%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM728^1 : 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 : 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 09:24:26 AM UTC 2026
% Result : Theorem 1.67s 1.42s
% Output : Refutation 1.67s
% 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 : 162 ( 11 ~; 4 |; 0 &; 144 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% 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,
nat: $tType ).
thf(func_def_3,type,
n: nat ).
thf(func_def_4,type,
eq: frac > frac > $o ).
thf(func_def_5,type,
fr: nat > nat > frac ).
thf(func_def_6,type,
ts: nat > nat > nat ).
thf(func_def_7,type,
c1x: frac > nat ).
thf(func_def_8,type,
c2x: frac > nat ).
thf(f20,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f19,f16]) ).
thf(f16,plain,
! [X0: frac,X1: nat] :
( ( eq @ X0 @ ( fr @ ( ts @ ( c1x @ X0 ) @ X1 ) @ ( ts @ ( c2x @ X0 ) @ X1 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: frac,X1: nat] :
( ( eq @ X0 @ ( fr @ ( ts @ ( c1x @ X0 ) @ X1 ) @ ( ts @ ( c2x @ X0 ) @ X1 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: frac,X1: nat] : ( eq @ X0 @ ( fr @ ( ts @ ( c1x @ X0 ) @ X1 ) @ ( ts @ ( c2x @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: frac,X2: nat] : ( eq @ X0 @ ( fr @ ( ts @ ( c1x @ X0 ) @ X2 ) @ ( ts @ ( c2x @ X0 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vWiDuBsleb/DTF2THF_17699.p',satz40) ).
thf(f19,plain,
( ( eq @ x @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( eq @ x @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f17,f15]) ).
thf(f15,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
| ( ( eq @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: frac,X1: frac] :
( ( eq @ X1 @ X0 )
=> ( eq @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: frac,X0: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.vWiDuBsleb/DTF2THF_17699.p',satz38) ).
thf(f17,plain,
( ( eq @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( eq @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) @ x )
!= $true ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( eq @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) @ x )
!= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( eq @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) @ x ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( eq @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) @ x ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
eq @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) @ x,
file('/export/starexec/sandbox/tmp/tmp.vWiDuBsleb/DTF2THF_17699.p',satz40a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM728^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n031.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 11:13:18 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : NUM728^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Number Theory
% 0.18/0.45 % Problem : Landau theorem 40a
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : eq (fr (ts (1x x) n) (ts (2x x) n)) x
% 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 : satz40a [Lan30]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % : Without extensionality : Theorem
% 0.18/0.45 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 12 ( 2 unt; 9 typ; 0 def)
% 0.18/0.45 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 2 ( 1 avg)
% 0.18/0.45 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 24 @)
% 0.18/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 9 ( 8 avg)
% 0.18/0.46 % Number of types : 3 ( 2 usr)
% 0.18/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.46 % Number of symbols : 7 ( 7 usr; 2 con; 0-2 aty)
% 0.18/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.18/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.46
% 0.18/0.46 % Comments :
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 thf(frac_type,type,
% 0.18/0.46 frac: $tType ).
% 0.18/0.46
% 0.18/0.46 thf(x,type,
% 0.18/0.46 x: frac ).
% 0.18/0.46
% 0.18/0.46 thf(nat_type,type,
% 0.18/0.46 nat: $tType ).
% 0.18/0.46
% 0.18/0.46 thf(n,type,
% 0.18/0.46 n: nat ).
% 0.18/0.46
% 0.18/0.46 thf(eq,type,
% 0.18/0.46 eq: frac > frac > $o ).
% 0.18/0.46
% 0.18/0.46 thf(fr,type,
% 0.18/0.46 fr: nat > nat > frac ).
% 0.18/0.46
% 0.18/0.46 thf(ts,type,
% 0.18/0.46 ts: nat > nat > nat ).
% 0.18/0.46
% 0.18/0.46 thf(c1x,type,
% 0.18/0.46 c1x: frac > nat ).
% 0.18/0.46
% 0.18/0.46 thf(c2x,type,
% 0.18/0.46 c2x: frac > nat ).
% 0.18/0.46
% 0.18/0.46 thf(satz38,axiom,
% 0.18/0.46 ! [Xx: frac,Xy: frac] :
% 0.18/0.46 ( ( eq @ Xx @ Xy )
% 0.18/0.46 => ( eq @ Xy @ Xx ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(satz40,axiom,
% 0.18/0.46 ! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( c1x @ Xx ) @ Xn ) @ ( ts @ ( c2x @ Xx ) @ Xn ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(satz40a,conjecture,
% 0.18/0.46 eq @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) @ x ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 1.47/1.39 ---- Embedded in THF ---
% 1.47/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.39 %%% Generated on Tue Feb 24 11:13:19 EST 2026
% 1.47/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.39 %%% Logic specification used:
% 1.47/1.39 %%% thf(spec, logic, $$dhol).
