%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM786^1 : 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 : n021.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 09:24:43 AM UTC 2026
% Result : Theorem 1.61s 1.30s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 32 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 140 ( 27 ~; 9 |; 1 &; 90 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 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,
more: rat > rat > $o ).
thf(func_def_5,type,
less: rat > rat > $o ).
thf(func_def_6,type,
is: rat > rat > $o ).
thf(f32,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f31,f26]) ).
thf(f26,plain,
( ( more @ x0 @ y0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( more @ x0 @ y0 )
!= $true ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( more @ x0 @ y0 )
!= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( more @ x0 @ y0 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ( more @ x0 @ y0 ),
file('/export/starexec/sandbox/tmp/tmp.x2lpd4M6kh/DTF2THF_16033.p',n) ).
thf(f31,plain,
( ( more @ x0 @ y0 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f30,f24]) ).
thf(f24,plain,
( ( less @ x0 @ y0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( is @ x0 @ y0 )
!= $true )
& ( ( less @ x0 @ y0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( ( ( less @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( ( less @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ~ ( less @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( ~ ( less @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( ~ ( less @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
file('/export/starexec/sandbox/tmp/tmp.x2lpd4M6kh/DTF2THF_16033.p',satz81e) ).
thf(f30,plain,
( ( ( less @ x0 @ y0 )
= $true )
| ( ( more @ x0 @ y0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true != $true )
| ( ( more @ x0 @ y0 )
= $true )
| ( ( less @ x0 @ y0 )
= $true ) ),
inference(superposition,[status(thm)],[f25,f23]) ).
thf(f23,plain,
! [X0: rat,X1: rat] :
( ( ( is @ X0 @ X1 )
= $true )
| ( $true
= ( less @ X0 @ X1 ) )
| ( ( more @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: rat,X1: rat] :
( ( ( is @ X0 @ X1 )
= $true )
| ( ( more @ X0 @ X1 )
= $true )
| ( $true
= ( less @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: rat,X0: rat] :
( ( $true
= ( less @ X0 @ X1 ) )
| ( ( more @ X0 @ X1 )
= $true )
| ( ( is @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: rat,X0: rat] :
( ( ( is @ X0 @ X1 )
!= $true )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( $true
= ( less @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: rat,X1: rat] :
( ( ( is @ X0 @ X1 )
!= $true )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( $true
= ( less @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: rat,X1: rat] :
( ~ ( is @ X0 @ X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: rat,X2: rat] :
( ~ ( is @ X1 @ X2 )
=> ( ~ ( more @ X1 @ X2 )
=> ( less @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x2lpd4M6kh/DTF2THF_16033.p',satz81a) ).
thf(f25,plain,
( ( is @ x0 @ y0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM786^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n021.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 11:14:08 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
% 0.26/0.48 ---- Original DTF file ---
% 0.26/0.48 thf(spec,logic,$$dhol).
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 % File : NUM786^1 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.48 % Domain : Number Theory
% 0.26/0.48 % Problem : Landau theorem 81e
% 0.26/0.48 % Version : Especial.
% 0.26/0.48 % English : ~(less x0 y0) -> is x0 y0
% 0.26/0.48
% 0.26/0.48 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.26/0.48 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.26/0.48 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.48 % Source : [Bro09]
% 0.26/0.48 % Names : satz81e [Lan30]
% 0.26/0.48 % : satz41e [Lan30]
% 0.26/0.48
% 0.26/0.48 % Status : Theorem
% 0.26/0.48 % : Without extensionality : Theorem
% 0.26/0.48 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.26/0.48 % Syntax : Number of formulae : 10 ( 1 unt; 6 typ; 0 def)
% 0.26/0.48 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.26/0.48 % Maximal formula atoms : 3 ( 1 avg)
% 0.26/0.48 % Number of connectives : 22 ( 6 ~; 0 |; 0 &; 12 @)
% 0.26/0.48 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.26/0.48 % Maximal formula depth : 8 ( 6 avg)
% 0.26/0.48 % Number of types : 2 ( 1 usr)
% 0.26/0.48 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.26/0.48 % Number of symbols : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.26/0.48 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.26/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.26/0.48
% 0.26/0.48 % Comments :
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 thf(rat_type,type,
% 0.26/0.48 rat: $tType ).
