%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM707^1 : 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 : 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 09:24:23 AM UTC 2026
% Result : Theorem 1.65s 1.32s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 19 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 114 ( 3 ~; 0 |; 0 &; 105 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 20 ( 8 ^; 12 !; 0 ?; 20 :)
% 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(f15,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f9,f14]) ).
thf(f14,plain,
! [X2: nat,X1: nat] :
( ( ts @ X1 @ ( suc @ X2 ) )
= ( pl @ ( ts @ X1 @ X2 ) @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: nat,X1: nat] :
( ( ( pl @ ( ts @ X1 @ X2 ) @ X1 )
= ( ts @ X1 @ ( suc @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: nat,X1: nat] :
( ( ^ [Y0: nat] :
( ( pl @ ( ts @ X1 @ Y0 ) @ X1 )
= ( ts @ X1 @ ( suc @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: nat] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( pl @ ( ts @ X1 @ Y0 ) @ X1 )
= ( ts @ X1 @ ( suc @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( pl @ ( ts @ Y0 @ Y1 ) @ Y0 )
= ( ts @ Y0 @ ( suc @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( pl @ ( ts @ Y0 @ Y1 ) @ Y0 )
= ( ts @ Y0 @ ( suc @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( pl @ ( ts @ Y0 @ Y1 ) @ Y0 )
= ( ts @ Y0 @ ( suc @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: nat,X1: nat] :
( ( pl @ ( ts @ X1 @ X0 ) @ X1 )
= ( ts @ X1 @ ( suc @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: nat,X0: nat] :
( ( ts @ X0 @ ( suc @ X1 ) )
= ( pl @ ( ts @ X0 @ X1 ) @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.mz2cnjR6DV/DTF2THF_824.p',satz28b) ).
thf(f9,plain,
( ( pl @ ( ts @ x @ y ) @ x )
!= ( ts @ x @ ( suc @ y ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( pl @ ( ts @ x @ y ) @ x )
!= ( ts @ x @ ( suc @ y ) ) ),
inference(flattening,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( pl @ ( ts @ x @ y ) @ x )
!= ( ts @ x @ ( suc @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( pl @ ( ts @ x @ y ) @ x )
= ( ts @ x @ ( suc @ y ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mz2cnjR6DV/DTF2THF_824.p',satz28f) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM707^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n009.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 11:11:40 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
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : NUM707^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.47 % Domain : Number Theory
% 0.20/0.47 % Problem : Landau theorem 28f
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : pl (ts x y) x = ts x (suc y)
% 0.20/0.47
% 0.20/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : satz28f [Lan30]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % : Without extensionality : Theorem
% 0.20/0.47 % 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
% 0.20/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 6 typ; 0 def)
% 0.20/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.47 % Number of connectives : 14 ( 0 ~; 0 |; 0 &; 14 @)
% 0.20/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 3 ( 2 avg)
% 0.20/0.47 % Number of types : 1 ( 1 usr)
% 0.20/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.20/0.47 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments :
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(nat_type,type,
% 0.20/0.47 nat: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(x,type,
% 0.20/0.47 x: nat ).
% 0.20/0.47
% 0.20/0.47 thf(y,type,
% 0.20/0.47 y: nat ).
% 0.20/0.47
% 0.20/0.47 thf(pl,type,
% 0.20/0.47 pl: nat > nat > nat ).
% 0.20/0.47
% 0.20/0.47 thf(ts,type,
% 0.20/0.47 ts: nat > nat > nat ).
% 0.20/0.47
% 0.20/0.47 thf(suc,type,
% 0.20/0.47 suc: nat > nat ).
% 0.20/0.47
% 0.20/0.47 thf(satz28b,axiom,
% 0.20/0.47 ! [Xx: nat,Xy: nat] :
% 0.20/0.47 ( ( ts @ Xx @ ( suc @ Xy ) )
% 0.20/0.47 = ( pl @ ( ts @ Xx @ Xy ) @ Xx ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz28f,conjecture,
% 0.20/0.47 ( ( pl @ ( ts @ x @ y ) @ x )
% 0.20/0.47 = ( ts @ x @ ( suc @ y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.47/1.29 ---- Embedded in THF ---
% 1.47/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.29 %%% Generated on Tue Feb 24 11:11:41 EST 2026
% 1.47/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.29 %%% Logic specification used:
% 1.47/1.29 %%% thf(spec, logic, $$dhol).
