%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM669^1 : 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 : n003.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 1.66s 1.31s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 10 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 53 ( 6 ~; 0 |; 0 &; 47 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 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,
more: nat > nat > $o ).
thf(func_def_3,type,
suc: nat > nat ).
thf(func_def_4,type,
pl: nat > nat > nat ).
thf(func_def_5,type,
n_1: nat ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$true != $true,
inference(superposition,[status(thm)],[f14,f15]) ).
thf(f15,plain,
! [X0: nat] :
( $true
= ( more @ ( suc @ X0 ) @ X0 ) ),
inference(superposition,[status(thm)],[f12,f13]) ).
thf(f13,plain,
! [X0: nat] :
( ( pl @ X0 @ n_1 )
= ( suc @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: nat] :
( ( pl @ X0 @ n_1 )
= ( suc @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.cEsxbgiKEr/DTF2THF_7214.p',satz4a) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( more @ ( pl @ X0 @ X1 ) @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( more @ ( pl @ X0 @ X1 ) @ X0 )
= $true ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: nat,X0: nat] :
( ( more @ ( pl @ X1 @ X0 ) @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: nat,X1: nat] : ( more @ ( pl @ X1 @ X0 ) @ X1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: nat,X0: nat] : ( more @ ( pl @ X0 @ X1 ) @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.cEsxbgiKEr/DTF2THF_7214.p',satz18) ).
thf(f14,plain,
( ( more @ ( suc @ x ) @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( more @ ( suc @ x ) @ x )
!= $true ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( more @ ( suc @ x ) @ x )
!= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( more @ ( suc @ x ) @ x ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( more @ ( suc @ x ) @ x ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
more @ ( suc @ x ) @ x,
file('/export/starexec/sandbox/tmp/tmp.cEsxbgiKEr/DTF2THF_7214.p',satz18b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM669^1 : 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 : n003.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 11:10:10 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
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : NUM669^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Number Theory
% 0.20/0.46 % Problem : Landau theorem 18b
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : more (suc x) x
% 0.20/0.46
% 0.20/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : satz18b [Lan30]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % : Without extensionality : Theorem
% 0.20/0.46 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 9 ( 3 unt; 6 typ; 0 def)
% 0.20/0.46 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.46 % Number of connectives : 10 ( 0 ~; 0 |; 0 &; 10 @)
% 0.20/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 7 ( 4 avg)
% 0.20/0.46 % Number of types : 2 ( 1 usr)
% 0.20/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(nat_type,type,
% 0.20/0.46 nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(x,type,
% 0.20/0.46 x: nat ).
% 0.20/0.46
% 0.20/0.46 thf(more,type,
% 0.20/0.46 more: nat > nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(suc,type,
% 0.20/0.46 suc: nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(pl,type,
% 0.20/0.46 pl: nat > nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(n_1,type,
% 0.20/0.46 n_1: nat ).
% 0.20/0.46
% 0.20/0.46 thf(satz18,axiom,
% 0.20/0.46 ! [Xx: nat,Xy: nat] : ( more @ ( pl @ Xx @ Xy ) @ Xx ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz4a,axiom,
% 0.20/0.46 ! [Xx: nat] :
% 0.20/0.46 ( ( pl @ Xx @ n_1 )
% 0.20/0.46 = ( suc @ Xx ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz18b,conjecture,
% 0.20/0.46 more @ ( suc @ x ) @ x ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.50/1.28 ---- Embedded in THF ---
% 1.50/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.28 %%% Generated on Tue Feb 24 11:10:11 EST 2026
% 1.50/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.28 %%% Logic specification used:
% 1.50/1.28 %%% thf(spec, logic, $$dhol).
% 1.50/1.28
% 1.50/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cEsxbgiKEr/DTF2DTF7214.p
% See solution above
% 1.50/1.28 ------------------------
% 1.50/1.29 ---- Cleaned THF ---
% 1.50/1.29 thf(nat_type,type,
% 1.50/1.29 nat: $tType ).
% 1.50/1.29
% 1.50/1.29 thf(x,type,
% 1.50/1.29 x: nat ).
% 1.50/1.29
% 1.50/1.29 thf(more,type,
% 1.50/1.29 more: nat > nat > $o ).
% 1.50/1.29
% 1.50/1.29 thf(suc,type,
% 1.50/1.29 suc: nat > nat ).
% 1.50/1.29
% 1.50/1.29 thf(pl,type,
% 1.50/1.29 pl: nat > nat > nat ).
% 1.50/1.29
% 1.50/1.29 thf(n_1,type,
% 1.50/1.29 n_1: nat ).
% 1.50/1.29
% 1.50/1.29 thf(satz18,axiom,
% 1.50/1.29 ! [Xx: nat,Xy: nat] : ( more @ ( pl @ Xx @ Xy ) @ Xx ) ).
% 1.50/1.29
% 1.50/1.29 thf(satz4a,axiom,
% 1.50/1.29 ! [Xx: nat] :
% 1.50/1.29 ( ( pl @ Xx @ n_1 )
% 1.50/1.29 = ( suc @ Xx ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(satz18b,conjecture,
% 1.50/1.29 more @ ( suc @ x ) @ x ).
