%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM789^1 : 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 : n026.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 09:24:44 AM UTC 2026
% Result : Theorem 1.47s 1.28s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 199 ( 54 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 277 ( 76 ~; 24 |; 6 &; 144 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% 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,
less: rat > rat > $o ).
thf(func_def_5,type,
more: rat > rat > $o ).
thf(func_def_6,type,
is: rat > rat > $o ).
thf(f47,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f42,f46]) ).
thf(f46,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f44,f25]) ).
thf(f25,plain,
( ( less @ x0 @ y0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( less @ x0 @ y0 )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
less @ x0 @ y0,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
less @ x0 @ y0,
file('/export/starexec/sandbox/tmp/tmp.ARmiMiHd3s/DTF2THF_6310.p',l) ).
thf(f44,plain,
( ( ( less @ x0 @ y0 )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true != $true )
| ( ( less @ x0 @ y0 )
!= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f28,f33]) ).
thf(f33,plain,
( ( ( is @ x0 @ y0 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl0_1
<=> ( ( is @ x0 @ y0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f28,plain,
! [X0: rat,X1: rat] :
( ( ( is @ X1 @ X0 )
!= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: rat,X1: rat] :
( ( ( ( less @ X1 @ X0 )
!= $true )
| ( ( is @ X1 @ X0 )
!= $true ) )
& ( ( $true
!= ( more @ X1 @ X0 ) )
| ( ( is @ X1 @ X0 )
!= $true ) )
& ( ( $true
!= ( more @ X1 @ X0 ) )
| ( ( less @ X1 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: rat,X0: rat] :
( ( ( $true
!= ( less @ X0 @ X1 ) )
| ( ( is @ X0 @ X1 )
!= $true ) )
& ( ( $true
!= ( more @ X0 @ X1 ) )
| ( ( is @ X0 @ X1 )
!= $true ) )
& ( ( $true
!= ( more @ X0 @ X1 ) )
| ( $true
!= ( less @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: rat,X1: rat] :
( ( ( $true
!= ( less @ X0 @ X1 ) )
| ( ( is @ X0 @ X1 )
!= $true ) )
& ( ( $true
!= ( more @ X0 @ X1 ) )
| ( $true
!= ( less @ X0 @ X1 ) ) )
& ( ( $true
!= ( more @ X0 @ X1 ) )
| ( ( is @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: rat,X1: rat] :
~ ( ( ( ( is @ X0 @ X1 )
= $true )
=> ( $true
!= ( more @ X0 @ X1 ) ) )
=> ( ( ( $true
= ( more @ X0 @ X1 ) )
=> ( $true
!= ( less @ X0 @ X1 ) ) )
=> ~ ( ( $true
= ( less @ X0 @ X1 ) )
=> ( ( is @ X0 @ X1 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: rat,X1: rat] :
~ ( ( ( ( is @ X0 @ X1 )
= $true )
=> ( $true
!= ( more @ X0 @ X1 ) ) )
=> ~ ~ ( ( ( $true
= ( more @ X0 @ X1 ) )
=> ( $true
!= ( less @ X0 @ X1 ) ) )
=> ~ ( ( $true
= ( less @ X0 @ X1 ) )
=> ( ( is @ X0 @ X1 )
!= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: rat,X1: rat] :
~ ( ( ( is @ X0 @ X1 )
=> ~ ( more @ X0 @ X1 ) )
=> ~ ~ ( ( ( more @ X0 @ X1 )
=> ~ ( less @ X0 @ X1 ) )
=> ~ ( ( less @ X0 @ X1 )
=> ~ ( is @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: rat,X2: rat] :
~ ( ( ( is @ X1 @ X2 )
=> ~ ( more @ X1 @ X2 ) )
=> ~ ~ ( ( ( more @ X1 @ X2 )
=> ~ ( less @ X1 @ X2 ) )
=> ~ ( ( less @ X1 @ X2 )
=> ~ ( is @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ARmiMiHd3s/DTF2THF_6310.p',satz81b) ).
