%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM771^1 : 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 : n001.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 09:24:40 AM UTC 2026
% Result : Theorem 1.59s 1.30s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 10 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 203 ( 7 ~; 0 |; 0 &; 196 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_7,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,
eq: frac > frac > $o ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
fr: nat > nat > frac ).
thf(func_def_6,type,
ts: nat > nat > nat ).
thf(func_def_7,type,
num: frac > nat ).
thf(func_def_8,type,
den: frac > nat ).
thf(f21,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f20,f14]) ).
thf(f14,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: frac] : ( eq @ X0 @ X0 ),
file('/export/starexec/sandbox2/tmp/tmp.LCQm5XtboF/DTF2THF_17882.p',satz37) ).
thf(f20,plain,
( $true
!= ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
inference(superposition,[status(thm)],[f15,f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.LCQm5XtboF/DTF2THF_17882.p',satz29) ).
thf(f15,plain,
( $true
!= ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
inference(superposition,[status(thm)],[f13,f12]) ).
thf(f13,plain,
( ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LCQm5XtboF/DTF2THF_17882.p',satz69) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM771^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:14:35 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : NUM771^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.47 % Domain : Number Theory
% 0.27/0.47 % Problem : Landau theorem 69
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English : eq (fr (ts (num x) (num y)) (ts (den x) (den y))) (fr (ts (num y)
% 0.27/0.47 % (num x)) (ts (den y) (den x)))
% 0.27/0.47
% 0.27/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.27/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.27/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : satz69 [Lan30]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % : Without extensionality : Theorem
% 0.27/0.47 % Rating : 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.27/0.47 % Syntax : Number of formulae : 12 ( 3 unt; 9 typ; 0 def)
% 0.27/0.47 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.27/0.47 % Number of connectives : 28 ( 0 ~; 0 |; 0 &; 28 @)
% 0.27/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 8 ( 5 avg)
% 0.27/0.47 % Number of types : 3 ( 2 usr)
% 0.27/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 8 ( 7 usr; 2 con; 0-2 aty)
% 0.27/0.47 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments :
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(frac_type,type,
% 0.27/0.47 frac: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(x,type,
% 0.27/0.47 x: frac ).
% 0.27/0.47
% 0.27/0.47 thf(y,type,
% 0.27/0.47 y: frac ).
% 0.27/0.47
% 0.27/0.47 thf(eq,type,
% 0.27/0.47 eq: frac > frac > $o ).
% 0.27/0.47
% 0.27/0.47 thf(nat_type,type,
% 0.27/0.47 nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(fr,type,
% 0.27/0.47 fr: nat > nat > frac ).
% 0.27/0.47
% 0.27/0.47 thf(ts,type,
% 0.27/0.47 ts: nat > nat > nat ).
% 0.27/0.47
% 0.27/0.47 thf(num,type,
% 0.27/0.47 num: frac > nat ).
% 0.27/0.47
% 0.27/0.47 thf(den,type,
% 0.27/0.47 den: frac > nat ).
% 0.27/0.47
% 0.27/0.47 thf(satz37,axiom,
% 0.27/0.47 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.27/0.47
% 0.27/0.47 thf(satz29,axiom,
% 0.27/0.47 ! [Xx: nat,Xy: nat] :
% 0.27/0.47 ( ( ts @ Xx @ Xy )
% 0.27/0.47 = ( ts @ Xy @ Xx ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(satz69,conjecture,
% 0.27/0.47 eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.44/1.27 ---- Embedded in THF ---
% 1.44/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.27 %%% Generated on Tue Feb 24 11:14:36 EST 2026
% 1.44/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.27 %%% Logic specification used:
% 1.44/1.27 %%% thf(spec, logic, $$dhol).
% 1.44/1.27
% 1.44/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LCQm5XtboF/DTF2DTF17882.p
% See solution above
% 1.44/1.27 ------------------------
% 1.44/1.28 ---- Cleaned THF ---
% 1.44/1.28 thf(frac_type,type,
% 1.44/1.28 frac: $tType ).
% 1.44/1.28
% 1.44/1.28 thf(x,type,
% 1.44/1.28 x: frac ).
