%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM709^1 : 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 : n009.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 09:24:24 AM UTC 2026
% Result : Theorem 1.63s 1.32s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 66 ( 4 ~; 0 |; 0 &; 62 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 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(func_def_4,type,
ts: nat > nat > nat ).
thf(func_def_5,type,
suc: nat > nat ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ts @ ( suc @ x ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(superposition,[status(thm)],[f9,f8]) ).
thf(f8,plain,
! [X0: nat,X1: nat] :
( ( ts @ ( suc @ X0 ) @ X1 )
= ( pl @ ( ts @ X0 @ X1 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: nat,X1: nat] :
( ( ts @ ( suc @ X0 ) @ X1 )
= ( pl @ ( ts @ X0 @ X1 ) @ X1 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
! [X1: nat,X0: nat] :
( ( ts @ ( suc @ X1 ) @ X0 )
= ( pl @ ( ts @ X1 @ X0 ) @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: nat,X0: nat] :
( ( ts @ ( suc @ X0 ) @ X1 )
= ( pl @ ( ts @ X0 @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.JD9ToxVk6A/DTF2THF_878.p',satz28d) ).
thf(f9,plain,
( ( pl @ ( ts @ x @ y ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( pl @ ( ts @ x @ y ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(flattening,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( pl @ ( ts @ x @ y ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( pl @ ( ts @ x @ y ) @ y )
= ( ts @ ( suc @ x ) @ y ) ),
file('/export/starexec/sandbox2/tmp/tmp.JD9ToxVk6A/DTF2THF_878.p',satz28h) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM709^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.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 11:11:40 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
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : NUM709^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.47 % Domain : Number Theory
% 0.19/0.47 % Problem : Landau theorem 28h
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English : pl (ts x y) y = ts (suc x) y
% 0.19/0.47
% 0.19/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : satz28h [Lan30]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % : Without extensionality : Theorem
% 0.19/0.47 % Rating : 0.00 v7.1.0, 0.12 v7.0.0, 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
% 0.19/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 6 typ; 0 def)
% 0.19/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.47 % Number of connectives : 14 ( 0 ~; 0 |; 0 &; 14 @)
% 0.19/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 3 ( 2 avg)
% 0.19/0.47 % Number of types : 1 ( 1 usr)
% 0.19/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments :
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(nat_type,type,
% 0.19/0.47 nat: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(x,type,
% 0.19/0.47 x: nat ).
% 0.19/0.47
% 0.19/0.47 thf(y,type,
% 0.19/0.47 y: nat ).
% 0.19/0.47
% 0.19/0.47 thf(pl,type,
% 0.19/0.47 pl: nat > nat > nat ).
% 0.19/0.47
% 0.19/0.47 thf(ts,type,
% 0.19/0.47 ts: nat > nat > nat ).
% 0.19/0.47
% 0.19/0.47 thf(suc,type,
% 0.19/0.47 suc: nat > nat ).
% 0.19/0.47
% 0.19/0.47 thf(satz28d,axiom,
% 0.19/0.47 ! [Xx: nat,Xy: nat] :
% 0.19/0.47 ( ( ts @ ( suc @ Xx ) @ Xy )
% 0.19/0.47 = ( pl @ ( ts @ Xx @ Xy ) @ Xy ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(satz28h,conjecture,
% 0.19/0.47 ( ( pl @ ( ts @ x @ y ) @ y )
% 0.19/0.47 = ( ts @ ( suc @ x ) @ y ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.45/1.29 ---- Embedded in THF ---
% 1.45/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.30 %%% Generated on Tue Feb 24 11:11:41 EST 2026
% 1.45/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.30 %%% Logic specification used:
% 1.45/1.30 %%% thf(spec, logic, $$dhol).
% 1.45/1.30
% 1.45/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.JD9ToxVk6A/DTF2DTF878.p
% See solution above
% 1.45/1.30 ------------------------
% 1.63/1.30 ---- Cleaned THF ---
% 1.63/1.31 thf(nat_type,type,
% 1.63/1.31 nat: $tType ).
% 1.63/1.31
% 1.63/1.31 thf(x,type,
% 1.63/1.31 x: nat ).
% 1.63/1.31
% 1.63/1.31 thf(y,type,
% 1.63/1.31 y: nat ).
% 1.63/1.31
% 1.63/1.31 thf(pl,type,
% 1.63/1.31 pl: nat > nat > nat ).
% 1.63/1.31
% 1.63/1.31 thf(ts,type,
% 1.63/1.31 ts: nat > nat > nat ).
% 1.63/1.31
% 1.63/1.31 thf(suc,type,
% 1.63/1.31 suc: nat > nat ).