% 1.50/1.29 ------------------------
% 1.66/1.31 % (7404)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7214 for (2999ds/183Mi)
% 1.66/1.31 % (7406)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_7214 for (2999ds/27Mi)
% 1.66/1.31 % (7404)First to succeed.
% 1.66/1.31 % (7406)Also succeeded, but the first one will report.
% 1.66/1.31 % (7404)Refutation found. Thanks to Tanya!
% 1.66/1.31 % SZS status Theorem for DTF2THF_7214
% 1.66/1.31 % SZS output start Proof for DTF2THF_7214
% 1.66/1.31 thf(type_def_5, type, nat: $tType).
% 1.66/1.31 thf(func_def_0, type, nat: $tType).
% 1.66/1.31 thf(func_def_1, type, x: nat).
% 1.66/1.31 thf(func_def_2, type, more: nat > nat > $o).
% 1.66/1.31 thf(func_def_3, type, suc: nat > nat).
% 1.66/1.31 thf(func_def_4, type, pl: nat > nat > nat).
% 1.66/1.31 thf(func_def_5, type, n_1: nat).
% 1.66/1.31 thf(f17,plain,(
% 1.66/1.31 $false),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.66/1.31 thf(f16,plain,(
% 1.66/1.31 ($true != $true)),
% 1.66/1.31 inference(superposition,[status(thm)],[f14,f15])).
% 1.66/1.31 thf(f15,plain,(
% 1.66/1.31 ( ! [X0 : nat] : (($true = (more @ (suc @ X0) @ X0))) )),
% 1.66/1.31 inference(superposition,[status(thm)],[f12,f13])).
% 1.66/1.31 thf(f13,plain,(
% 1.66/1.31 ( ! [X0 : nat] : (((pl @ X0 @ n_1) = (suc @ X0))) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f2])).
% 1.66/1.31 thf(f2,axiom,(
% 1.66/1.31 ! [X0 : nat] : ((pl @ X0 @ n_1) = (suc @ X0))),
% 1.66/1.31 file('/export/starexec/sandbox/tmp/tmp.cEsxbgiKEr/DTF2THF_7214.p',satz4a)).
% 1.66/1.31 thf(f12,plain,(
% 1.66/1.31 ( ! [X0 : nat,X1 : nat] : (((more @ (pl @ X0 @ X1) @ X0) = $true)) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.66/1.31 thf(f11,plain,(
% 1.66/1.31 ! [X0 : nat,X1 : nat] : ((more @ (pl @ X0 @ X1) @ X0) = $true)),
% 1.66/1.31 inference(rectify,[status(thm)],[f9])).
% 1.66/1.31 thf(f9,plain,(
% 1.66/1.31 ! [X1 : nat,X0 : nat] : ((more @ (pl @ X1 @ X0) @ X1) = $true)),
% 1.66/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.66/1.31 thf(f8,plain,(
% 1.66/1.31 ! [X0 : nat,X1 : nat] : (more @ (pl @ X1 @ X0) @ X1)),
% 1.66/1.31 inference(rectify,[status(thm)],[f1])).
% 1.66/1.31 thf(f1,axiom,(
% 1.66/1.31 ! [X1 : nat,X0 : nat] : (more @ (pl @ X0 @ X1) @ X0)),
% 1.66/1.31 file('/export/starexec/sandbox/tmp/tmp.cEsxbgiKEr/DTF2THF_7214.p',satz18)).
% 1.66/1.31 thf(f14,plain,(
% 1.66/1.31 ((more @ (suc @ x) @ x) != $true)),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.31 thf(f10,plain,(
% 1.66/1.31 ((more @ (suc @ x) @ x) != $true)),
% 1.66/1.31 inference(flattening,[status(thm)],[f7])).
% 1.66/1.31 thf(f7,plain,(
% 1.66/1.31 ~((more @ (suc @ x) @ x) = $true)),
% 1.66/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.66/1.31 thf(f6,plain,(
% 1.66/1.31 ~(more @ (suc @ x) @ x)),
% 1.66/1.31 inference(rectify,[status(thm)],[f4])).
% 1.66/1.31 thf(f4,negated_conjecture,(
% 1.66/1.31 ~(more @ (suc @ x) @ x)),
% 1.66/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.66/1.31 thf(f3,conjecture,(
% 1.66/1.31 (more @ (suc @ x) @ x)),
% 1.66/1.31 file('/export/starexec/sandbox/tmp/tmp.cEsxbgiKEr/DTF2THF_7214.p',satz18b)).
% 1.66/1.31 % SZS output end Proof for DTF2THF_7214
% 1.66/1.31 % (7404)------------------------------
% 1.66/1.31 % (7404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (7404)Termination reason: Refutation
% 1.66/1.31
% 1.66/1.31 % (7404)Memory used [KB]: 5500
% 1.66/1.31 % (7404)Time elapsed: 0.003 s
% 1.66/1.31 % (7404)Instructions burned: 1 (million)
% 1.66/1.31 % (7404)------------------------------
% 1.66/1.31 % (7404)------------------------------
% 1.66/1.31 % (7403)Success in time 0.013 s
%------------------------------------------------------------------------------