 0.31/0.46 num: frac > nat ).
% 0.31/0.46
% 0.31/0.46 thf(den,type,
% 0.31/0.46 den: frac > nat ).
% 0.31/0.46
% 0.31/0.46 thf(m,axiom,
% 0.31/0.46 more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(less,type,
% 0.31/0.46 less: nat > nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(satz11,axiom,
% 0.31/0.46 ! [Xx: nat,Xy: nat] :
% 0.31/0.46 ( ( more @ Xx @ Xy )
% 0.31/0.46 => ( less @ Xy @ Xx ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(satz42,conjecture,
% 0.31/0.46 less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.51/1.24 ---- Embedded in THF ---
% 1.51/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.24 %%% Generated on Tue Feb 24 11:12:41 EST 2026
% 1.51/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.24 %%% Logic specification used:
% 1.51/1.24 %%% thf(spec, logic, $$dhol).
% 1.51/1.24
% 1.51/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.DGvrMWLiUU/DTF2DTF30001.p
% See solution above
% 1.51/1.24 ------------------------
% 1.51/1.25 ---- Cleaned THF ---
% 1.51/1.25 thf(frac_type,type,
% 1.51/1.25 frac: $tType ).
% 1.51/1.25
% 1.51/1.25 thf(x,type,
% 1.51/1.25 x: frac ).
% 1.51/1.25
% 1.51/1.25 thf(y,type,
% 1.51/1.25 y: frac ).
% 1.51/1.25
% 1.51/1.25 thf(nat_type,type,
% 1.51/1.25 nat: $tType ).
% 1.51/1.25
% 1.51/1.25 thf(more,type,
% 1.51/1.25 more: nat > nat > $o ).
% 1.51/1.25
% 1.51/1.25 thf(ts,type,
% 1.51/1.25 ts: nat > nat > nat ).
% 1.51/1.25
% 1.51/1.25 thf(num,type,
% 1.51/1.25 num: frac > nat ).
% 1.51/1.25
% 1.51/1.25 thf(den,type,
% 1.51/1.25 den: frac > nat ).
% 1.51/1.25
% 1.51/1.25 thf(m,axiom,
% 1.51/1.25 more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ).
% 1.51/1.25
% 1.51/1.25 thf(less,type,
% 1.51/1.25 less: nat > nat > $o ).
% 1.51/1.25
% 1.51/1.25 thf(satz11,axiom,
% 1.51/1.25 ! [Xx: nat,Xy: nat] :
% 1.51/1.25 ( ( more @ Xx @ Xy )
% 1.51/1.25 => ( less @ Xy @ Xx ) ) ).
% 1.51/1.25
% 1.51/1.25 thf(satz42,conjecture,
% 1.51/1.25 less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ).
% 1.51/1.25 ------------------------
% 1.51/1.26 % (30282)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30001 for (3000ds/18Mi)
% 1.51/1.26 % (30277)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_30001 for (3000ds/4Mi)
% 1.51/1.26 % (30282)First to succeed.
% 1.51/1.26 % (30277)Also succeeded, but the first one will report.
% 1.51/1.26 % (30282)Refutation found. Thanks to Tanya!
% 1.51/1.26 % SZS status Theorem for DTF2THF_30001
% 1.51/1.26 % SZS output start Proof for DTF2THF_30001
% 1.51/1.26 thf(type_def_5, type, frac: $tType).
% 1.51/1.26 thf(type_def_6, type, nat: $tType).
% 1.51/1.26 thf(func_def_0, type, frac: $tType).
% 1.51/1.26 thf(func_def_1, type, x: frac).
% 1.51/1.26 thf(func_def_2, type, y: frac).
% 1.51/1.26 thf(func_def_3, type, nat: $tType).
% 1.51/1.26 thf(func_def_4, type, more: nat > nat > $o).
% 1.51/1.26 thf(func_def_5, type, ts: nat > nat > nat).
% 1.51/1.26 thf(func_def_6, type, num: frac > nat).
% 1.51/1.26 thf(func_def_7, type, den: frac > nat).
% 1.51/1.26 thf(func_def_9, type, less: nat > nat > $o).
% 1.51/1.26 thf(f20,plain,(
% 1.51/1.26 $false),
% 1.51/1.26 inference(subsumption_resolution,[status(thm)],[f19,f16])).
% 1.51/1.26 thf(f16,plain,(
% 1.51/1.26 ((less @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) != $true)),
% 1.51/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.26 thf(f12,plain,(
% 1.51/1.26 ((less @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) != $true)),
% 1.51/1.26 inference(flattening,[status(thm)],[f9])).