thf(f42,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f40,f25]) ).
thf(f40,plain,
( ( ( less @ x0 @ y0 )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( less @ x0 @ y0 )
!= $true )
| ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f26,f37]) ).
thf(f37,plain,
( ( ( more @ x0 @ y0 )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl0_2
<=> ( ( more @ x0 @ y0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f26,plain,
! [X0: rat,X1: rat] :
( ( $true
!= ( more @ X1 @ X0 ) )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f38,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f35,f31]) ).
thf(f24,plain,
( ( ( more @ x0 @ y0 )
= $true )
| ( ( is @ x0 @ y0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( more @ x0 @ y0 )
= $true )
| ( ( is @ x0 @ y0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( more @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
~ ~ ( ( ( more @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ~ ( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ~ ( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
~ ( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
file('/export/starexec/sandbox/tmp/tmp.ARmiMiHd3s/DTF2THF_6310.p',satz81h) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM789^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.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 11:14:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : NUM789^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Number Theory
% 0.20/0.46 % Problem : Landau theorem 81h
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : ~(~(more x0 y0) -> is x0 y0)
% 0.20/0.46
% 0.20/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : satz81h [Lan30]
% 0.20/0.46 % : satz41h [Lan30]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % : Without extensionality : Theorem
% 0.20/0.46 % 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
% 0.20/0.46 % Syntax : Number of formulae : 10 ( 1 unt; 6 typ; 0 def)
% 0.20/0.46 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 6 ( 2 avg)
% 0.20/0.46 % Number of connectives : 36 ( 11 ~; 0 |; 0 &; 18 @)
% 0.20/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 13 ( 7 avg)
% 0.20/0.46 % Number of types : 2 ( 1 usr)
% 0.20/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.20/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(rat_type,type,
% 0.20/0.46 rat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(x0,type,
% 0.20/0.46 x0: rat ).
% 0.20/0.46
% 0.20/0.46 thf(y0,type,
% 0.20/0.46 y0: rat ).
% 0.20/0.46
% 0.20/0.46 thf(less,type,
% 0.20/0.46 less: rat > rat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(l,axiom,
% 0.20/0.46 less @ x0 @ y0 ).
% 0.20/0.46
% 0.20/0.46 thf(more,type,
% 0.20/0.46 more: rat > rat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(is,type,
% 0.20/0.46 is: rat > rat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(et,axiom,
% 0.20/0.46 ! [Xa: $o] :
% 0.20/0.46 ( ~ ~ Xa
% 0.20/0.46 => Xa ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz81b,axiom,
% 0.20/0.46 ! [Xx0: rat,Xy0: rat] :
% 0.20/0.46 ~ ( ( ( is @ Xx0 @ Xy0 )
% 0.20/0.46 => ~ ( more @ Xx0 @ Xy0 ) )
% 0.20/0.46 => ~ ~ ( ( ( more @ Xx0 @ Xy0 )
% 0.20/0.46 => ~ ( less @ Xx0 @ Xy0 ) )
% 0.20/0.46 => ~ ( ( less @ Xx0 @ Xy0 )
% 0.20/0.46 => ~ ( is @ Xx0 @ Xy0 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz81h,conjecture,
% 0.20/0.46 ~ ( ~ ( more @ x0 @ y0 )
% 0.20/0.46 => ( is @ x0 @ y0 ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 11:14:41 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ARmiMiHd3s/DTF2DTF6310.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(rat_type,type,
% 1.47/1.27 rat: $tType ).
% 1.47/1.27
% 1.47/1.27 thf(x0,type,
% 1.47/1.27 x0: rat ).
% 1.47/1.27
% 1.47/1.27 thf(y0,type,
% 1.47/1.27 y0: rat ).
% 1.47/1.27
% 1.47/1.27 thf(less,type,
% 1.47/1.27 less: rat > rat > $o ).
% 1.47/1.27
% 1.47/1.27 thf(l,axiom,
% 1.47/1.27 less @ x0 @ y0 ).