% 1.44/1.28
% 1.44/1.28 thf(y,type,
% 1.44/1.28 y: frac ).
% 1.44/1.28
% 1.44/1.28 thf(eq,type,
% 1.44/1.28 eq: frac > frac > $o ).
% 1.44/1.28
% 1.44/1.28 thf(nat_type,type,
% 1.44/1.28 nat: $tType ).
% 1.44/1.28
% 1.44/1.28 thf(fr,type,
% 1.44/1.28 fr: nat > nat > frac ).
% 1.44/1.28
% 1.44/1.28 thf(ts,type,
% 1.44/1.28 ts: nat > nat > nat ).
% 1.44/1.28
% 1.44/1.28 thf(num,type,
% 1.44/1.28 num: frac > nat ).
% 1.44/1.28
% 1.44/1.28 thf(den,type,
% 1.44/1.28 den: frac > nat ).
% 1.44/1.28
% 1.44/1.28 thf(satz37,axiom,
% 1.44/1.28 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 1.44/1.28
% 1.44/1.28 thf(satz29,axiom,
% 1.44/1.28 ! [Xx: nat,Xy: nat] :
% 1.44/1.28 ( ( ts @ Xx @ Xy )
% 1.44/1.28 = ( ts @ Xy @ Xx ) ) ).
% 1.44/1.28
% 1.44/1.28 thf(satz69,conjecture,
% 1.44/1.28 eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ).
% 1.44/1.28 ------------------------
% 1.44/1.29 % (18039)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17882 for (2999ds/183Mi)
% 1.44/1.30 % (18039)First to succeed.
% 1.44/1.30 % (18044)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_17882 for (2999ds/275Mi)
% 1.59/1.30 % (18044)Also succeeded, but the first one will report.
% 1.59/1.30 % (18039)Refutation found. Thanks to Tanya!
% 1.59/1.30 % SZS status Theorem for DTF2THF_17882
% 1.59/1.30 % SZS output start Proof for DTF2THF_17882
% 1.59/1.30 thf(type_def_5, type, frac: $tType).
% 1.59/1.30 thf(type_def_7, type, nat: $tType).
% 1.59/1.30 thf(func_def_0, type, frac: $tType).
% 1.59/1.30 thf(func_def_1, type, x: frac).
% 1.59/1.30 thf(func_def_2, type, y: frac).
% 1.59/1.30 thf(func_def_3, type, eq: frac > frac > $o).
% 1.59/1.30 thf(func_def_4, type, nat: $tType).
% 1.59/1.30 thf(func_def_5, type, fr: nat > nat > frac).
% 1.59/1.30 thf(func_def_6, type, ts: nat > nat > nat).
% 1.59/1.30 thf(func_def_7, type, num: frac > nat).
% 1.59/1.30 thf(func_def_8, type, den: frac > nat).
% 1.59/1.30 thf(f21,plain,(
% 1.59/1.30 $false),
% 1.59/1.30 inference(subsumption_resolution,[status(thm)],[f20,f14])).
% 1.59/1.30 thf(f14,plain,(
% 1.59/1.30 ( ! [X0 : frac] : (((eq @ X0 @ X0) = $true)) )),
% 1.59/1.30 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.30 thf(f9,plain,(
% 1.59/1.30 ! [X0 : frac] : ((eq @ X0 @ X0) = $true)),
% 1.59/1.30 inference(fool_elimination,[status(thm)],[f8])).
% 1.59/1.30 thf(f8,plain,(
% 1.59/1.30 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.59/1.30 inference(rectify,[status(thm)],[f1])).
% 1.59/1.30 thf(f1,axiom,(
% 1.59/1.30 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.59/1.30 file('/export/starexec/sandbox2/tmp/tmp.LCQm5XtboF/DTF2THF_17882.p',satz37)).
% 1.59/1.30 thf(f20,plain,(
% 1.59/1.30 ($true != (eq @ (fr @ (ts @ (num @ x) @ (num @ y)) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (ts @ (num @ x) @ (num @ y)) @ (ts @ (den @ x) @ (den @ y)))))),
% 1.59/1.30 inference(superposition,[status(thm)],[f15,f12])).