% 0.26/0.48
% 0.26/0.48 thf(x0,type,
% 0.26/0.48 x0: rat ).
% 0.26/0.48
% 0.26/0.48 thf(y0,type,
% 0.26/0.48 y0: rat ).
% 0.26/0.48
% 0.26/0.48 thf(more,type,
% 0.26/0.48 more: rat > rat > $o ).
% 0.26/0.48
% 0.26/0.48 thf(n,axiom,
% 0.26/0.48 ~ ( more @ x0 @ y0 ) ).
% 0.26/0.48
% 0.26/0.48 thf(less,type,
% 0.26/0.48 less: rat > rat > $o ).
% 0.26/0.48
% 0.26/0.48 thf(is,type,
% 0.26/0.48 is: rat > rat > $o ).
% 0.26/0.48
% 0.26/0.48 thf(et,axiom,
% 0.26/0.48 ! [Xa: $o] :
% 0.26/0.48 ( ~ ~ Xa
% 0.26/0.48 => Xa ) ).
% 0.26/0.48
% 0.26/0.48 thf(satz81a,axiom,
% 0.26/0.48 ! [Xx0: rat,Xy0: rat] :
% 0.26/0.48 ( ~ ( is @ Xx0 @ Xy0 )
% 0.26/0.48 => ( ~ ( more @ Xx0 @ Xy0 )
% 0.26/0.48 => ( less @ Xx0 @ Xy0 ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(satz81e,conjecture,
% 0.26/0.48 ( ~ ( less @ x0 @ y0 )
% 0.26/0.48 => ( is @ x0 @ y0 ) ) ).
% 0.26/0.48
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 ------------------------
% 1.44/1.27 ---- Embedded in THF ---
% 1.44/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.27 %%% Generated on Tue Feb 24 11:14:09 EST 2026
% 1.44/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.27 %%% Logic specification used:
% 1.44/1.27 %%% thf(spec, logic, $$dhol).
% 1.44/1.27
% 1.44/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.x2lpd4M6kh/DTF2DTF16033.p
% See solution above
% 1.44/1.27 ------------------------
% 1.44/1.28 ---- Cleaned THF ---
% 1.44/1.28 thf(rat_type,type,
% 1.44/1.28 rat: $tType ).
% 1.44/1.28
% 1.44/1.28 thf(x0,type,
% 1.44/1.28 x0: rat ).
% 1.44/1.28
% 1.44/1.28 thf(y0,type,
% 1.44/1.28 y0: rat ).
% 1.44/1.28
% 1.44/1.28 thf(more,type,
% 1.44/1.28 more: rat > rat > $o ).
% 1.44/1.28
% 1.44/1.28 thf(n,axiom,
% 1.44/1.28 ~ ( more @ x0 @ y0 ) ).
% 1.44/1.28
% 1.44/1.28 thf(less,type,
% 1.44/1.28 less: rat > rat > $o ).
% 1.44/1.28
% 1.44/1.28 thf(is,type,
% 1.44/1.28 is: rat > rat > $o ).
% 1.44/1.28
% 1.44/1.28 thf(et,axiom,
% 1.44/1.28 ! [Xa: $o] :
% 1.44/1.28 ( ~ ~ Xa
% 1.44/1.28 => Xa ) ).
% 1.44/1.28
% 1.44/1.28 thf(satz81a,axiom,
% 1.44/1.28 ! [Xx0: rat,Xy0: rat] :
% 1.44/1.28 ( ~ ( is @ Xx0 @ Xy0 )
% 1.44/1.28 => ( ~ ( more @ Xx0 @ Xy0 )
% 1.44/1.28 => ( less @ Xx0 @ Xy0 ) ) ) ).