% 1.47/1.27
% 1.47/1.27 thf(more,type,
% 1.47/1.27 more: rat > rat > $o ).
% 1.47/1.27
% 1.47/1.27 thf(is,type,
% 1.47/1.27 is: rat > rat > $o ).
% 1.47/1.27
% 1.47/1.27 thf(et,axiom,
% 1.47/1.27 ! [Xa: $o] :
% 1.47/1.27 ( ~ ~ Xa
% 1.47/1.27 => Xa ) ).
% 1.47/1.27
% 1.47/1.27 thf(satz81b,axiom,
% 1.47/1.27 ! [Xx0: rat,Xy0: rat] :
% 1.47/1.27 ~ ( ( ( is @ Xx0 @ Xy0 )
% 1.47/1.27 => ~ ( more @ Xx0 @ Xy0 ) )
% 1.47/1.27 => ~ ~ ( ( ( more @ Xx0 @ Xy0 )
% 1.47/1.27 => ~ ( less @ Xx0 @ Xy0 ) )
% 1.47/1.27 => ~ ( ( less @ Xx0 @ Xy0 )
% 1.47/1.27 => ~ ( is @ Xx0 @ Xy0 ) ) ) ) ).
% 1.47/1.27
% 1.47/1.27 thf(satz81h,conjecture,
% 1.47/1.27 ~ ( ~ ( more @ x0 @ y0 )
% 1.47/1.27 => ( is @ x0 @ y0 ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.28 % (6416)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6310 for (3000ds/183Mi)
% 1.47/1.28 % (6422)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6310 for (3000ds/18Mi)
% 1.47/1.28 % (6416)First to succeed.
% 1.47/1.28 % (6422)Also succeeded, but the first one will report.
% 1.47/1.28 % (6416)Refutation found. Thanks to Tanya!
% 1.47/1.28 % SZS status Theorem for DTF2THF_6310
% 1.47/1.28 % SZS output start Proof for DTF2THF_6310
% 1.47/1.28 thf(type_def_5, type, rat: $tType).
% 1.47/1.28 thf(func_def_0, type, rat: $tType).
% 1.47/1.28 thf(func_def_1, type, x0: rat).
% 1.47/1.28 thf(func_def_2, type, y0: rat).
% 1.47/1.28 thf(func_def_3, type, less: rat > rat > $o).
% 1.47/1.28 thf(func_def_5, type, more: rat > rat > $o).
% 1.47/1.28 thf(func_def_6, type, is: rat > rat > $o).
% 1.47/1.28 thf(f47,plain,(
% 1.47/1.28 $false),
% 1.47/1.28 inference(avatar_sat_refutation,[status(thm)],[f38,f42,f46])).
% 1.47/1.28 thf(f46,plain,(
% 1.47/1.28 ~spl0_1),
% 1.47/1.28 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.47/1.28 thf(f45,plain,(
% 1.47/1.28 $false | ~spl0_1),
% 1.47/1.28 inference(subsumption_resolution,[status(thm)],[f44,f25])).
% 1.47/1.28 thf(f25,plain,(
% 1.47/1.28 ((less @ x0 @ y0) = $true)),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f14])).
% 1.47/1.28 thf(f14,plain,(
% 1.47/1.28 ((less @ x0 @ y0) = $true)),
% 1.47/1.28 inference(fool_elimination,[status(thm)],[f13])).
% 1.47/1.28 thf(f13,plain,(
% 1.47/1.28 (less @ x0 @ y0)),
% 1.47/1.28 inference(rectify,[status(thm)],[f1])).
% 1.47/1.28 thf(f1,axiom,(
% 1.47/1.28 (less @ x0 @ y0)),
% 1.47/1.28 file('/export/starexec/sandbox/tmp/tmp.ARmiMiHd3s/DTF2THF_6310.p',l)).
