%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM783^1 : 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 : n011.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 09:24:42 AM UTC 2026
% Result : Theorem 1.48s 1.27s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 10 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 171 ( 13 ~; 0 |; 1 &; 153 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
rat: $tType ).
thf(func_def_0,type,
rat: $tType ).
thf(func_def_1,type,
x0: rat ).
thf(func_def_2,type,
y0: rat ).
thf(func_def_3,type,
or3: $o > $o > $o > $o ).
thf(func_def_4,type,
is: rat > rat > $o ).
thf(func_def_5,type,
more: rat > rat > $o ).
thf(func_def_6,type,
less: rat > rat > $o ).
thf(func_def_7,type,
ec3: $o > $o > $o > $o ).
thf(f22,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f20,f19]) ).
thf(f19,plain,
! [X0: rat,X1: rat] :
( ( or3 @ ( is @ X0 @ X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: rat,X1: rat] :
( ( ( or3 @ ( is @ X0 @ X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) )
= $true )
& ( ( ec3 @ ( is @ X0 @ X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: rat,X0: rat] :
~ ( ( ( or3 @ ( is @ X0 @ X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) )
= $true )
=> ( ( ec3 @ ( is @ X0 @ X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: rat,X1: rat] :
~ ( ( ( or3 @ ( is @ X0 @ X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) )
= $true )
=> ( ( ec3 @ ( is @ X0 @ X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: rat,X1: rat] :
~ ( ( or3 @ ( is @ X0 @ X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) )
=> ~ ( ec3 @ ( is @ X0 @ X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: rat,X2: rat] :
~ ( ( or3 @ ( is @ X1 @ X2 ) @ ( more @ X1 @ X2 ) @ ( less @ X1 @ X2 ) )
=> ~ ( ec3 @ ( is @ X1 @ X2 ) @ ( more @ X1 @ X2 ) @ ( less @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NkWamEG61S/DTF2THF_18103.p',satz81) ).
thf(f20,plain,
( ( or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ) )
!= $true ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ),
file('/export/starexec/sandbox2/tmp/tmp.NkWamEG61S/DTF2THF_18103.p',satz81a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM783^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 11:13:47 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : NUM783^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Number Theory
% 0.29/0.46 % Problem : Landau theorem 81a
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : or3 (is x0 y0) (more x0 y0) (less x0 y0)
% 0.29/0.46
% 0.29/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.29/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : satz81a [Lan30]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % : Without extensionality : Theorem
% 0.29/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 11 ( 0 unt; 8 typ; 0 def)
% 0.29/0.46 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 8 ( 4 avg)
% 0.29/0.46 % Number of connectives : 33 ( 4 ~; 0 |; 0 &; 27 @)
% 0.29/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 11 ( 7 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 7 ( 7 usr; 2 con; 0-3 aty)
% 0.29/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(rat_type,type,
% 0.29/0.46 rat: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(x0,type,
% 0.29/0.46 x0: rat ).
% 0.29/0.46
% 0.29/0.46 thf(y0,type,
% 0.29/0.46 y0: rat ).
% 0.29/0.46
% 0.29/0.46 thf(or3,type,
% 0.29/0.46 or3: $o > $o > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(is,type,
% 0.29/0.46 is: rat > rat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(more,type,
% 0.29/0.46 more: rat > rat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(less,type,
% 0.29/0.46 less: rat > rat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(et,axiom,
% 0.29/0.46 ! [Xa: $o] :
% 0.29/0.46 ( ~ ~ Xa
% 0.29/0.46 => Xa ) ).
% 0.29/0.46
% 0.29/0.46 thf(ec3,type,
% 0.29/0.46 ec3: $o > $o > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(satz81,axiom,
% 0.29/0.46 ! [Xx0: rat,Xy0: rat] :
% 0.29/0.46 ~ ( ( or3 @ ( is @ Xx0 @ Xy0 ) @ ( more @ Xx0 @ Xy0 ) @ ( less @ Xx0 @ Xy0 ) )
% 0.29/0.46 => ~ ( ec3 @ ( is @ Xx0 @ Xy0 ) @ ( more @ Xx0 @ Xy0 ) @ ( less @ Xx0 @ Xy0 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz81a,conjecture,
% 0.29/0.46 or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.24 %%% Generated on Tue Feb 24 11:13:48 EST 2026
% 1.48/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.24 %%% Logic specification used:
% 1.48/1.24 %%% thf(spec, logic, $$dhol).
% 1.48/1.24
% 1.48/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.NkWamEG61S/DTF2DTF18103.p
% See solution above
% 1.48/1.24 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.25 thf(rat_type,type,
% 1.48/1.25 rat: $tType ).
% 1.48/1.25
% 1.48/1.25 thf(x0,type,
% 1.48/1.25 x0: rat ).
% 1.48/1.25
% 1.48/1.25 thf(y0,type,
% 1.48/1.25 y0: rat ).
