%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM695^1 : 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 : n014.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 09:24:19 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% 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 : 30 ( 10 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 52 ( 6 ~; 0 |; 0 &; 46 @)
% ( 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 : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 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,
n_1: nat ).
thf(func_def_6,type,
pl: nat > nat > nat ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
sK0: nat > nat ).
thf(f35,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
$true != $true,
inference(superposition,[status(thm)],[f24,f32]) ).
thf(f32,plain,
! [X0: nat] :
( ( more @ ( suc @ X0 ) @ n_1 )
= $true ),
inference(superposition,[status(thm)],[f25,f28]) ).
thf(f28,plain,
! [X0: nat] :
( ( pl @ n_1 @ X0 )
= ( suc @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat] :
( ( pl @ n_1 @ X0 )
= ( suc @ X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: nat] :
( ( suc @ X1 )
= ( pl @ n_1 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qch2cDbeou/DTF2THF_16930.p',satz4g) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( $true
= ( more @ ( pl @ X0 @ X1 ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( $true
= ( more @ ( pl @ X0 @ X1 ) @ X0 ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat] : ( more @ ( pl @ X0 @ X1 ) @ X0 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: nat,X3: nat] : ( more @ ( pl @ X1 @ X3 ) @ X1 ),
file('/export/starexec/sandbox2/tmp/tmp.Qch2cDbeou/DTF2THF_16930.p',satz18) ).
thf(f24,plain,
( ( more @ ( suc @ x ) @ n_1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( more @ ( suc @ x ) @ n_1 )
!= $true ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( more @ ( suc @ x ) @ n_1 )
!= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( more @ ( suc @ x ) @ n_1 ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( more @ ( suc @ x ) @ n_1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
more @ ( suc @ x ) @ n_1,
file('/export/starexec/sandbox2/tmp/tmp.Qch2cDbeou/DTF2THF_16930.p',satz24b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM695^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n014.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 11:11:27 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
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : NUM695^1 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.46 % Domain : Number Theory
% 0.21/0.46 % Problem : Landau theorem 24b
% 0.21/0.46 % Version : Especial.
% 0.21/0.46 % English : more (suc x) n_1
% 0.21/0.46
% 0.21/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.46 % Source : [Bro09]
% 0.21/0.46 % Names : satz24b [Lan30]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % : Without extensionality : Theorem
% 0.21/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v6.1.0, 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
% 0.21/0.46 % Syntax : Number of formulae : 12 ( 4 unt; 6 typ; 0 def)
% 0.21/0.46 % Number of atoms : 6 ( 4 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.21/0.46 % Number of connectives : 20 ( 6 ~; 0 |; 0 &; 12 @)
% 0.21/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 7 ( 5 avg)
% 0.21/0.46 % Number of types : 2 ( 1 usr)
% 0.21/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.21/0.46 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.21/0.46 % SPC : TH0_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments :
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(nat_type,type,
% 0.21/0.46 nat: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(x,type,
% 0.21/0.46 x: nat ).
% 0.21/0.46
% 0.21/0.46 thf(more,type,
% 0.21/0.46 more: nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(suc,type,
% 0.21/0.46 suc: nat > nat ).
% 0.21/0.46
% 0.21/0.46 thf(n_1,type,
% 0.21/0.46 n_1: nat ).
% 0.21/0.46
% 0.21/0.46 thf(et,axiom,
% 0.21/0.46 ! [Xa: $o] :
% 0.21/0.46 ( ~ ~ Xa
% 0.21/0.46 => Xa ) ).
% 0.21/0.46
% 0.21/0.46 thf(satz3,axiom,
% 0.21/0.46 ! [Xx: nat] :
% 0.21/0.46 ( ( Xx != n_1 )
% 0.21/0.46 => ~ ! [Xx_0: nat] :
% 0.21/0.46 ( Xx
% 0.21/0.46 != ( suc @ Xx_0 ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(ax3,axiom,
% 0.21/0.46 ! [Xx: nat] :
% 0.21/0.46 ( ( suc @ Xx )
% 0.21/0.46 != n_1 ) ).