% 1.47/1.39
% 1.47/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vWiDuBsleb/DTF2DTF17699.p
% See solution above
% 1.47/1.39 ------------------------
% 1.67/1.40 ---- Cleaned THF ---
% 1.67/1.40 thf(frac_type,type,
% 1.67/1.40 frac: $tType ).
% 1.67/1.40
% 1.67/1.40 thf(x,type,
% 1.67/1.40 x: frac ).
% 1.67/1.40
% 1.67/1.40 thf(nat_type,type,
% 1.67/1.40 nat: $tType ).
% 1.67/1.40
% 1.67/1.40 thf(n,type,
% 1.67/1.40 n: nat ).
% 1.67/1.40
% 1.67/1.40 thf(eq,type,
% 1.67/1.40 eq: frac > frac > $o ).
% 1.67/1.40
% 1.67/1.40 thf(fr,type,
% 1.67/1.40 fr: nat > nat > frac ).
% 1.67/1.40
% 1.67/1.40 thf(ts,type,
% 1.67/1.40 ts: nat > nat > nat ).
% 1.67/1.40
% 1.67/1.40 thf(c1x,type,
% 1.67/1.40 c1x: frac > nat ).
% 1.67/1.40
% 1.67/1.40 thf(c2x,type,
% 1.67/1.40 c2x: frac > nat ).
% 1.67/1.40
% 1.67/1.40 thf(satz38,axiom,
% 1.67/1.40 ! [Xx: frac,Xy: frac] :
% 1.67/1.40 ( ( eq @ Xx @ Xy )
% 1.67/1.40 => ( eq @ Xy @ Xx ) ) ).
% 1.67/1.40
% 1.67/1.40 thf(satz40,axiom,
% 1.67/1.40 ! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( c1x @ Xx ) @ Xn ) @ ( ts @ ( c2x @ Xx ) @ Xn ) ) ) ).
% 1.67/1.40
% 1.67/1.40 thf(satz40a,conjecture,
% 1.67/1.40 eq @ ( fr @ ( ts @ ( c1x @ x ) @ n ) @ ( ts @ ( c2x @ x ) @ n ) ) @ x ).
% 1.67/1.40 ------------------------
% 1.67/1.42 % (17818)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_17699 for (2999ds/275Mi)
% 1.67/1.42 % (17818)First to succeed.
% 1.67/1.42 % (17818)Refutation found. Thanks to Tanya!
% 1.67/1.42 % SZS status Theorem for DTF2THF_17699
% 1.67/1.42 % SZS output start Proof for DTF2THF_17699
% 1.67/1.42 thf(type_def_5, type, frac: $tType).
% 1.67/1.42 thf(type_def_6, type, nat: $tType).
% 1.67/1.42 thf(func_def_0, type, frac: $tType).
% 1.67/1.42 thf(func_def_1, type, x: frac).
% 1.67/1.42 thf(func_def_2, type, nat: $tType).
% 1.67/1.42 thf(func_def_3, type, n: nat).
% 1.67/1.42 thf(func_def_4, type, eq: frac > frac > $o).
% 1.67/1.42 thf(func_def_5, type, fr: nat > nat > frac).
% 1.67/1.42 thf(func_def_6, type, ts: nat > nat > nat).
% 1.67/1.42 thf(func_def_7, type, c1x: frac > nat).
% 1.67/1.42 thf(func_def_8, type, c2x: frac > nat).
% 1.67/1.42 thf(f20,plain,(
% 1.67/1.42 $false),
% 1.67/1.42 inference(subsumption_resolution,[status(thm)],[f19,f16])).
% 1.67/1.42 thf(f16,plain,(
% 1.67/1.42 ( ! [X0 : frac,X1 : nat] : (((eq @ X0 @ (fr @ (ts @ (c1x @ X0) @ X1) @ (ts @ (c2x @ X0) @ X1))) = $true)) )),
% 1.67/1.42 inference(cnf_transformation,[status(thm)],[f7])).
% 1.67/1.42 thf(f7,plain,(
% 1.67/1.42 ! [X0 : frac,X1 : nat] : ((eq @ X0 @ (fr @ (ts @ (c1x @ X0) @ X1) @ (ts @ (c2x @ X0) @ X1))) = $true)),
% 1.67/1.42 inference(fool_elimination,[status(thm)],[f6])).
% 1.67/1.42 thf(f6,plain,(
% 1.67/1.42 ! [X0 : frac,X1 : nat] : (eq @ X0 @ (fr @ (ts @ (c1x @ X0) @ X1) @ (ts @ (c2x @ X0) @ X1)))),
% 1.67/1.42 inference(rectify,[status(thm)],[f2])).
% 1.67/1.42 thf(f2,axiom,(
% 1.67/1.42 ! [X0 : frac,X2 : nat] : (eq @ X0 @ (fr @ (ts @ (c1x @ X0) @ X2) @ (ts @ (c2x @ X0) @ X2)))),
% 1.67/1.42 file('/export/starexec/sandbox/tmp/tmp.vWiDuBsleb/DTF2THF_17699.p',satz40)).
