%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM641^1 : 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 : n005.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 09:24:02 AM UTC 2026
% Result : Theorem 1.56s 1.32s
% Output : Refutation 1.56s
% 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 : 21 ( 3 ~; 0 |; 0 &; 18 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 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,
suc: nat > nat ).
thf(func_def_3,type,
pl: nat > nat > nat ).
thf(func_def_4,type,
n_1: nat ).
thf(f8,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f6,f7]) ).
thf(f7,plain,
! [X0: nat] :
( ( pl @ n_1 @ X0 )
= ( suc @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: nat] :
( ( pl @ n_1 @ X0 )
= ( suc @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.5w16epzOjj/DTF2THF_7043.p',satz4c) ).
thf(f6,plain,
( ( suc @ x )
!= ( pl @ n_1 @ x ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( suc @ x )
!= ( pl @ n_1 @ x ) ),
inference(flattening,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( suc @ x )
!= ( pl @ n_1 @ x ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( suc @ x )
= ( pl @ n_1 @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.5w16epzOjj/DTF2THF_7043.p',satz4g) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM641^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n005.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 11:08:44 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : NUM641^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Number Theory
% 0.16/0.39 % Problem : Landau theorem 4g
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : suc x = pl n_1 x
% 0.16/0.39
% 0.16/0.39 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.16/0.39 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.16/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : satz4g [Lan30]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % : Without extensionality : Theorem
% 0.16/0.39 % 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
% 0.16/0.39 % Syntax : Number of formulae : 7 ( 2 unt; 5 typ; 0 def)
% 0.16/0.39 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 1 ( 1 avg)
% 0.16/0.39 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 6 @)
% 0.16/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 2 ( 2 avg)
% 0.16/0.39 % Number of types : 1 ( 1 usr)
% 0.16/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments :
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(nat_type,type,
% 0.16/0.39 nat: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(x,type,
% 0.16/0.39 x: nat ).
% 0.16/0.39
% 0.16/0.39 thf(suc,type,
% 0.16/0.39 suc: nat > nat ).
% 0.16/0.39
% 0.16/0.39 thf(pl,type,
% 0.16/0.39 pl: nat > nat > nat ).
% 0.16/0.39
% 0.16/0.39 thf(n_1,type,
% 0.16/0.39 n_1: nat ).
% 0.16/0.39
% 0.16/0.39 thf(satz4c,axiom,
% 0.16/0.39 ! [Xx: nat] :
% 0.16/0.39 ( ( pl @ n_1 @ Xx )
% 0.16/0.39 = ( suc @ Xx ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(satz4g,conjecture,
% 0.16/0.39 ( ( suc @ x )
% 0.16/0.39 = ( pl @ n_1 @ x ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.36/1.29 ---- Embedded in THF ---
% 1.36/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.29 %%% Generated on Tue Feb 24 11:08:45 EST 2026
% 1.36/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.29 %%% Logic specification used:
% 1.36/1.29 %%% thf(spec, logic, $$dhol).
% 1.36/1.29
% 1.36/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5w16epzOjj/DTF2DTF7043.p
% See solution above
% 1.36/1.29 ------------------------
% 1.56/1.30 ---- Cleaned THF ---
% 1.56/1.30 thf(nat_type,type,
% 1.56/1.30 nat: $tType ).
% 1.56/1.30
% 1.56/1.30 thf(x,type,
% 1.56/1.30 x: nat ).
% 1.56/1.30
% 1.56/1.30 thf(suc,type,
% 1.56/1.30 suc: nat > nat ).
% 1.56/1.30
% 1.56/1.30 thf(pl,type,
% 1.56/1.30 pl: nat > nat > nat ).
% 1.56/1.30
% 1.56/1.30 thf(n_1,type,
% 1.56/1.30 n_1: nat ).
% 1.56/1.30
% 1.56/1.30 thf(satz4c,axiom,
% 1.56/1.30 ! [Xx: nat] :
% 1.56/1.30 ( ( pl @ n_1 @ Xx )
% 1.56/1.30 = ( suc @ Xx ) ) ).
% 1.56/1.30
% 1.56/1.30 thf(satz4g,conjecture,
% 1.56/1.30 ( ( suc @ x )
% 1.56/1.30 = ( pl @ n_1 @ x ) ) ).
