%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM749^1 : 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 : n018.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 09:24:32 AM UTC 2026
% Result : Theorem 1.46s 1.26s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 83 ( 9 ~; 3 |; 0 &; 68 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(func_def_0,type,
frac: $tType ).
thf(func_def_1,type,
x: frac ).
thf(func_def_2,type,
y: frac ).
thf(func_def_3,type,
less: frac > frac > $o ).
thf(func_def_4,type,
pf: frac > frac > frac ).
thf(func_def_5,type,
more: frac > frac > $o ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
$true != $true,
inference(superposition,[status(thm)],[f14,f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac] :
( ( less @ X0 @ ( pf @ X0 @ X1 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: frac,X1: frac] :
( ( ( less @ X0 @ ( pf @ X0 @ X1 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f15,f16]) ).
thf(f16,plain,
! [X0: frac,X1: frac] :
( ( more @ ( pf @ X1 @ X0 ) @ X1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: frac,X1: frac] :
( ( more @ ( pf @ X1 @ X0 ) @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: frac,X1: frac] : ( more @ ( pf @ X1 @ X0 ) @ X1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: frac,X0: frac] : ( more @ ( pf @ X0 @ X1 ) @ X0 ),
file('/export/starexec/sandbox2/tmp/tmp.EU8uS0YxNP/DTF2THF_7839.p',satz60) ).
thf(f15,plain,
! [X0: frac,X1: frac] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: frac,X1: frac] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X1: frac,X0: frac] :
( ( ( more @ X0 @ X1 )
= $true )
=> ( ( less @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: frac,X1: frac] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: frac,X1: frac] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EU8uS0YxNP/DTF2THF_7839.p',satz42) ).
thf(f14,plain,
( ( less @ x @ ( pf @ x @ y ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( less @ x @ ( pf @ x @ y ) )
!= $true ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( less @ x @ ( pf @ x @ y ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( less @ x @ ( pf @ x @ y ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( less @ x @ ( pf @ x @ y ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
less @ x @ ( pf @ x @ y ),
file('/export/starexec/sandbox2/tmp/tmp.EU8uS0YxNP/DTF2THF_7839.p',satz60a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM749^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:12:46 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : NUM749^1 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.46 % Domain : Number Theory
% 0.26/0.46 % Problem : Landau theorem 60a
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English : less x (pf x y)
% 0.26/0.46
% 0.26/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.26/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.26/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.46 % Source : [Bro09]
% 0.26/0.46 % Names : satz60a [Lan30]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % : Without extensionality : Theorem
% 0.26/0.46 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.26/0.46 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 0 def)
% 0.26/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.26/0.46 % Number of connectives : 13 ( 0 ~; 0 |; 0 &; 12 @)
% 0.26/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 7 ( 6 avg)
% 0.26/0.46 % Number of types : 2 ( 1 usr)
% 0.26/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.26/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.26/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.26/0.46
% 0.26/0.46 % Comments :
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(frac_type,type,
% 0.26/0.46 frac: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(x,type,
% 0.26/0.46 x: frac ).
% 0.26/0.46
% 0.26/0.46 thf(y,type,
% 0.26/0.46 y: frac ).
% 0.26/0.46
% 0.26/0.46 thf(less,type,
% 0.26/0.46 less: frac > frac > $o ).
% 0.26/0.46
% 0.26/0.46 thf(pf,type,
% 0.26/0.46 pf: frac > frac > frac ).
% 0.26/0.46
% 0.26/0.46 thf(more,type,
% 0.26/0.46 more: frac > frac > $o ).
% 0.26/0.46
% 0.26/0.46 thf(satz42,axiom,
% 0.26/0.46 ! [Xx: frac,Xy: frac] :
% 0.26/0.46 ( ( more @ Xx @ Xy )
% 0.26/0.46 => ( less @ Xy @ Xx ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(satz60,axiom,
% 0.26/0.46 ! [Xx: frac,Xy: frac] : ( more @ ( pf @ Xx @ Xy ) @ Xx ) ).