% 1.47/1.28 thf(f44,plain,(
% 1.47/1.28 ((less @ x0 @ y0) != $true) | ~spl0_1),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.47/1.28 thf(f43,plain,(
% 1.47/1.28 ($true != $true) | ((less @ x0 @ y0) != $true) | ~spl0_1),
% 1.47/1.28 inference(superposition,[status(thm)],[f28,f33])).
% 1.47/1.28 thf(f33,plain,(
% 1.47/1.28 ((is @ x0 @ y0) = $true) | ~spl0_1),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.47/1.28 thf(f31,definition,(
% 1.47/1.28 spl0_1 <=> ((is @ x0 @ y0) = $true)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.47/1.28 thf(f28,plain,(
% 1.47/1.28 ( ! [X0 : rat,X1 : rat] : (((is @ X1 @ X0) != $true) | ((less @ X1 @ X0) != $true)) )),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f22])).
% 1.47/1.28 thf(f22,plain,(
% 1.47/1.28 ! [X0 : rat,X1 : rat] : ((((less @ X1 @ X0) != $true) | ((is @ X1 @ X0) != $true)) & (($true != (more @ X1 @ X0)) | ((is @ X1 @ X0) != $true)) & (($true != (more @ X1 @ X0)) | ((less @ X1 @ X0) != $true)))),
% 1.47/1.28 inference(rectify,[status(thm)],[f19])).
% 1.47/1.28 thf(f19,plain,(
% 1.47/1.28 ! [X1 : rat,X0 : rat] : ((($true != (less @ X0 @ X1)) | ((is @ X0 @ X1) != $true)) & (($true != (more @ X0 @ X1)) | ((is @ X0 @ X1) != $true)) & (($true != (more @ X0 @ X1)) | ($true != (less @ X0 @ X1))))),
% 1.47/1.28 inference(flattening,[status(thm)],[f18])).
% 1.47/1.28 thf(f18,plain,(
% 1.47/1.28 ! [X0 : rat,X1 : rat] : (((($true != (less @ X0 @ X1)) | ((is @ X0 @ X1) != $true)) & (($true != (more @ X0 @ X1)) | ($true != (less @ X0 @ X1)))) & (($true != (more @ X0 @ X1)) | ((is @ X0 @ X1) != $true)))),
% 1.47/1.28 inference(ennf_transformation,[status(thm)],[f16])).
% 1.47/1.28 thf(f16,plain,(
% 1.47/1.28 ! [X0 : rat,X1 : rat] : ~((((is @ X0 @ X1) = $true) => ($true != (more @ X0 @ X1))) => ((($true = (more @ X0 @ X1)) => ($true != (less @ X0 @ X1))) => ~(($true = (less @ X0 @ X1)) => ((is @ X0 @ X1) != $true))))),
% 1.47/1.28 inference(flattening,[status(thm)],[f10])).
% 1.47/1.28 thf(f10,plain,(
% 1.47/1.28 ! [X0 : rat,X1 : rat] : ~((((is @ X0 @ X1) = $true) => ~($true = (more @ X0 @ X1))) => ~~((($true = (more @ X0 @ X1)) => ~($true = (less @ X0 @ X1))) => ~(($true = (less @ X0 @ X1)) => ~((is @ X0 @ X1) = $true))))),
% 1.47/1.28 inference(fool_elimination,[status(thm)],[f9])).
% 1.47/1.28 thf(f9,plain,(
% 1.47/1.28 ! [X0 : rat,X1 : rat] : ~(((is @ X0 @ X1) => ~(more @ X0 @ X1)) => ~~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => ~(is @ X0 @ X1))))),
% 1.47/1.28 inference(rectify,[status(thm)],[f3])).
% 1.47/1.28 thf(f3,axiom,(
% 1.47/1.28 ! [X1 : rat,X2 : rat] : ~(((is @ X1 @ X2) => ~(more @ X1 @ X2)) => ~~(((more @ X1 @ X2) => ~(less @ X1 @ X2)) => ~((less @ X1 @ X2) => ~(is @ X1 @ X2))))),
% 1.47/1.28 file('/export/starexec/sandbox/tmp/tmp.ARmiMiHd3s/DTF2THF_6310.p',satz81b)).