% 1.47/1.29
% 1.47/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.mz2cnjR6DV/DTF2DTF824.p
% See solution above
% 1.47/1.29 ------------------------
% 1.65/1.30 ---- Cleaned THF ---
% 1.65/1.31 thf(nat_type,type,
% 1.65/1.31 nat: $tType ).
% 1.65/1.31
% 1.65/1.31 thf(x,type,
% 1.65/1.31 x: nat ).
% 1.65/1.31
% 1.65/1.31 thf(y,type,
% 1.65/1.31 y: nat ).
% 1.65/1.31
% 1.65/1.31 thf(pl,type,
% 1.65/1.31 pl: nat > nat > nat ).
% 1.65/1.31
% 1.65/1.31 thf(ts,type,
% 1.65/1.31 ts: nat > nat > nat ).
% 1.65/1.31
% 1.65/1.31 thf(suc,type,
% 1.65/1.31 suc: nat > nat ).
% 1.65/1.31
% 1.65/1.31 thf(satz28b,axiom,
% 1.65/1.31 ! [Xx: nat,Xy: nat] :
% 1.65/1.31 ( ( ts @ Xx @ ( suc @ Xy ) )
% 1.65/1.31 = ( pl @ ( ts @ Xx @ Xy ) @ Xx ) ) ).
% 1.65/1.31
% 1.65/1.31 thf(satz28f,conjecture,
% 1.65/1.31 ( ( pl @ ( ts @ x @ y ) @ x )
% 1.65/1.31 = ( ts @ x @ ( suc @ y ) ) ) ).
% 1.65/1.31 ------------------------
% 1.65/1.32 % (1039)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_824 for (2999ds/4Mi)
% 1.65/1.32 % (1051)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_824 for (2999ds/2Mi)
% 1.65/1.32 % (1039)First to succeed.
% 1.65/1.32 % (1053)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_824 for (2999ds/18Mi)
% 1.65/1.32 % (1053)Also succeeded, but the first one will report.
% 1.65/1.32 % (1051)Refutation not found, incomplete strategy
% 1.65/1.32 % (1051)------------------------------
% 1.65/1.32 % (1051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (1051)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.32
% 1.65/1.32
% 1.65/1.32 % (1051)Memory used [KB]: 5500
% 1.65/1.32 % (1051)Time elapsed: 0.002 s
% 1.65/1.32 % (1051)Instructions burned: 1 (million)
% 1.65/1.32 % (1051)------------------------------
% 1.65/1.32 % (1051)------------------------------
% 1.65/1.32 % (1039)Refutation found. Thanks to Tanya!
% 1.65/1.32 % SZS status Theorem for DTF2THF_824
% 1.65/1.32 % SZS output start Proof for DTF2THF_824
% 1.65/1.32 thf(type_def_5, type, nat: $tType).
% 1.65/1.32 thf(func_def_0, type, nat: $tType).
% 1.65/1.32 thf(func_def_1, type, x: nat).
% 1.65/1.32 thf(func_def_2, type, y: nat).
% 1.65/1.32 thf(func_def_3, type, pl: nat > nat > nat).
% 1.65/1.32 thf(func_def_4, type, ts: nat > nat > nat).
% 1.65/1.32 thf(func_def_5, type, suc: nat > nat).
% 1.65/1.32 thf(f15,plain,(
% 1.65/1.32 $false),
% 1.65/1.32 inference(subsumption_resolution,[status(thm)],[f9,f14])).
% 1.65/1.32 thf(f14,plain,(
% 1.65/1.32 ( ! [X2 : nat,X1 : nat] : (((ts @ X1 @ (suc @ X2)) = (pl @ (ts @ X1 @ X2) @ X1))) )),
% 1.65/1.32 inference(equality_proxy_clausification,[status(thm)],[f13])).