% 0.26/0.46
% 0.26/0.46 thf(satz60a,conjecture,
% 0.26/0.46 less @ x @ ( pf @ x @ y ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.46/1.23 ---- Embedded in THF ---
% 1.46/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.23 %%% Generated on Tue Feb 24 11:12:47 EST 2026
% 1.46/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.23 %%% Logic specification used:
% 1.46/1.23 %%% thf(spec, logic, $$dhol).
% 1.46/1.23
% 1.46/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.EU8uS0YxNP/DTF2DTF7839.p
% See solution above
% 1.46/1.23 ------------------------
% 1.46/1.24 ---- Cleaned THF ---
% 1.46/1.25 thf(frac_type,type,
% 1.46/1.25 frac: $tType ).
% 1.46/1.25
% 1.46/1.25 thf(x,type,
% 1.46/1.25 x: frac ).
% 1.46/1.25
% 1.46/1.25 thf(y,type,
% 1.46/1.25 y: frac ).
% 1.46/1.25
% 1.46/1.25 thf(less,type,
% 1.46/1.25 less: frac > frac > $o ).
% 1.46/1.25
% 1.46/1.25 thf(pf,type,
% 1.46/1.25 pf: frac > frac > frac ).
% 1.46/1.25
% 1.46/1.25 thf(more,type,
% 1.46/1.25 more: frac > frac > $o ).
% 1.46/1.25
% 1.46/1.25 thf(satz42,axiom,
% 1.46/1.25 ! [Xx: frac,Xy: frac] :
% 1.46/1.25 ( ( more @ Xx @ Xy )
% 1.46/1.25 => ( less @ Xy @ Xx ) ) ).
% 1.46/1.25
% 1.46/1.25 thf(satz60,axiom,
% 1.46/1.25 ! [Xx: frac,Xy: frac] : ( more @ ( pf @ Xx @ Xy ) @ Xx ) ).
% 1.46/1.25
% 1.46/1.25 thf(satz60a,conjecture,
% 1.46/1.25 less @ x @ ( pf @ x @ y ) ).
% 1.46/1.25 ------------------------
% 1.46/1.26 % (8109)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7839 for (2999ds/2Mi)
% 1.46/1.26 % (8108)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_7839 for (2999ds/27Mi)
% 1.46/1.26 % (8109)First to succeed.
% 1.46/1.26 % (8108)Also succeeded, but the first one will report.
% 1.46/1.26 % (8109)Refutation found. Thanks to Tanya!
% 1.46/1.26 % SZS status Theorem for DTF2THF_7839
% 1.46/1.26 % SZS output start Proof for DTF2THF_7839
% 1.46/1.26 thf(type_def_5, type, frac: $tType).
% 1.46/1.26 thf(func_def_0, type, frac: $tType).
% 1.46/1.26 thf(func_def_1, type, x: frac).
% 1.46/1.26 thf(func_def_2, type, y: frac).
% 1.46/1.26 thf(func_def_3, type, less: frac > frac > $o).
% 1.46/1.26 thf(func_def_4, type, pf: frac > frac > frac).
% 1.46/1.26 thf(func_def_5, type, more: frac > frac > $o).
% 1.46/1.26 thf(f20,plain,(
% 1.46/1.26 $false),
% 1.46/1.26 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.46/1.26 thf(f19,plain,(
% 1.46/1.26 ($true != $true)),
% 1.46/1.26 inference(superposition,[status(thm)],[f14,f18])).
% 1.46/1.26 thf(f18,plain,(
% 1.46/1.26 ( ! [X0 : frac,X1 : frac] : (((less @ X0 @ (pf @ X0 @ X1)) = $true)) )),
% 1.46/1.26 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.46/1.26 thf(f17,plain,(
% 1.46/1.26 ( ! [X0 : frac,X1 : frac] : (((less @ X0 @ (pf @ X0 @ X1)) = $true) | ($true != $true)) )),
% 1.46/1.26 inference(superposition,[status(thm)],[f15,f16])).
% 1.46/1.26 thf(f16,plain,(
% 1.46/1.26 ( ! [X0 : frac,X1 : frac] : (((more @ (pf @ X1 @ X0) @ X1) = $true)) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.26 thf(f9,plain,(
% 1.46/1.26 ! [X0 : frac,X1 : frac] : ((more @ (pf @ X1 @ X0) @ X1) = $true)),
% 1.46/1.26 inference(fool_elimination,[status(thm)],[f8])).
