%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM668^1 : 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 : n002.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 09:24:11 AM UTC 2026
% Result : Theorem 1.50s 1.27s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 5 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 5 ( 4 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 23 ( 7 ~; 0 |; 0 &; 16 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 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,
pl: nat > nat > nat ).
thf(f6,plain,
$false,
inference(equality_resolution,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
! [X0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ X0 ) ),
inference(flattening,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ! [X0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ! [X0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.AGoEoxRueK/DTF2THF_4547.p',satz18) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM668^1 : 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
% 0.16/0.33 % Computer : n002.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 11:10:33 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : NUM668^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.45 % Domain : Number Theory
% 0.30/0.45 % Problem : Landau theorem 18
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English : ~(forall x_0:nat.~(pl x y = pl x x_0))
% 0.30/0.45
% 0.30/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : satz18 [Lan30]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % : Without extensionality : Theorem
% 0.30/0.45 % 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
% 0.30/0.45 % Syntax : Number of formulae : 5 ( 1 unt; 4 typ; 0 def)
% 0.30/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.45 % Number of connectives : 6 ( 2 ~; 0 |; 0 &; 4 @)
% 0.30/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 4 ( 4 avg)
% 0.30/0.45 % Number of types : 1 ( 1 usr)
% 0.30/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.30/0.45 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments :
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(nat_type,type,
% 0.30/0.45 nat: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(x,type,
% 0.30/0.45 x: nat ).
% 0.30/0.45
% 0.30/0.45 thf(y,type,
% 0.30/0.45 y: nat ).
% 0.30/0.45
% 0.30/0.45 thf(pl,type,
% 0.30/0.45 pl: nat > nat > nat ).
% 0.30/0.45
% 0.30/0.45 thf(satz18,conjecture,
% 0.30/0.45 ~ ! [Xx_0: nat] :
% 0.30/0.45 ( ( pl @ x @ y )
% 0.30/0.45 != ( pl @ x @ Xx_0 ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.50/1.24 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 11:10:34 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.AGoEoxRueK/DTF2DTF4547.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.25 ---- Cleaned THF ---
% 1.50/1.25 thf(nat_type,type,
% 1.50/1.25 nat: $tType ).
% 1.50/1.25
% 1.50/1.25 thf(x,type,
% 1.50/1.25 x: nat ).
% 1.50/1.25
% 1.50/1.25 thf(y,type,
% 1.50/1.25 y: nat ).
% 1.50/1.25
% 1.50/1.25 thf(pl,type,
% 1.50/1.25 pl: nat > nat > nat ).
% 1.50/1.25
% 1.50/1.25 thf(satz18,conjecture,
% 1.50/1.25 ~ ! [Xx_0: nat] :
% 1.50/1.25 ( ( pl @ x @ y )
% 1.50/1.25 != ( pl @ x @ Xx_0 ) ) ).
% 1.50/1.25 ------------------------
% 1.50/1.27 % (4840)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_4547 for (2999ds/4Mi)
% 1.50/1.27 % (4840)First to succeed.
% 1.50/1.27 % (4839)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4547 for (2999ds/183Mi)
% 1.50/1.27 % (4839)Also succeeded, but the first one will report.
% 1.50/1.27 % (4840)Refutation found. Thanks to Tanya!
% 1.50/1.27 % SZS status Theorem for DTF2THF_4547
% 1.50/1.27 % SZS output start Proof for DTF2THF_4547
% 1.50/1.27 thf(type_def_5, type, nat: $tType).
% 1.50/1.27 thf(func_def_0, type, nat: $tType).
% 1.50/1.27 thf(func_def_1, type, x: nat).
% 1.50/1.27 thf(func_def_2, type, y: nat).
% 1.50/1.27 thf(func_def_3, type, pl: nat > nat > nat).
% 1.50/1.27 thf(f6,plain,(
% 1.50/1.27 $false),
% 1.50/1.27 inference(equality_resolution,[status(thm)],[f5])).
% 1.50/1.27 thf(f5,plain,(
% 1.50/1.27 ( ! [X0 : nat] : (((pl @ x @ y) != (pl @ x @ X0))) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f4])).
% 1.50/1.27 thf(f4,plain,(
% 1.50/1.27 ! [X0 : nat] : ((pl @ x @ y) != (pl @ x @ X0))),
% 1.50/1.27 inference(flattening,[status(thm)],[f2])).
% 1.50/1.27 thf(f2,negated_conjecture,(
% 1.50/1.27 ~~! [X0 : nat] : ((pl @ x @ y) != (pl @ x @ X0))),
% 1.50/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.27 thf(f1,conjecture,(
% 1.50/1.27 ~! [X0 : nat] : ((pl @ x @ y) != (pl @ x @ X0))),
% 1.50/1.27 file('/export/starexec/sandbox/tmp/tmp.AGoEoxRueK/DTF2THF_4547.p',satz18)).
% 1.50/1.27 % SZS output end Proof for DTF2THF_4547
% 1.50/1.27 % (4840)------------------------------
% 1.50/1.27 % (4840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (4840)Termination reason: Refutation
% 1.50/1.27
% 1.50/1.27 % (4840)Memory used [KB]: 5373
% 1.50/1.27 % (4840)Time elapsed: 0.002 s
% 1.50/1.27 % (4840)------------------------------
% 1.50/1.27 % (4840)------------------------------
% 1.50/1.27 % (4838)Success in time 0.011 s
%------------------------------------------------------------------------------