% 1.67/1.42 thf(f19,plain,(
% 1.67/1.42 ((eq @ x @ (fr @ (ts @ (c1x @ x) @ n) @ (ts @ (c2x @ x) @ n))) != $true)),
% 1.67/1.42 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.67/1.42 thf(f18,plain,(
% 1.67/1.42 ((eq @ x @ (fr @ (ts @ (c1x @ x) @ n) @ (ts @ (c2x @ x) @ n))) != $true) | ($true != $true)),
% 1.67/1.42 inference(superposition,[status(thm)],[f17,f15])).
% 1.67/1.42 thf(f15,plain,(
% 1.67/1.42 ( ! [X0 : frac,X1 : frac] : (((eq @ X1 @ X0) = $true) | ((eq @ X0 @ X1) != $true)) )),
% 1.67/1.42 inference(cnf_transformation,[status(thm)],[f14])).
% 1.67/1.42 thf(f14,plain,(
% 1.67/1.42 ! [X0 : frac,X1 : frac] : (((eq @ X1 @ X0) = $true) | ((eq @ X0 @ X1) != $true))),
% 1.67/1.42 inference(rectify,[status(thm)],[f13])).
% 1.67/1.42 thf(f13,plain,(
% 1.67/1.42 ! [X1 : frac,X0 : frac] : (((eq @ X0 @ X1) = $true) | ((eq @ X1 @ X0) != $true))),
% 1.67/1.42 inference(ennf_transformation,[status(thm)],[f9])).
% 1.67/1.42 thf(f9,plain,(
% 1.67/1.42 ! [X1 : frac,X0 : frac] : (((eq @ X1 @ X0) = $true) => ((eq @ X0 @ X1) = $true))),
% 1.67/1.42 inference(fool_elimination,[status(thm)],[f8])).
% 1.67/1.42 thf(f8,plain,(
% 1.67/1.42 ! [X0 : frac,X1 : frac] : ((eq @ X1 @ X0) => (eq @ X0 @ X1))),
% 1.67/1.42 inference(rectify,[status(thm)],[f1])).
% 1.67/1.42 thf(f1,axiom,(
% 1.67/1.42 ! [X1 : frac,X0 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 1.67/1.42 file('/export/starexec/sandbox/tmp/tmp.vWiDuBsleb/DTF2THF_17699.p',satz38)).
% 1.67/1.42 thf(f17,plain,(
% 1.67/1.42 ((eq @ (fr @ (ts @ (c1x @ x) @ n) @ (ts @ (c2x @ x) @ n)) @ x) != $true)),
% 1.67/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.42 thf(f12,plain,(
% 1.67/1.42 ((eq @ (fr @ (ts @ (c1x @ x) @ n) @ (ts @ (c2x @ x) @ n)) @ x) != $true)),
% 1.67/1.42 inference(flattening,[status(thm)],[f11])).
% 1.67/1.42 thf(f11,plain,(
% 1.67/1.42 ~((eq @ (fr @ (ts @ (c1x @ x) @ n) @ (ts @ (c2x @ x) @ n)) @ x) = $true)),
% 1.67/1.42 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.42 thf(f10,plain,(
% 1.67/1.42 ~(eq @ (fr @ (ts @ (c1x @ x) @ n) @ (ts @ (c2x @ x) @ n)) @ x)),
% 1.67/1.42 inference(rectify,[status(thm)],[f4])).
% 1.67/1.42 thf(f4,negated_conjecture,(
% 1.67/1.42 ~(eq @ (fr @ (ts @ (c1x @ x) @ n) @ (ts @ (c2x @ x) @ n)) @ x)),
% 1.67/1.42 inference(negated_conjecture,[status(cth)],[f3])).
% 1.67/1.42 thf(f3,conjecture,(
% 1.67/1.42 (eq @ (fr @ (ts @ (c1x @ x) @ n) @ (ts @ (c2x @ x) @ n)) @ x)),
% 1.67/1.42 file('/export/starexec/sandbox/tmp/tmp.vWiDuBsleb/DTF2THF_17699.p',satz40a)).
% 1.67/1.42 % SZS output end Proof for DTF2THF_17699
% 1.67/1.42 % (17818)------------------------------
% 1.67/1.42 % (17818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (17818)Termination reason: Refutation
% 1.67/1.42
% 1.67/1.42 % (17818)Memory used [KB]: 5500
% 1.67/1.42 % (17818)Time elapsed: 0.002 s
% 1.67/1.42 % (17818)Instructions burned: 2 (million)
% 1.67/1.42 % (17818)------------------------------
% 1.67/1.42 % (17818)------------------------------
% 1.67/1.42 % (17812)Success in time 0.01 s
%------------------------------------------------------------------------------