%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM660^1 : 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 : n024.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 09:24:09 AM UTC 2026
% Result : Theorem 1.56s 1.31s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 35 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 98 ( 24 ~; 7 |; 1 &; 54 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 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,
y: nat ).
thf(func_def_3,type,
more: nat > nat > $o ).
thf(func_def_5,type,
less: nat > nat > $o ).
thf(f26,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f25,f18]) ).
thf(f18,plain,
x != y,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( less @ y @ x )
!= $true )
& ( x != y ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( ( less @ y @ x )
!= $true )
=> ( x = y ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( ( less @ y @ x )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ~ ( less @ y @ x )
=> ( x = y ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( ~ ( less @ y @ x )
=> ( x = y ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( ~ ( less @ y @ x )
=> ( x = y ) ),
file('/export/starexec/sandbox/tmp/tmp.SHT5I5Lc70/DTF2THF_12455.p',satz13) ).
thf(f25,plain,
x = y,
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( x = y )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f23,f21]) ).
thf(f21,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( x = y )
| ( ( more @ x @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/tmp/tmp.SHT5I5Lc70/DTF2THF_12455.p',m) ).
thf(f23,plain,
( ( more @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true != $true )
| ( ( more @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f19,f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( less @ X0 @ X1 ) )
| ( $true
!= ( more @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( more @ X1 @ X0 ) )
| ( $true
= ( less @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: nat,X0: nat] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X1: nat,X0: nat] :
( ( ( more @ X0 @ X1 )
= $true )
=> ( ( less @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: nat,X1: nat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.SHT5I5Lc70/DTF2THF_12455.p',satz11) ).
thf(f19,plain,
( ( less @ y @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM660^1 : 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
% 0.10/0.29 % Computer : n024.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 06:09:40 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.38 ---- Original DTF file ---
% 0.16/0.38 thf(spec,logic,$$dhol).
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 % File : NUM660^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.38 % Domain : Number Theory
% 0.16/0.38 % Problem : Landau theorem 13
% 0.16/0.38 % Version : Especial.
% 0.16/0.38 % English : ~(more y x) -> y = x
% 0.16/0.38
% 0.16/0.38 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.16/0.38 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.16/0.38 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.38 % Source : [Bro09]
% 0.16/0.38 % Names : satz13 [Lan30]
% 0.16/0.38 % : satz14 [Lan30]
% 0.16/0.38
% 0.16/0.38 % Status : Theorem
% 0.16/0.38 % : Without extensionality : Theorem
% 0.16/0.38 % 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
% 0.16/0.38 % Syntax : Number of formulae : 8 ( 0 unt; 5 typ; 0 def)
% 0.16/0.38 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.16/0.38 % Maximal formula atoms : 2 ( 2 avg)
% 0.16/0.38 % Number of connectives : 13 ( 2 ~; 0 |; 0 &; 8 @)
% 0.16/0.38 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.38 % Maximal formula depth : 6 ( 5 avg)
% 0.16/0.38 % Number of types : 2 ( 1 usr)
% 0.16/0.38 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.16/0.38 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.16/0.38 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.16/0.38 % SPC : TH0_THM_EQU_NAR
% 0.16/0.38
% 0.16/0.38 % Comments :
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 thf(nat_type,type,
% 0.16/0.38 nat: $tType ).
% 0.16/0.38
% 0.16/0.38 thf(x,type,
% 0.16/0.38 x: nat ).
% 0.16/0.38
% 0.16/0.38 thf(y,type,
% 0.16/0.38 y: nat ).
% 0.16/0.38
% 0.16/0.38 thf(more,type,
% 0.16/0.38 more: nat > nat > $o ).
% 0.16/0.38
% 0.16/0.38 thf(m,axiom,
% 0.16/0.38 ( ~ ( more @ x @ y )
% 0.16/0.38 => ( x = y ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(less,type,
% 0.16/0.38 less: nat > nat > $o ).
% 0.16/0.38
% 0.16/0.38 thf(satz11,axiom,
% 0.16/0.38 ! [Xx: nat,Xy: nat] :
% 0.16/0.38 ( ( more @ Xx @ Xy )
% 0.16/0.38 => ( less @ Xy @ Xx ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(satz13,conjecture,
% 0.16/0.38 ( ~ ( less @ y @ x )
% 0.16/0.38 => ( y = x ) ) ).
% 0.16/0.38
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 ------------------------
% 1.38/1.28 ---- Embedded in THF ---
% 1.38/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.28 %%% Generated on Tue Feb 24 06:09:41 EST 2026
% 1.38/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.28 %%% Logic specification used:
% 1.38/1.28 %%% thf(spec, logic, $$dhol).