% 1.51/1.26 thf(f9,plain,(
% 1.51/1.26 ~((less @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) = $true)),
% 1.51/1.26 inference(fool_elimination,[status(thm)],[f8])).
% 1.51/1.26 thf(f8,plain,(
% 1.51/1.26 ~(less @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y)))),
% 1.51/1.26 inference(rectify,[status(thm)],[f4])).
% 1.51/1.26 thf(f4,negated_conjecture,(
% 1.51/1.26 ~(less @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y)))),
% 1.51/1.26 inference(negated_conjecture,[status(cth)],[f3])).
% 1.51/1.26 thf(f3,conjecture,(
% 1.51/1.26 (less @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y)))),
% 1.51/1.26 file('/export/starexec/sandbox/tmp/tmp.DGvrMWLiUU/DTF2THF_30001.p',satz42)).
% 1.51/1.26 thf(f19,plain,(
% 1.51/1.26 ((less @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) = $true)),
% 1.51/1.26 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.51/1.26 thf(f18,plain,(
% 1.51/1.26 ((less @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) = $true) | ($true != $true)),
% 1.51/1.26 inference(superposition,[status(thm)],[f17,f15])).
% 1.51/1.26 thf(f15,plain,(
% 1.51/1.26 ((more @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) = $true)),
% 1.51/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.51/1.26 thf(f7,plain,(
% 1.51/1.26 ((more @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) = $true)),
% 1.51/1.26 inference(fool_elimination,[status(thm)],[f6])).
% 1.51/1.26 thf(f6,plain,(
% 1.51/1.26 (more @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x)))),
% 1.51/1.26 inference(rectify,[status(thm)],[f1])).
% 1.51/1.26 thf(f1,axiom,(
% 1.51/1.26 (more @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x)))),
% 1.51/1.26 file('/export/starexec/sandbox/tmp/tmp.DGvrMWLiUU/DTF2THF_30001.p',m)).
% 1.51/1.26 thf(f17,plain,(
% 1.51/1.26 ( ! [X0 : nat,X1 : nat] : (((more @ X0 @ X1) != $true) | ((less @ X1 @ X0) = $true)) )),
% 1.51/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.51/1.26 thf(f14,plain,(
% 1.51/1.26 ! [X0 : nat,X1 : nat] : (((more @ X0 @ X1) != $true) | ((less @ X1 @ X0) = $true))),
% 1.51/1.26 inference(rectify,[status(thm)],[f13])).
% 1.51/1.26 thf(f13,plain,(
% 1.51/1.26 ! [X1 : nat,X0 : nat] : (($true != (more @ X1 @ X0)) | ($true = (less @ X0 @ X1)))),
% 1.51/1.26 inference(ennf_transformation,[status(thm)],[f11])).
% 1.51/1.26 thf(f11,plain,(
% 1.51/1.26 ! [X0 : nat,X1 : nat] : (($true = (more @ X1 @ X0)) => ($true = (less @ X0 @ X1)))),
% 1.51/1.26 inference(fool_elimination,[status(thm)],[f10])).
% 1.51/1.26 thf(f10,plain,(
% 1.51/1.26 ! [X0 : nat,X1 : nat] : ((more @ X1 @ X0) => (less @ X0 @ X1))),
% 1.51/1.26 inference(rectify,[status(thm)],[f2])).
% 1.51/1.26 thf(f2,axiom,(
% 1.51/1.26 ! [X1 : nat,X0 : nat] : ((more @ X0 @ X1) => (less @ X1 @ X0))),
% 1.51/1.26 file('/export/starexec/sandbox/tmp/tmp.DGvrMWLiUU/DTF2THF_30001.p',satz11)).
% 1.51/1.26 % SZS output end Proof for DTF2THF_30001
% 1.51/1.26 % (30282)------------------------------
% 1.51/1.26 % (30282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (30282)Termination reason: Refutation
% 1.51/1.26
% 1.51/1.26 % (30282)Memory used [KB]: 5500
% 1.51/1.26 % (30282)Time elapsed: 0.002 s
% 1.51/1.26 % (30282)Instructions burned: 2 (million)
% 1.51/1.26 % (30282)------------------------------
% 1.51/1.26 % (30282)------------------------------
% 1.51/1.26 % (30275)Success in time 0.011 s
%------------------------------------------------------------------------------