% 1.63/1.31
% 1.63/1.31 thf(satz28d,axiom,
% 1.63/1.31 ! [Xx: nat,Xy: nat] :
% 1.63/1.31 ( ( ts @ ( suc @ Xx ) @ Xy )
% 1.63/1.31 = ( pl @ ( ts @ Xx @ Xy ) @ Xy ) ) ).
% 1.63/1.31
% 1.63/1.31 thf(satz28h,conjecture,
% 1.63/1.31 ( ( pl @ ( ts @ x @ y ) @ y )
% 1.63/1.31 = ( ts @ ( suc @ x ) @ y ) ) ).
% 1.63/1.31 ------------------------
% 1.63/1.32 % (1072)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_878 for (2999ds/27Mi)
% 1.63/1.32 % (1072)First to succeed.
% 1.63/1.32 % (1072)Refutation found. Thanks to Tanya!
% 1.63/1.32 % SZS status Theorem for DTF2THF_878
% 1.63/1.32 % SZS output start Proof for DTF2THF_878
% 1.63/1.32 thf(type_def_5, type, nat: $tType).
% 1.63/1.32 thf(func_def_0, type, nat: $tType).
% 1.63/1.32 thf(func_def_1, type, x: nat).
% 1.63/1.32 thf(func_def_2, type, y: nat).
% 1.63/1.32 thf(func_def_3, type, pl: nat > nat > nat).
% 1.63/1.32 thf(func_def_4, type, ts: nat > nat > nat).
% 1.63/1.32 thf(func_def_5, type, suc: nat > nat).
% 1.63/1.32 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.32 thf(f11,plain,(
% 1.63/1.32 $false),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 1.63/1.32 thf(f10,plain,(
% 1.63/1.32 ((ts @ (suc @ x) @ y) != (ts @ (suc @ x) @ y))),
% 1.63/1.32 inference(superposition,[status(thm)],[f9,f8])).
% 1.63/1.32 thf(f8,plain,(
% 1.63/1.32 ( ! [X0 : nat,X1 : nat] : (((ts @ (suc @ X0) @ X1) = (pl @ (ts @ X0 @ X1) @ X1))) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.32 thf(f7,plain,(
% 1.63/1.32 ! [X0 : nat,X1 : nat] : ((ts @ (suc @ X0) @ X1) = (pl @ (ts @ X0 @ X1) @ X1))),
% 1.63/1.32 inference(rectify,[status(thm)],[f5])).
% 1.63/1.32 thf(f5,plain,(
% 1.63/1.32 ! [X1 : nat,X0 : nat] : ((ts @ (suc @ X1) @ X0) = (pl @ (ts @ X1 @ X0) @ X0))),
% 1.63/1.32 inference(rectify,[status(thm)],[f1])).
% 1.63/1.32 thf(f1,axiom,(
% 1.63/1.32 ! [X1 : nat,X0 : nat] : ((ts @ (suc @ X0) @ X1) = (pl @ (ts @ X0 @ X1) @ X1))),
% 1.63/1.32 file('/export/starexec/sandbox2/tmp/tmp.JD9ToxVk6A/DTF2THF_878.p',satz28d)).
% 1.63/1.32 thf(f9,plain,(
% 1.63/1.32 ((pl @ (ts @ x @ y) @ y) != (ts @ (suc @ x) @ y))),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f6])).
% 1.63/1.32 thf(f6,plain,(
% 1.63/1.32 ((pl @ (ts @ x @ y) @ y) != (ts @ (suc @ x) @ y))),
% 1.63/1.32 inference(flattening,[status(thm)],[f3])).
% 1.63/1.32 thf(f3,negated_conjecture,(
% 1.63/1.32 ~((pl @ (ts @ x @ y) @ y) = (ts @ (suc @ x) @ y))),
% 1.63/1.32 inference(negated_conjecture,[status(cth)],[f2])).
% 1.63/1.32 thf(f2,conjecture,(
% 1.63/1.32 ((pl @ (ts @ x @ y) @ y) = (ts @ (suc @ x) @ y))),
% 1.63/1.32 file('/export/starexec/sandbox2/tmp/tmp.JD9ToxVk6A/DTF2THF_878.p',satz28h)).
% 1.63/1.32 % SZS output end Proof for DTF2THF_878
% 1.63/1.32 % (1072)------------------------------
% 1.63/1.32 % (1072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (1072)Termination reason: Refutation
% 1.63/1.32
% 1.63/1.32 % (1072)Memory used [KB]: 5500
% 1.63/1.32 % (1072)Time elapsed: 0.003 s
% 1.63/1.32 % (1072)Instructions burned: 2 (million)
% 1.63/1.32 % (1072)------------------------------
% 1.63/1.32 % (1072)------------------------------
% 1.63/1.32 % (1062)Success in time 0.005 s
%------------------------------------------------------------------------------