% 1.44/1.28
% 1.44/1.28 thf(satz81e,conjecture,
% 1.44/1.28 ( ~ ( less @ x0 @ y0 )
% 1.44/1.28 => ( is @ x0 @ y0 ) ) ).
% 1.44/1.28 ------------------------
% 1.44/1.30 % (16320)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16033 for (2999ds/2Mi)
% 1.44/1.30 % (16318)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_16033 for (2999ds/4Mi)
% 1.44/1.30 % (16320)First to succeed.
% 1.61/1.30 % (16318)Instruction limit reached!
% 1.61/1.30 % (16318)------------------------------
% 1.61/1.30 % (16318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (16318)Termination reason: Unknown
% 1.61/1.30 % (16318)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (16318)Memory used [KB]: 5500
% 1.61/1.30 % (16318)Time elapsed: 0.003 s
% 1.61/1.30 % (16318)Instructions burned: 4 (million)
% 1.61/1.30 % (16318)------------------------------
% 1.61/1.30 % (16318)------------------------------
% 1.61/1.30 % (16320)Refutation found. Thanks to Tanya!
% 1.61/1.30 % SZS status Theorem for DTF2THF_16033
% 1.61/1.30 % SZS output start Proof for DTF2THF_16033
% 1.61/1.30 thf(type_def_5, type, rat: $tType).
% 1.61/1.30 thf(func_def_0, type, rat: $tType).
% 1.61/1.30 thf(func_def_1, type, x0: rat).
% 1.61/1.30 thf(func_def_2, type, y0: rat).
% 1.61/1.30 thf(func_def_3, type, more: rat > rat > $o).
% 1.61/1.30 thf(func_def_5, type, less: rat > rat > $o).
% 1.61/1.30 thf(func_def_6, type, is: rat > rat > $o).
% 1.61/1.30 thf(f32,plain,(
% 1.61/1.30 $false),
% 1.61/1.30 inference(subsumption_resolution,[status(thm)],[f31,f26])).
% 1.61/1.30 thf(f26,plain,(
% 1.61/1.30 ((more @ x0 @ y0) != $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.61/1.30 thf(f16,plain,(
% 1.61/1.30 ((more @ x0 @ y0) != $true)),
% 1.61/1.30 inference(flattening,[status(thm)],[f10])).
% 1.61/1.30 thf(f10,plain,(
% 1.61/1.30 ~((more @ x0 @ y0) = $true)),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f9])).
% 1.61/1.30 thf(f9,plain,(
% 1.61/1.30 ~(more @ x0 @ y0)),
% 1.61/1.30 inference(rectify,[status(thm)],[f1])).
% 1.61/1.30 thf(f1,axiom,(
% 1.61/1.30 ~(more @ x0 @ y0)),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.x2lpd4M6kh/DTF2THF_16033.p',n)).
% 1.61/1.30 thf(f31,plain,(
% 1.61/1.30 ((more @ x0 @ y0) = $true)),
% 1.61/1.30 inference(subsumption_resolution,[status(thm)],[f30,f24])).
% 1.61/1.30 thf(f24,plain,(
% 1.61/1.30 ((less @ x0 @ y0) != $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f19])).
% 1.61/1.30 thf(f19,plain,(
% 1.61/1.30 ((is @ x0 @ y0) != $true) & ((less @ x0 @ y0) != $true)),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f18])).
% 1.61/1.30 thf(f18,plain,(
% 1.61/1.30 ~(((less @ x0 @ y0) != $true) => ((is @ x0 @ y0) = $true))),
% 1.61/1.30 inference(flattening,[status(thm)],[f14])).
% 1.61/1.30 thf(f14,plain,(
% 1.61/1.30 ~(~((less @ x0 @ y0) = $true) => ((is @ x0 @ y0) = $true))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f13])).