% 1.65/1.32 thf(f13,plain,(
% 1.65/1.32 ( ! [X2 : nat,X1 : nat] : ((((pl @ (ts @ X1 @ X2) @ X1) = (ts @ X1 @ (suc @ X2))) = $true)) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.65/1.32 thf(f12,plain,(
% 1.65/1.32 ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: ((pl @ (ts @ X1 @ Y0) @ X1) = (ts @ X1 @ (suc @ Y0)))) @ X2) = $true)) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f11])).
% 1.65/1.32 thf(f11,plain,(
% 1.65/1.32 ( ! [X1 : nat] : (((!! @ nat @ (^[Y0 : nat]: ((pl @ (ts @ X1 @ Y0) @ X1) = (ts @ X1 @ (suc @ Y0))))) = $true)) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.65/1.32 thf(f10,plain,(
% 1.65/1.32 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((pl @ (ts @ Y0 @ Y1) @ Y0) = (ts @ Y0 @ (suc @ Y1)))))) @ X1) = $true)) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f8])).
% 1.65/1.32 thf(f8,plain,(
% 1.65/1.32 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((pl @ (ts @ Y0 @ Y1) @ Y0) = (ts @ Y0 @ (suc @ Y1))))))) = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f6])).
% 1.65/1.32 thf(f6,plain,(
% 1.65/1.32 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((pl @ (ts @ Y0 @ Y1) @ Y0) = (ts @ Y0 @ (suc @ Y1))))))) = $true)),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f5])).
% 1.65/1.32 thf(f5,plain,(
% 1.65/1.32 ! [X0 : nat,X1 : nat] : ((pl @ (ts @ X1 @ X0) @ X1) = (ts @ X1 @ (suc @ X0)))),
% 1.65/1.32 inference(rectify,[status(thm)],[f1])).
% 1.65/1.32 thf(f1,axiom,(
% 1.65/1.32 ! [X1 : nat,X0 : nat] : ((ts @ X0 @ (suc @ X1)) = (pl @ (ts @ X0 @ X1) @ X0))),
% 1.65/1.32 file('/export/starexec/sandbox/tmp/tmp.mz2cnjR6DV/DTF2THF_824.p',satz28b)).
% 1.65/1.32 thf(f9,plain,(
% 1.65/1.32 ((pl @ (ts @ x @ y) @ x) != (ts @ x @ (suc @ y)))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f7])).
% 1.65/1.32 thf(f7,plain,(
% 1.65/1.32 ((pl @ (ts @ x @ y) @ x) != (ts @ x @ (suc @ y)))),
% 1.65/1.32 inference(flattening,[status(thm)],[f3])).
% 1.65/1.32 thf(f3,negated_conjecture,(
% 1.65/1.32 ~((pl @ (ts @ x @ y) @ x) = (ts @ x @ (suc @ y)))),
% 1.65/1.32 inference(negated_conjecture,[status(cth)],[f2])).
% 1.65/1.32 thf(f2,conjecture,(
% 1.65/1.32 ((pl @ (ts @ x @ y) @ x) = (ts @ x @ (suc @ y)))),
% 1.65/1.32 file('/export/starexec/sandbox/tmp/tmp.mz2cnjR6DV/DTF2THF_824.p',satz28f)).
% 1.65/1.32 % SZS output end Proof for DTF2THF_824
% 1.65/1.32 % (1039)------------------------------
% 1.65/1.32 % (1039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (1039)Termination reason: Refutation
% 1.65/1.32
% 1.65/1.32 % (1039)Memory used [KB]: 5500
% 1.65/1.32 % (1039)Time elapsed: 0.002 s
% 1.65/1.32 % (1039)Instructions burned: 1 (million)
% 1.65/1.32 % (1039)------------------------------
% 1.65/1.32 % (1039)------------------------------
% 1.65/1.32 % (1036)Success in time 0.002 s
%------------------------------------------------------------------------------