% 1.47/1.28 thf(f42,plain,(
% 1.47/1.28 ~spl0_2),
% 1.47/1.28 inference(avatar_contradiction_clause,[status(thm)],[f41])).
% 1.47/1.28 thf(f41,plain,(
% 1.47/1.28 $false | ~spl0_2),
% 1.47/1.28 inference(subsumption_resolution,[status(thm)],[f40,f25])).
% 1.47/1.28 thf(f40,plain,(
% 1.47/1.28 ((less @ x0 @ y0) != $true) | ~spl0_2),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.47/1.28 thf(f39,plain,(
% 1.47/1.28 ((less @ x0 @ y0) != $true) | ($true != $true) | ~spl0_2),
% 1.47/1.28 inference(superposition,[status(thm)],[f26,f37])).
% 1.47/1.28 thf(f37,plain,(
% 1.47/1.28 ((more @ x0 @ y0) = $true) | ~spl0_2),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.47/1.28 thf(f35,definition,(
% 1.47/1.28 spl0_2 <=> ((more @ x0 @ y0) = $true)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.47/1.28 thf(f26,plain,(
% 1.47/1.28 ( ! [X0 : rat,X1 : rat] : (($true != (more @ X1 @ X0)) | ((less @ X1 @ X0) != $true)) )),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f22])).
% 1.47/1.28 thf(f38,plain,(
% 1.47/1.28 spl0_1 | spl0_2),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f24,f35,f31])).
% 1.47/1.28 thf(f24,plain,(
% 1.47/1.28 ((more @ x0 @ y0) = $true) | ((is @ x0 @ y0) = $true)),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f21])).
% 1.47/1.28 thf(f21,plain,(
% 1.47/1.28 ((more @ x0 @ y0) = $true) | ((is @ x0 @ y0) = $true)),
% 1.47/1.28 inference(ennf_transformation,[status(thm)],[f17])).
% 1.47/1.28 thf(f17,plain,(
% 1.47/1.28 ((more @ x0 @ y0) != $true) => ((is @ x0 @ y0) = $true)),
% 1.47/1.28 inference(flattening,[status(thm)],[f12])).
% 1.47/1.28 thf(f12,plain,(
% 1.47/1.28 ~~(~((more @ x0 @ y0) = $true) => ((is @ x0 @ y0) = $true))),
% 1.47/1.28 inference(fool_elimination,[status(thm)],[f11])).
% 1.47/1.28 thf(f11,plain,(
% 1.47/1.28 ~~(~(more @ x0 @ y0) => (is @ x0 @ y0))),
% 1.47/1.28 inference(rectify,[status(thm)],[f5])).
% 1.47/1.28 thf(f5,negated_conjecture,(
% 1.47/1.28 ~~(~(more @ x0 @ y0) => (is @ x0 @ y0))),
% 1.47/1.28 inference(negated_conjecture,[status(cth)],[f4])).
% 1.47/1.28 thf(f4,conjecture,(
% 1.47/1.28 ~(~(more @ x0 @ y0) => (is @ x0 @ y0))),
% 1.47/1.28 file('/export/starexec/sandbox/tmp/tmp.ARmiMiHd3s/DTF2THF_6310.p',satz81h)).
% 1.47/1.28 % SZS output end Proof for DTF2THF_6310
% 1.47/1.28 % (6416)------------------------------
% 1.47/1.28 % (6416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (6416)Termination reason: Refutation
% 1.47/1.28
% 1.47/1.28 % (6416)Memory used [KB]: 5500
% 1.47/1.28 % (6416)Time elapsed: 0.003 s
% 1.47/1.28 % (6416)Instructions burned: 2 (million)
% 1.47/1.28 % (6416)------------------------------
% 1.47/1.28 % (6416)------------------------------
% 1.47/1.28 % (6415)Success in time 0.003 s
%------------------------------------------------------------------------------