% 0.21/0.46
% 0.21/0.46 thf(pl,type,
% 0.21/0.46 pl: nat > nat > nat ).
% 0.21/0.46
% 0.21/0.46 thf(satz18,axiom,
% 0.21/0.46 ! [Xx: nat,Xy: nat] : ( more @ ( pl @ Xx @ Xy ) @ Xx ) ).
% 0.21/0.46
% 0.21/0.46 thf(satz4g,axiom,
% 0.21/0.46 ! [Xx: nat] :
% 0.21/0.46 ( ( suc @ Xx )
% 0.21/0.46 = ( pl @ n_1 @ Xx ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(satz24b,conjecture,
% 0.21/0.46 more @ ( suc @ x ) @ n_1 ).
% 0.21/0.46
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 11:11:28 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Qch2cDbeou/DTF2DTF16930.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(nat_type,type,
% 1.48/1.26 nat: $tType ).
% 1.48/1.26
% 1.48/1.26 thf(x,type,
% 1.48/1.26 x: nat ).
% 1.48/1.26
% 1.48/1.26 thf(more,type,
% 1.48/1.26 more: nat > nat > $o ).
% 1.48/1.26
% 1.48/1.26 thf(suc,type,
% 1.48/1.26 suc: nat > nat ).
% 1.48/1.26
% 1.48/1.26 thf(n_1,type,
% 1.48/1.26 n_1: nat ).
% 1.48/1.26
% 1.48/1.26 thf(et,axiom,
% 1.48/1.26 ! [Xa: $o] :
% 1.48/1.26 ( ~ ~ Xa
% 1.48/1.26 => Xa ) ).
% 1.48/1.26
% 1.48/1.26 thf(satz3,axiom,
% 1.48/1.26 ! [Xx: nat] :
% 1.48/1.26 ( ( Xx != n_1 )
% 1.48/1.26 => ~ ! [Xx_0: nat] :
% 1.48/1.26 ( Xx
% 1.48/1.26 != ( suc @ Xx_0 ) ) ) ).
% 1.48/1.26
% 1.48/1.26 thf(ax3,axiom,
% 1.48/1.26 ! [Xx: nat] :
% 1.48/1.26 ( ( suc @ Xx )
% 1.48/1.26 != n_1 ) ).
% 1.48/1.26
% 1.48/1.26 thf(pl,type,
% 1.48/1.26 pl: nat > nat > nat ).
% 1.48/1.26
% 1.48/1.26 thf(satz18,axiom,
% 1.48/1.26 ! [Xx: nat,Xy: nat] : ( more @ ( pl @ Xx @ Xy ) @ Xx ) ).
% 1.48/1.26
% 1.48/1.26 thf(satz4g,axiom,
% 1.48/1.26 ! [Xx: nat] :
% 1.48/1.26 ( ( suc @ Xx )
% 1.48/1.26 = ( pl @ n_1 @ Xx ) ) ).
% 1.48/1.26
% 1.48/1.26 thf(satz24b,conjecture,
% 1.48/1.26 more @ ( suc @ x ) @ n_1 ).
% 1.48/1.26 ------------------------
% 1.48/1.27 % (17041)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_16930 for (2999ds/275Mi)
% 1.48/1.27 % (17038)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_16930 for (2999ds/27Mi)
% 1.48/1.28 % (17041)Refutation not found, incomplete strategy
% 1.48/1.28 % (17041)------------------------------
% 1.48/1.28 % (17041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (17041)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.28
% 1.48/1.28
% 1.48/1.28 % (17041)Memory used [KB]: 5500
% 1.48/1.28 % (17041)Time elapsed: 0.002 s
% 1.48/1.28 % (17041)Instructions burned: 2 (million)
% 1.48/1.28 % (17041)------------------------------
% 1.48/1.28 % (17041)------------------------------
% 1.48/1.28 % (17038)First to succeed.