% 1.59/1.30 thf(f12,plain,(
% 1.59/1.30 ( ! [X0 : nat,X1 : nat] : (((ts @ X0 @ X1) = (ts @ X1 @ X0))) )),
% 1.59/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.59/1.30 thf(f11,plain,(
% 1.59/1.30 ! [X0 : nat,X1 : nat] : ((ts @ X0 @ X1) = (ts @ X1 @ X0))),
% 1.59/1.30 inference(rectify,[status(thm)],[f2])).
% 1.59/1.30 thf(f2,axiom,(
% 1.59/1.30 ! [X1 : nat,X0 : nat] : ((ts @ X0 @ X1) = (ts @ X1 @ X0))),
% 1.59/1.30 file('/export/starexec/sandbox2/tmp/tmp.LCQm5XtboF/DTF2THF_17882.p',satz29)).
% 1.59/1.30 thf(f15,plain,(
% 1.59/1.30 ($true != (eq @ (fr @ (ts @ (num @ x) @ (num @ y)) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (ts @ (num @ y) @ (num @ x)) @ (ts @ (den @ x) @ (den @ y)))))),
% 1.59/1.30 inference(superposition,[status(thm)],[f13,f12])).
% 1.59/1.30 thf(f13,plain,(
% 1.59/1.30 ((eq @ (fr @ (ts @ (num @ x) @ (num @ y)) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (ts @ (num @ y) @ (num @ x)) @ (ts @ (den @ y) @ (den @ x)))) != $true)),
% 1.59/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.59/1.30 thf(f10,plain,(
% 1.59/1.30 ((eq @ (fr @ (ts @ (num @ x) @ (num @ y)) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (ts @ (num @ y) @ (num @ x)) @ (ts @ (den @ y) @ (den @ x)))) != $true)),
% 1.59/1.30 inference(flattening,[status(thm)],[f7])).
% 1.59/1.30 thf(f7,plain,(
% 1.59/1.30 ~((eq @ (fr @ (ts @ (num @ x) @ (num @ y)) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (ts @ (num @ y) @ (num @ x)) @ (ts @ (den @ y) @ (den @ x)))) = $true)),
% 1.59/1.30 inference(fool_elimination,[status(thm)],[f6])).
% 1.59/1.30 thf(f6,plain,(
% 1.59/1.30 ~(eq @ (fr @ (ts @ (num @ x) @ (num @ y)) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (ts @ (num @ y) @ (num @ x)) @ (ts @ (den @ y) @ (den @ x))))),
% 1.59/1.30 inference(rectify,[status(thm)],[f4])).
% 1.59/1.30 thf(f4,negated_conjecture,(
% 1.59/1.30 ~(eq @ (fr @ (ts @ (num @ x) @ (num @ y)) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (ts @ (num @ y) @ (num @ x)) @ (ts @ (den @ y) @ (den @ x))))),
% 1.59/1.30 inference(negated_conjecture,[status(cth)],[f3])).
% 1.59/1.30 thf(f3,conjecture,(
% 1.59/1.30 (eq @ (fr @ (ts @ (num @ x) @ (num @ y)) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (ts @ (num @ y) @ (num @ x)) @ (ts @ (den @ y) @ (den @ x))))),
% 1.59/1.30 file('/export/starexec/sandbox2/tmp/tmp.LCQm5XtboF/DTF2THF_17882.p',satz69)).
% 1.59/1.30 % SZS output end Proof for DTF2THF_17882
% 1.59/1.30 % (18039)------------------------------
% 1.59/1.30 % (18039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (18039)Termination reason: Refutation
% 1.59/1.30
% 1.59/1.30 % (18039)Memory used [KB]: 5500
% 1.59/1.30 % (18039)Time elapsed: 0.003 s
% 1.59/1.30 % (18039)Instructions burned: 3 (million)
% 1.59/1.30 % (18039)------------------------------
% 1.59/1.30 % (18039)------------------------------
% 1.59/1.30 % (18038)Success in time 0.002 s
%------------------------------------------------------------------------------