% 1.61/1.30 thf(f13,plain,(
% 1.61/1.30 ~(~(less @ x0 @ y0) => (is @ x0 @ y0))),
% 1.61/1.30 inference(rectify,[status(thm)],[f5])).
% 1.61/1.30 thf(f5,negated_conjecture,(
% 1.61/1.30 ~(~(less @ x0 @ y0) => (is @ x0 @ y0))),
% 1.61/1.30 inference(negated_conjecture,[status(cth)],[f4])).
% 1.61/1.30 thf(f4,conjecture,(
% 1.61/1.30 ~(less @ x0 @ y0) => (is @ x0 @ y0)),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.x2lpd4M6kh/DTF2THF_16033.p',satz81e)).
% 1.61/1.30 thf(f30,plain,(
% 1.61/1.30 ((less @ x0 @ y0) = $true) | ((more @ x0 @ y0) = $true)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.61/1.30 thf(f29,plain,(
% 1.61/1.30 ($true != $true) | ((more @ x0 @ y0) = $true) | ((less @ x0 @ y0) = $true)),
% 1.61/1.30 inference(superposition,[status(thm)],[f25,f23])).
% 1.61/1.30 thf(f23,plain,(
% 1.61/1.30 ( ! [X0 : rat,X1 : rat] : (((is @ X0 @ X1) = $true) | ($true = (less @ X0 @ X1)) | ((more @ X0 @ X1) = $true)) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f22])).
% 1.61/1.30 thf(f22,plain,(
% 1.61/1.30 ! [X0 : rat,X1 : rat] : (((is @ X0 @ X1) = $true) | ((more @ X0 @ X1) = $true) | ($true = (less @ X0 @ X1)))),
% 1.61/1.30 inference(flattening,[status(thm)],[f21])).
% 1.61/1.30 thf(f21,plain,(
% 1.61/1.30 ! [X1 : rat,X0 : rat] : ((($true = (less @ X0 @ X1)) | ((more @ X0 @ X1) = $true)) | ((is @ X0 @ X1) = $true))),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f17])).
% 1.61/1.30 thf(f17,plain,(
% 1.61/1.30 ! [X1 : rat,X0 : rat] : (((is @ X0 @ X1) != $true) => (((more @ X0 @ X1) != $true) => ($true = (less @ X0 @ X1))))),
% 1.61/1.30 inference(flattening,[status(thm)],[f12])).
% 1.61/1.30 thf(f12,plain,(
% 1.61/1.30 ! [X0 : rat,X1 : rat] : (~((is @ X0 @ X1) = $true) => (~((more @ X0 @ X1) = $true) => ($true = (less @ X0 @ X1))))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f11])).
% 1.61/1.30 thf(f11,plain,(
% 1.61/1.30 ! [X0 : rat,X1 : rat] : (~(is @ X0 @ X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 1.61/1.30 inference(rectify,[status(thm)],[f3])).
% 1.61/1.30 thf(f3,axiom,(
% 1.61/1.30 ! [X1 : rat,X2 : rat] : (~(is @ X1 @ X2) => (~(more @ X1 @ X2) => (less @ X1 @ X2)))),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.x2lpd4M6kh/DTF2THF_16033.p',satz81a)).
% 1.61/1.30 thf(f25,plain,(
% 1.61/1.30 ((is @ x0 @ y0) != $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f19])).
% 1.61/1.30 % SZS output end Proof for DTF2THF_16033
% 1.61/1.30 % (16320)------------------------------
% 1.61/1.30 % (16320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (16320)Termination reason: Refutation
% 1.61/1.30
% 1.61/1.30 % (16320)Memory used [KB]: 5500
% 1.61/1.30 % (16320)Time elapsed: 0.003 s
% 1.61/1.30 % (16320)Instructions burned: 1 (million)
% 1.61/1.30 % (16320)------------------------------
% 1.61/1.30 % (16320)------------------------------
% 1.61/1.30 % (16316)Success in time 0.012 s
%------------------------------------------------------------------------------