% 1.48/1.25
% 1.48/1.25 thf(or3,type,
% 1.48/1.25 or3: $o > $o > $o > $o ).
% 1.48/1.25
% 1.48/1.25 thf(is,type,
% 1.48/1.25 is: rat > rat > $o ).
% 1.48/1.25
% 1.48/1.25 thf(more,type,
% 1.48/1.25 more: rat > rat > $o ).
% 1.48/1.25
% 1.48/1.25 thf(less,type,
% 1.48/1.25 less: rat > rat > $o ).
% 1.48/1.25
% 1.48/1.25 thf(et,axiom,
% 1.48/1.25 ! [Xa: $o] :
% 1.48/1.25 ( ~ ~ Xa
% 1.48/1.25 => Xa ) ).
% 1.48/1.25
% 1.48/1.25 thf(ec3,type,
% 1.48/1.25 ec3: $o > $o > $o > $o ).
% 1.48/1.25
% 1.48/1.25 thf(satz81,axiom,
% 1.48/1.25 ! [Xx0: rat,Xy0: rat] :
% 1.48/1.25 ~ ( ( or3 @ ( is @ Xx0 @ Xy0 ) @ ( more @ Xx0 @ Xy0 ) @ ( less @ Xx0 @ Xy0 ) )
% 1.48/1.25 => ~ ( ec3 @ ( is @ Xx0 @ Xy0 ) @ ( more @ Xx0 @ Xy0 ) @ ( less @ Xx0 @ Xy0 ) ) ) ).
% 1.48/1.25
% 1.48/1.25 thf(satz81a,conjecture,
% 1.48/1.25 or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ) ).
% 1.48/1.25 ------------------------
% 1.48/1.26 % (18274)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_18103 for (3000ds/2Mi)
% 1.48/1.26 % (18271)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_18103 for (3000ds/4Mi)
% 1.48/1.26 % (18274)Instruction limit reached!
% 1.48/1.26 % (18274)------------------------------
% 1.48/1.26 % (18274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (18274)Termination reason: Unknown
% 1.48/1.26 % (18274)Termination phase: Saturation
% 1.48/1.26
% 1.48/1.26 % (18274)Memory used [KB]: 895
% 1.48/1.26 % (18274)Time elapsed: 0.002 s
% 1.48/1.26 % (18274)Instructions burned: 2 (million)
% 1.48/1.26 % (18274)------------------------------
% 1.48/1.26 % (18274)------------------------------
% 1.48/1.26 % (18271)Instruction limit reached!
% 1.48/1.26 % (18271)------------------------------
% 1.48/1.26 % (18271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (18271)Termination reason: Unknown
% 1.48/1.26 % (18271)Termination phase: Saturation
% 1.48/1.26
% 1.48/1.26 % (18271)Memory used [KB]: 5500
% 1.48/1.26 % (18271)Time elapsed: 0.003 s
% 1.48/1.26 % (18271)Instructions burned: 5 (million)
% 1.48/1.26 % (18271)------------------------------
% 1.48/1.26 % (18271)------------------------------
% 1.48/1.27 % (18276)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18103 for (3000ds/18Mi)
% 1.48/1.27 % (18276)First to succeed.
% 1.48/1.27 % (18275)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_18103 for (3000ds/275Mi)
% 1.48/1.27 % (18270)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18103 for (3000ds/183Mi)
% 1.48/1.27 % (18275)Refutation not found, incomplete strategy
% 1.48/1.27 % (18275)------------------------------
% 1.48/1.27 % (18275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (18275)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.27
% 1.48/1.27
% 1.48/1.27 % (18275)Memory used [KB]: 5373
% 1.48/1.27 % (18275)Time elapsed: 0.003 s
% 1.48/1.27 % (18275)Instructions burned: 1 (million)
% 1.48/1.27 % (18276)Refutation found. Thanks to Tanya!
% 1.48/1.27 % SZS status Theorem for DTF2THF_18103
% 1.48/1.27 % SZS output start Proof for DTF2THF_18103
% 1.48/1.27 thf(type_def_5, type, rat: $tType).
% 1.48/1.27 thf(func_def_0, type, rat: $tType).
% 1.48/1.27 thf(func_def_1, type, x0: rat).
% 1.48/1.27 thf(func_def_2, type, y0: rat).
% 1.48/1.27 thf(func_def_3, type, or3: $o > $o > $o > $o).
% 1.48/1.27 thf(func_def_4, type, is: rat > rat > $o).
% 1.48/1.27 thf(func_def_5, type, more: rat > rat > $o).
% 1.48/1.27 thf(func_def_6, type, less: rat > rat > $o).
% 1.48/1.27 thf(func_def_7, type, ec3: $o > $o > $o > $o).
% 1.48/1.27 thf(f22,plain,(
% 1.48/1.27 $false),
% 1.48/1.27 inference(subsumption_resolution,[status(thm)],[f20,f19])).