% 1.56/1.30 ------------------------
% 1.56/1.32 % (7146)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_7043 for (3000ds/275Mi)
% 1.56/1.32 % (7147)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7043 for (3000ds/18Mi)
% 1.56/1.32 % (7143)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_7043 for (3000ds/27Mi)
% 1.56/1.32 % (7144)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7043 for (3000ds/2Mi)
% 1.56/1.32 % (7141)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7043 for (3000ds/183Mi)
% 1.56/1.32 % (7142)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_7043 for (3000ds/4Mi)
% 1.56/1.32 % (7145)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_7043 for (3000ds/2Mi)
% 1.56/1.32 % (7146)First to succeed.
% 1.56/1.32 % (7145)Instruction limit reached!
% 1.56/1.32 % (7145)------------------------------
% 1.56/1.32 % (7145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (7145)Termination reason: Unknown
% 1.56/1.32 % (7145)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (7145)Memory used [KB]: 5500
% 1.56/1.32 % (7145)Time elapsed: 0.003 s
% 1.56/1.32 % (7145)Instructions burned: 2 (million)
% 1.56/1.32 % (7145)------------------------------
% 1.56/1.32 % (7145)------------------------------
% 1.56/1.32 % (7141)Also succeeded, but the first one will report.
% 1.56/1.32 % (7144)Also succeeded, but the first one will report.
% 1.56/1.32 % (7146)Refutation found. Thanks to Tanya!
% 1.56/1.32 % SZS status Theorem for DTF2THF_7043
% 1.56/1.32 % SZS output start Proof for DTF2THF_7043
% 1.56/1.32 thf(type_def_5, type, nat: $tType).
% 1.56/1.32 thf(func_def_0, type, nat: $tType).
% 1.56/1.32 thf(func_def_1, type, x: nat).
% 1.56/1.32 thf(func_def_2, type, suc: nat > nat).
% 1.56/1.32 thf(func_def_3, type, pl: nat > nat > nat).
% 1.56/1.32 thf(func_def_4, type, n_1: nat).
% 1.56/1.32 thf(f8,plain,(
% 1.56/1.32 $false),
% 1.56/1.32 inference(subsumption_resolution,[status(thm)],[f6,f7])).
% 1.56/1.32 thf(f7,plain,(
% 1.56/1.32 ( ! [X0 : nat] : (((pl @ n_1 @ X0) = (suc @ X0))) )),
% 1.56/1.32 inference(cnf_transformation,[status(thm)],[f1])).
% 1.56/1.32 thf(f1,axiom,(
% 1.56/1.32 ! [X0 : nat] : ((pl @ n_1 @ X0) = (suc @ X0))),
% 1.56/1.32 file('/export/starexec/sandbox/tmp/tmp.5w16epzOjj/DTF2THF_7043.p',satz4c)).
% 1.56/1.32 thf(f6,plain,(
% 1.56/1.32 ((suc @ x) != (pl @ n_1 @ x))),
% 1.56/1.32 inference(cnf_transformation,[status(thm)],[f5])).
% 1.56/1.32 thf(f5,plain,(
% 1.56/1.32 ((suc @ x) != (pl @ n_1 @ x))),
% 1.56/1.32 inference(flattening,[status(thm)],[f3])).
% 1.56/1.32 thf(f3,negated_conjecture,(
% 1.56/1.32 ~((suc @ x) = (pl @ n_1 @ x))),
% 1.56/1.32 inference(negated_conjecture,[status(cth)],[f2])).
% 1.56/1.32 thf(f2,conjecture,(
% 1.56/1.32 ((suc @ x) = (pl @ n_1 @ x))),
% 1.56/1.32 file('/export/starexec/sandbox/tmp/tmp.5w16epzOjj/DTF2THF_7043.p',satz4g)).
% 1.56/1.32 % SZS output end Proof for DTF2THF_7043
% 1.56/1.32 % (7146)------------------------------
% 1.56/1.32 % (7146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (7146)Termination reason: Refutation
% 1.56/1.32
% 1.56/1.32 % (7146)Memory used [KB]: 5373
% 1.56/1.32 % (7146)Time elapsed: 0.003 s
% 1.56/1.32 % (7146)Instructions burned: 1 (million)
% 1.56/1.32 % (7146)------------------------------
% 1.56/1.32 % (7146)------------------------------
% 1.56/1.32 % (7140)Success in time 0.017 s
%------------------------------------------------------------------------------