% 1.38/1.28
% 1.38/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SHT5I5Lc70/DTF2DTF12455.p
% See solution above
% 1.38/1.28 ------------------------
% 1.38/1.29 ---- Cleaned THF ---
% 1.38/1.29 thf(nat_type,type,
% 1.38/1.29 nat: $tType ).
% 1.38/1.29
% 1.38/1.29 thf(x,type,
% 1.38/1.29 x: nat ).
% 1.38/1.29
% 1.38/1.29 thf(y,type,
% 1.38/1.29 y: nat ).
% 1.38/1.29
% 1.38/1.29 thf(more,type,
% 1.38/1.29 more: nat > nat > $o ).
% 1.38/1.29
% 1.38/1.29 thf(m,axiom,
% 1.38/1.29 ( ~ ( more @ x @ y )
% 1.38/1.29 => ( x = y ) ) ).
% 1.38/1.29
% 1.38/1.29 thf(less,type,
% 1.38/1.29 less: nat > nat > $o ).
% 1.38/1.29
% 1.38/1.29 thf(satz11,axiom,
% 1.38/1.29 ! [Xx: nat,Xy: nat] :
% 1.38/1.29 ( ( more @ Xx @ Xy )
% 1.38/1.29 => ( less @ Xy @ Xx ) ) ).
% 1.38/1.29
% 1.38/1.29 thf(satz13,conjecture,
% 1.38/1.29 ( ~ ( less @ y @ x )
% 1.38/1.29 => ( y = x ) ) ).
% 1.38/1.29 ------------------------
% 1.56/1.31 % (12554)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_12455 for (3000ds/4Mi)
% 1.56/1.31 % (12556)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12455 for (3000ds/2Mi)
% 1.56/1.31 % (12555)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_12455 for (3000ds/27Mi)
% 1.56/1.31 % (12557)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_12455 for (3000ds/2Mi)
% 1.56/1.31 % (12553)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12455 for (3000ds/183Mi)
% 1.56/1.31 % (12558)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_12455 for (3000ds/275Mi)
% 1.56/1.31 % (12559)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12455 for (3000ds/18Mi)
% 1.56/1.31 % (12558)First to succeed.
% 1.56/1.31 % (12556)Instruction limit reached!
% 1.56/1.31 % (12556)------------------------------
% 1.56/1.31 % (12556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (12556)Termination reason: Unknown
% 1.56/1.31 % (12556)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (12556)Memory used [KB]: 5500
% 1.56/1.31 % (12556)Time elapsed: 0.003 s
% 1.56/1.31 % (12556)Instructions burned: 2 (million)
% 1.56/1.31 % (12556)------------------------------
% 1.56/1.31 % (12556)------------------------------
% 1.56/1.31 % (12557)Instruction limit reached!
% 1.56/1.31 % (12557)------------------------------
% 1.56/1.31 % (12557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (12557)Termination reason: Unknown
% 1.56/1.31 % (12557)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (12557)Memory used [KB]: 5500
% 1.56/1.31 % (12557)Time elapsed: 0.003 s
% 1.56/1.31 % (12557)Instructions burned: 2 (million)
% 1.56/1.31 % (12557)------------------------------
% 1.56/1.31 % (12557)------------------------------
% 1.56/1.31 % (12553)Also succeeded, but the first one will report.
% 1.56/1.31 % (12554)Also succeeded, but the first one will report.
% 1.56/1.31 % (12558)Refutation found. Thanks to Tanya!
% 1.56/1.31 % SZS status Theorem for DTF2THF_12455
% 1.56/1.31 % SZS output start Proof for DTF2THF_12455
% 1.56/1.31 thf(type_def_5, type, nat: $tType).
% 1.56/1.31 thf(func_def_0, type, nat: $tType).
% 1.56/1.31 thf(func_def_1, type, x: nat).
% 1.56/1.31 thf(func_def_2, type, y: nat).
% 1.56/1.31 thf(func_def_3, type, more: nat > nat > $o).
% 1.56/1.31 thf(func_def_5, type, less: nat > nat > $o).
% 1.56/1.31 thf(f26,plain,(
% 1.56/1.31 $false),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f25,f18])).
% 1.56/1.31 thf(f18,plain,(
% 1.56/1.31 (x != y)),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.56/1.31 thf(f16,plain,(
% 1.56/1.31 ((less @ y @ x) != $true) & (x != y)),
% 1.56/1.31 inference(ennf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f12,plain,(
% 1.56/1.31 ~(((less @ y @ x) != $true) => (x = y))),
% 1.56/1.31 inference(flattening,[status(thm)],[f9])).
% 1.56/1.31 thf(f9,plain,(
% 1.56/1.31 ~(~((less @ y @ x) = $true) => (x = y))),
% 1.56/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.56/1.31 thf(f8,plain,(
% 1.56/1.31 ~(~(less @ y @ x) => (x = y))),
% 1.56/1.31 inference(rectify,[status(thm)],[f4])).
