%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM726^1 : 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 : n015.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 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 51 ( 3 ~; 0 |; 0 &; 48 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 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,
ts: nat > nat > nat ).
thf(func_def_5,type,
num: frac > nat ).
thf(func_def_6,type,
den: frac > nat ).
thf(f8,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f7,f6]) ).
thf(f6,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.m84QCixrAj/DTF2THF_4186.p',e) ).
thf(f7,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
inference(flattening,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.m84QCixrAj/DTF2THF_4186.p',satz38) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM726^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n015.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % 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 11:12:16 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
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : NUM726^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Number Theory
% 0.31/0.47 % Problem : Landau theorem 38
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : ts (num y) (den x) = ts (num x) (den y)
% 0.31/0.47
% 0.31/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.31/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.31/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : satz38 [Lan30]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % : Without extensionality : Theorem
% 0.31/0.47 % Rating : 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
% 0.31/0.47 % Syntax : Number of formulae : 9 ( 2 unt; 7 typ; 0 def)
% 0.31/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.31/0.47 % Number of connectives : 16 ( 0 ~; 0 |; 0 &; 16 @)
% 0.31/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 1 ( 1 avg)
% 0.31/0.47 % Number of types : 2 ( 2 usr)
% 0.31/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments :
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(frac_type,type,
% 0.31/0.47 frac: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(x,type,
% 0.31/0.47 x: frac ).
% 0.31/0.47
% 0.31/0.47 thf(y,type,
% 0.31/0.47 y: frac ).
% 0.31/0.47
% 0.31/0.47 thf(nat_type,type,
% 0.31/0.47 nat: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ts,type,
% 0.31/0.47 ts: nat > nat > nat ).
% 0.31/0.47
% 0.31/0.47 thf(num,type,
% 0.31/0.47 num: frac > nat ).
% 0.31/0.47
% 0.31/0.47 thf(den,type,
% 0.31/0.47 den: frac > nat ).
% 0.31/0.47
% 0.31/0.47 thf(e,axiom,
% 0.31/0.47 ( ( ts @ ( num @ x ) @ ( den @ y ) )
% 0.31/0.47 = ( ts @ ( num @ y ) @ ( den @ x ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(satz38,conjecture,
% 0.31/0.47 ( ( ts @ ( num @ y ) @ ( den @ x ) )
% 0.31/0.47 = ( ts @ ( num @ x ) @ ( den @ y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 11:12:17 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.m84QCixrAj/DTF2DTF4186.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.28 thf(frac_type,type,
% 1.47/1.28 frac: $tType ).
% 1.47/1.28
% 1.47/1.28 thf(x,type,
% 1.47/1.28 x: frac ).
% 1.47/1.28
% 1.47/1.28 thf(y,type,
% 1.47/1.28 y: frac ).
% 1.47/1.28
% 1.47/1.28 thf(nat_type,type,
% 1.47/1.28 nat: $tType ).
% 1.47/1.28
% 1.47/1.28 thf(ts,type,
% 1.47/1.28 ts: nat > nat > nat ).
% 1.47/1.28
% 1.47/1.28 thf(num,type,
% 1.47/1.28 num: frac > nat ).
% 1.47/1.28
% 1.47/1.28 thf(den,type,
% 1.47/1.28 den: frac > nat ).
% 1.47/1.28
% 1.47/1.28 thf(e,axiom,
% 1.47/1.28 ( ( ts @ ( num @ x ) @ ( den @ y ) )
% 1.47/1.28 = ( ts @ ( num @ y ) @ ( den @ x ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(satz38,conjecture,
% 1.47/1.28 ( ( ts @ ( num @ y ) @ ( den @ x ) )
% 1.47/1.28 = ( ts @ ( num @ x ) @ ( den @ y ) ) ) ).
% 1.47/1.28 ------------------------
% 1.47/1.29 % (4520)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_4186 for (2999ds/275Mi)
% 1.47/1.29 % (4519)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_4186 for (2999ds/2Mi)
% 1.47/1.29 % (4520)First to succeed.
% 1.47/1.29 % (4519)Instruction limit reached!
% 1.47/1.29 % (4519)------------------------------
% 1.47/1.29 % (4519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (4519)Termination reason: Unknown
% 1.47/1.29 % (4519)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (4519)Memory used [KB]: 5373
% 1.47/1.29 % (4519)Time elapsed: 0.002 s
% 1.47/1.29 % (4519)Instructions burned: 2 (million)
% 1.47/1.29 % (4519)------------------------------
% 1.47/1.29 % (4519)------------------------------
% 1.47/1.29 % (4520)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_4186
% 1.47/1.29 % SZS output start Proof for DTF2THF_4186
% 1.47/1.29 thf(type_def_5, type, frac: $tType).
% 1.47/1.29 thf(type_def_6, type, nat: $tType).
% 1.47/1.29 thf(func_def_0, type, frac: $tType).
% 1.47/1.29 thf(func_def_1, type, x: frac).
% 1.47/1.29 thf(func_def_2, type, y: frac).
% 1.47/1.29 thf(func_def_3, type, nat: $tType).
% 1.47/1.29 thf(func_def_4, type, ts: nat > nat > nat).
% 1.47/1.29 thf(func_def_5, type, num: frac > nat).
% 1.47/1.29 thf(func_def_6, type, den: frac > nat).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f7,f6])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ((ts @ (num @ x) @ (den @ y)) = (ts @ (num @ y) @ (den @ x)))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f1])).
% 1.47/1.29 thf(f1,axiom,(
% 1.47/1.29 ((ts @ (num @ x) @ (den @ y)) = (ts @ (num @ y) @ (den @ x)))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.m84QCixrAj/DTF2THF_4186.p',e)).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 ((ts @ (num @ x) @ (den @ y)) != (ts @ (num @ y) @ (den @ x)))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,plain,(
% 1.47/1.29 ((ts @ (num @ x) @ (den @ y)) != (ts @ (num @ y) @ (den @ x)))),
% 1.47/1.29 inference(flattening,[status(thm)],[f3])).
% 1.47/1.29 thf(f3,negated_conjecture,(
% 1.47/1.29 ~((ts @ (num @ x) @ (den @ y)) = (ts @ (num @ y) @ (den @ x)))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f2])).
% 1.47/1.29 thf(f2,conjecture,(
% 1.47/1.29 ((ts @ (num @ x) @ (den @ y)) = (ts @ (num @ y) @ (den @ x)))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.m84QCixrAj/DTF2THF_4186.p',satz38)).
% 1.47/1.29 % SZS output end Proof for DTF2THF_4186
% 1.47/1.29 % (4520)------------------------------
% 1.47/1.29 % (4520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (4520)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (4520)Memory used [KB]: 5373
% 1.47/1.29 % (4520)Time elapsed: 0.002 s
% 1.47/1.29 % (4520)Instructions burned: 1 (million)
% 1.47/1.29 % (4520)------------------------------
% 1.47/1.29 % (4520)------------------------------
% 1.47/1.29 % (4514)Success in time 0.012 s
%------------------------------------------------------------------------------