% 1.48/1.27 thf(f19,plain,(
% 1.48/1.27 ( ! [X0 : rat,X1 : rat] : (((or3 @ (is @ X0 @ X1) @ (more @ X0 @ X1) @ (less @ X0 @ X1)) = $true)) )),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f15])).
% 1.48/1.27 thf(f15,plain,(
% 1.48/1.27 ! [X0 : rat,X1 : rat] : (((or3 @ (is @ X0 @ X1) @ (more @ X0 @ X1) @ (less @ X0 @ X1)) = $true) & ((ec3 @ (is @ X0 @ X1) @ (more @ X0 @ X1) @ (less @ X0 @ X1)) = $true))),
% 1.48/1.27 inference(ennf_transformation,[status(thm)],[f13])).
% 1.48/1.27 thf(f13,plain,(
% 1.48/1.27 ! [X1 : rat,X0 : rat] : ~(((or3 @ (is @ X0 @ X1) @ (more @ X0 @ X1) @ (less @ X0 @ X1)) = $true) => ((ec3 @ (is @ X0 @ X1) @ (more @ X0 @ X1) @ (less @ X0 @ X1)) != $true))),
% 1.48/1.27 inference(flattening,[status(thm)],[f9])).
% 1.48/1.27 thf(f9,plain,(
% 1.48/1.27 ! [X0 : rat,X1 : rat] : ~(((or3 @ (is @ X0 @ X1) @ (more @ X0 @ X1) @ (less @ X0 @ X1)) = $true) => ~((ec3 @ (is @ X0 @ X1) @ (more @ X0 @ X1) @ (less @ X0 @ X1)) = $true))),
% 1.48/1.27 inference(fool_elimination,[status(thm)],[f8])).
% 1.48/1.27 thf(f8,plain,(
% 1.48/1.27 ! [X0 : rat,X1 : rat] : ~((or3 @ (is @ X0 @ X1) @ (more @ X0 @ X1) @ (less @ X0 @ X1)) => ~(ec3 @ (is @ X0 @ X1) @ (more @ X0 @ X1) @ (less @ X0 @ X1)))),
% 1.48/1.27 inference(rectify,[status(thm)],[f2])).
% 1.48/1.27 thf(f2,axiom,(
% 1.48/1.27 ! [X1 : rat,X2 : rat] : ~((or3 @ (is @ X1 @ X2) @ (more @ X1 @ X2) @ (less @ X1 @ X2)) => ~(ec3 @ (is @ X1 @ X2) @ (more @ X1 @ X2) @ (less @ X1 @ X2)))),
% 1.48/1.27 file('/export/starexec/sandbox2/tmp/tmp.NkWamEG61S/DTF2THF_18103.p',satz81)).
% 1.48/1.27 thf(f20,plain,(
% 1.48/1.27 ((or3 @ (is @ x0 @ y0) @ (more @ x0 @ y0) @ (less @ x0 @ y0)) != $true)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.27 thf(f14,plain,(
% 1.48/1.27 ((or3 @ (is @ x0 @ y0) @ (more @ x0 @ y0) @ (less @ x0 @ y0)) != $true)),
% 1.48/1.27 inference(flattening,[status(thm)],[f11])).
% 1.48/1.27 thf(f11,plain,(
% 1.48/1.27 ~((or3 @ (is @ x0 @ y0) @ (more @ x0 @ y0) @ (less @ x0 @ y0)) = $true)),
% 1.48/1.27 inference(fool_elimination,[status(thm)],[f10])).
% 1.48/1.27 thf(f10,plain,(
% 1.48/1.27 ~(or3 @ (is @ x0 @ y0) @ (more @ x0 @ y0) @ (less @ x0 @ y0))),
% 1.48/1.27 inference(rectify,[status(thm)],[f4])).
% 1.48/1.27 thf(f4,negated_conjecture,(
% 1.48/1.27 ~(or3 @ (is @ x0 @ y0) @ (more @ x0 @ y0) @ (less @ x0 @ y0))),
% 1.48/1.27 inference(negated_conjecture,[status(cth)],[f3])).
% 1.48/1.27 thf(f3,conjecture,(
% 1.48/1.27 (or3 @ (is @ x0 @ y0) @ (more @ x0 @ y0) @ (less @ x0 @ y0))),
% 1.48/1.27 file('/export/starexec/sandbox2/tmp/tmp.NkWamEG61S/DTF2THF_18103.p',satz81a)).
% 1.48/1.27 % SZS output end Proof for DTF2THF_18103
% 1.48/1.27 % (18276)------------------------------
% 1.48/1.27 % (18276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (18276)Termination reason: Refutation
% 1.48/1.27
% 1.48/1.27 % (18276)Memory used [KB]: 5500
% 1.48/1.27 % (18276)Time elapsed: 0.003 s
% 1.48/1.27 % (18276)Instructions burned: 2 (million)
% 1.48/1.27 % (18276)------------------------------
% 1.48/1.27 % (18276)------------------------------
% 1.48/1.27 % (18269)Success in time 0.017 s
%------------------------------------------------------------------------------