% 1.56/1.31 thf(f4,negated_conjecture,(
% 1.56/1.31 ~(~(less @ y @ x) => (x = y))),
% 1.56/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.56/1.31 thf(f3,conjecture,(
% 1.56/1.31 ~(less @ y @ x) => (x = y)),
% 1.56/1.31 file('/export/starexec/sandbox/tmp/tmp.SHT5I5Lc70/DTF2THF_12455.p',satz13)).
% 1.56/1.31 thf(f25,plain,(
% 1.56/1.31 (x = y)),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.56/1.31 thf(f24,plain,(
% 1.56/1.31 (x = y) | ($true != $true)),
% 1.56/1.31 inference(superposition,[status(thm)],[f23,f21])).
% 1.56/1.31 thf(f21,plain,(
% 1.56/1.31 ((more @ x @ y) = $true) | (x = y)),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.56/1.31 thf(f15,plain,(
% 1.56/1.31 (x = y) | ((more @ x @ y) = $true)),
% 1.56/1.31 inference(ennf_transformation,[status(thm)],[f13])).
% 1.56/1.31 thf(f13,plain,(
% 1.56/1.31 ((more @ x @ y) != $true) => (x = y)),
% 1.56/1.31 inference(flattening,[status(thm)],[f11])).
% 1.56/1.31 thf(f11,plain,(
% 1.56/1.31 ~((more @ x @ y) = $true) => (x = y)),
% 1.56/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.56/1.31 thf(f10,plain,(
% 1.56/1.31 ~(more @ x @ y) => (x = y)),
% 1.56/1.31 inference(rectify,[status(thm)],[f1])).
% 1.56/1.31 thf(f1,axiom,(
% 1.56/1.31 ~(more @ x @ y) => (x = y)),
% 1.56/1.31 file('/export/starexec/sandbox/tmp/tmp.SHT5I5Lc70/DTF2THF_12455.p',m)).
% 1.56/1.31 thf(f23,plain,(
% 1.56/1.31 ((more @ x @ y) != $true)),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.56/1.31 thf(f22,plain,(
% 1.56/1.31 ($true != $true) | ((more @ x @ y) != $true)),
% 1.56/1.31 inference(superposition,[status(thm)],[f19,f20])).
% 1.56/1.31 thf(f20,plain,(
% 1.56/1.31 ( ! [X0 : nat,X1 : nat] : (($true = (less @ X0 @ X1)) | ($true != (more @ X1 @ X0))) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 1.56/1.31 thf(f17,plain,(
% 1.56/1.31 ! [X0 : nat,X1 : nat] : (($true != (more @ X1 @ X0)) | ($true = (less @ X0 @ X1)))),
% 1.56/1.31 inference(rectify,[status(thm)],[f14])).
% 1.56/1.31 thf(f14,plain,(
% 1.56/1.31 ! [X1 : nat,X0 : nat] : (((more @ X0 @ X1) != $true) | ((less @ X1 @ X0) = $true))),
% 1.56/1.31 inference(ennf_transformation,[status(thm)],[f7])).
% 1.56/1.31 thf(f7,plain,(
% 1.56/1.31 ! [X1 : nat,X0 : nat] : (((more @ X0 @ X1) = $true) => ((less @ X1 @ X0) = $true))),
% 1.56/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.56/1.31 thf(f6,plain,(
% 1.56/1.31 ! [X0 : nat,X1 : nat] : ((more @ X0 @ X1) => (less @ X1 @ X0))),
% 1.56/1.31 inference(rectify,[status(thm)],[f2])).
% 1.56/1.31 thf(f2,axiom,(
% 1.56/1.31 ! [X0 : nat,X1 : nat] : ((more @ X0 @ X1) => (less @ X1 @ X0))),
% 1.56/1.31 file('/export/starexec/sandbox/tmp/tmp.SHT5I5Lc70/DTF2THF_12455.p',satz11)).
% 1.56/1.31 thf(f19,plain,(
% 1.56/1.31 ((less @ y @ x) != $true)),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.56/1.31 % SZS output end Proof for DTF2THF_12455
% 1.56/1.31 % (12558)------------------------------
% 1.56/1.31 % (12558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (12558)Termination reason: Refutation
% 1.56/1.31
% 1.56/1.31 % (12558)Memory used [KB]: 5500
% 1.56/1.31 % (12558)Time elapsed: 0.003 s
% 1.56/1.31 % (12558)Instructions burned: 1 (million)
% 1.56/1.31 % (12558)------------------------------
% 1.56/1.31 % (12558)------------------------------
% 1.56/1.31 % (12552)Success in time 0.017 s
%------------------------------------------------------------------------------