% 1.46/1.26 thf(f8,plain,(
% 1.46/1.26 ! [X0 : frac,X1 : frac] : (more @ (pf @ X1 @ X0) @ X1)),
% 1.46/1.26 inference(rectify,[status(thm)],[f2])).
% 1.46/1.26 thf(f2,axiom,(
% 1.46/1.26 ! [X1 : frac,X0 : frac] : (more @ (pf @ X0 @ X1) @ X0)),
% 1.46/1.26 file('/export/starexec/sandbox2/tmp/tmp.EU8uS0YxNP/DTF2THF_7839.p',satz60)).
% 1.46/1.26 thf(f15,plain,(
% 1.46/1.26 ( ! [X0 : frac,X1 : frac] : (((more @ X0 @ X1) != $true) | ((less @ X1 @ X0) = $true)) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.46/1.26 thf(f13,plain,(
% 1.46/1.26 ! [X0 : frac,X1 : frac] : (((more @ X0 @ X1) != $true) | ((less @ X1 @ X0) = $true))),
% 1.46/1.26 inference(ennf_transformation,[status(thm)],[f7])).
% 1.46/1.26 thf(f7,plain,(
% 1.46/1.26 ! [X1 : frac,X0 : frac] : (((more @ X0 @ X1) = $true) => ((less @ X1 @ X0) = $true))),
% 1.46/1.26 inference(fool_elimination,[status(thm)],[f6])).
% 1.46/1.26 thf(f6,plain,(
% 1.46/1.26 ! [X0 : frac,X1 : frac] : ((more @ X0 @ X1) => (less @ X1 @ X0))),
% 1.46/1.26 inference(rectify,[status(thm)],[f1])).
% 1.46/1.26 thf(f1,axiom,(
% 1.46/1.26 ! [X0 : frac,X1 : frac] : ((more @ X0 @ X1) => (less @ X1 @ X0))),
% 1.46/1.26 file('/export/starexec/sandbox2/tmp/tmp.EU8uS0YxNP/DTF2THF_7839.p',satz42)).
% 1.46/1.26 thf(f14,plain,(
% 1.46/1.26 ((less @ x @ (pf @ x @ y)) != $true)),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.46/1.26 thf(f12,plain,(
% 1.46/1.26 ((less @ x @ (pf @ x @ y)) != $true)),
% 1.46/1.26 inference(flattening,[status(thm)],[f11])).
% 1.46/1.26 thf(f11,plain,(
% 1.46/1.26 ~((less @ x @ (pf @ x @ y)) = $true)),
% 1.46/1.26 inference(fool_elimination,[status(thm)],[f10])).
% 1.46/1.26 thf(f10,plain,(
% 1.46/1.26 ~(less @ x @ (pf @ x @ y))),
% 1.46/1.26 inference(rectify,[status(thm)],[f4])).
% 1.46/1.26 thf(f4,negated_conjecture,(
% 1.46/1.26 ~(less @ x @ (pf @ x @ y))),
% 1.46/1.26 inference(negated_conjecture,[status(cth)],[f3])).
% 1.46/1.26 thf(f3,conjecture,(
% 1.46/1.26 (less @ x @ (pf @ x @ y))),
% 1.46/1.26 file('/export/starexec/sandbox2/tmp/tmp.EU8uS0YxNP/DTF2THF_7839.p',satz60a)).
% 1.46/1.26 % SZS output end Proof for DTF2THF_7839
% 1.46/1.26 % (8109)------------------------------
% 1.46/1.26 % (8109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (8109)Termination reason: Refutation
% 1.46/1.26
% 1.46/1.26 % (8109)Memory used [KB]: 5500
% 1.46/1.26 % (8109)Time elapsed: 0.003 s
% 1.46/1.26 % (8109)Instructions burned: 1 (million)
% 1.46/1.26 % (8109)------------------------------
% 1.46/1.26 % (8109)------------------------------
% 1.46/1.26 % (8105)Success in time 0.013 s
%------------------------------------------------------------------------------