% 1.48/1.28 % (17038)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_16930
% 1.48/1.28 % SZS output start Proof for DTF2THF_16930
% 1.48/1.28 thf(type_def_5, type, nat: $tType).
% 1.48/1.28 thf(func_def_0, type, nat: $tType).
% 1.48/1.28 thf(func_def_1, type, x: nat).
% 1.48/1.28 thf(func_def_2, type, more: nat > nat > $o).
% 1.48/1.28 thf(func_def_3, type, suc: nat > nat).
% 1.48/1.28 thf(func_def_4, type, n_1: nat).
% 1.48/1.28 thf(func_def_6, type, pl: nat > nat > nat).
% 1.48/1.28 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.48/1.28 thf(func_def_10, type, sK0: nat > nat).
% 1.48/1.28 thf(f35,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.48/1.28 thf(f34,plain,(
% 1.48/1.28 ($true != $true)),
% 1.48/1.28 inference(superposition,[status(thm)],[f24,f32])).
% 1.48/1.28 thf(f32,plain,(
% 1.48/1.28 ( ! [X0 : nat] : (((more @ (suc @ X0) @ n_1) = $true)) )),
% 1.48/1.28 inference(superposition,[status(thm)],[f25,f28])).
% 1.48/1.28 thf(f28,plain,(
% 1.48/1.28 ( ! [X0 : nat] : (((pl @ n_1 @ X0) = (suc @ X0))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f17])).
% 1.48/1.28 thf(f17,plain,(
% 1.48/1.28 ! [X0 : nat] : ((pl @ n_1 @ X0) = (suc @ X0))),
% 1.48/1.28 inference(rectify,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,axiom,(
% 1.48/1.28 ! [X1 : nat] : ((suc @ X1) = (pl @ n_1 @ X1))),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.Qch2cDbeou/DTF2THF_16930.p',satz4g)).
% 1.48/1.28 thf(f25,plain,(
% 1.48/1.28 ( ! [X0 : nat,X1 : nat] : (($true = (more @ (pl @ X0 @ X1) @ X0))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 ! [X0 : nat,X1 : nat] : ($true = (more @ (pl @ X0 @ X1) @ X0))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f11])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 ! [X0 : nat,X1 : nat] : (more @ (pl @ X0 @ X1) @ X0)),
% 1.48/1.28 inference(rectify,[status(thm)],[f4])).
% 1.48/1.28 thf(f4,axiom,(
% 1.48/1.28 ! [X1 : nat,X3 : nat] : (more @ (pl @ X1 @ X3) @ X1)),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.Qch2cDbeou/DTF2THF_16930.p',satz18)).
% 1.48/1.28 thf(f24,plain,(
% 1.48/1.28 ((more @ (suc @ x) @ n_1) != $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.48/1.28 thf(f15,plain,(
% 1.48/1.28 ((more @ (suc @ x) @ n_1) != $true)),
% 1.48/1.28 inference(flattening,[status(thm)],[f10])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ~((more @ (suc @ x) @ n_1) = $true)),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f9])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ~(more @ (suc @ x) @ n_1)),
% 1.48/1.28 inference(rectify,[status(thm)],[f7])).
% 1.48/1.28 thf(f7,negated_conjecture,(
% 1.48/1.28 ~(more @ (suc @ x) @ n_1)),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f6])).
% 1.48/1.28 thf(f6,conjecture,(
% 1.48/1.28 (more @ (suc @ x) @ n_1)),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.Qch2cDbeou/DTF2THF_16930.p',satz24b)).
% 1.48/1.28 % SZS output end Proof for DTF2THF_16930
% 1.48/1.28 % (17038)------------------------------
% 1.48/1.28 % (17038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (17038)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (17038)Memory used [KB]: 5500
% 1.48/1.28 % (17038)Time elapsed: 0.003 s
% 1.48/1.28 % (17038)Instructions burned: 1 (million)
% 1.48/1.28 % (17038)------------------------------
% 1.48/1.28 % (17038)------------------------------
% 1.48/1.28 % (17032)Success in time 0.01 s
%------------------------------------------------------------------------------