%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM796^1 : 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 : n020.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 09:24:46 AM UTC 2026
% Result : Theorem 1.63s 1.30s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 18 unt; 0 typ; 2 def)
% Number of atoms : 222 ( 60 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 307 ( 38 ~; 30 |; 0 &; 222 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% 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,
z0: rat ).
thf(func_def_4,type,
u0: rat ).
thf(func_def_5,type,
less: rat > rat > $o ).
thf(func_def_7,type,
lessis: rat > rat > $o ).
thf(func_def_8,type,
pl: rat > rat > rat ).
thf(func_def_9,type,
more: rat > rat > $o ).
thf(func_def_10,type,
moreis: rat > rat > $o ).
thf(f62,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f53,f57,f61]) ).
thf(f61,plain,
spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f59,f32]) ).
thf(f32,plain,
( ( less @ x0 @ y0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( less @ x0 @ y0 )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
less @ x0 @ y0,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
less @ x0 @ y0,
file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',l) ).
thf(f59,plain,
( ( ( less @ x0 @ y0 )
!= $true )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( ( less @ x0 @ y0 )
!= $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f52,f35]) ).
thf(f35,plain,
! [X0: rat,X1: rat] :
( ( ( more @ X1 @ X0 )
= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: rat,X1: rat] :
( ( ( more @ X1 @ X0 )
= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: rat,X0: rat] :
( ( ( less @ X0 @ X1 )
= $true )
=> ( ( more @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: rat,X1: rat] :
( ( less @ X0 @ X1 )
=> ( more @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: rat,X1: rat] :
( ( less @ X0 @ X1 )
=> ( more @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz83) ).
thf(f52,plain,
( ( $true
!= ( more @ y0 @ x0 ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl0_2
<=> ( $true
= ( more @ y0 @ x0 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f57,plain,
spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f55,f36]) ).
thf(f36,plain,
( ( lessis @ z0 @ u0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( lessis @ z0 @ u0 )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
lessis @ z0 @ u0,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
lessis @ z0 @ u0,
file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',k) ).
thf(f55,plain,
( ( ( lessis @ z0 @ u0 )
!= $true )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( lessis @ z0 @ u0 )
!= $true )
| ( $true != $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f48,f37]) ).
thf(f37,plain,
! [X0: rat,X1: rat] :
( ( ( moreis @ X1 @ X0 )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: rat,X1: rat] :
( ( ( moreis @ X1 @ X0 )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: rat,X0: rat] :
( ( $true
= ( moreis @ X0 @ X1 ) )
| ( ( lessis @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: rat,X1: rat] :
( ( ( lessis @ X1 @ X0 )
= $true )
=> ( $true
= ( moreis @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: rat,X1: rat] :
( ( lessis @ X1 @ X0 )
=> ( moreis @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: rat,X0: rat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz85) ).
thf(f48,plain,
( ( $true
!= ( moreis @ u0 @ z0 ) )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl0_1
<=> ( $true
= ( moreis @ u0 @ z0 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f53,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f44,f50,f46]) ).
thf(f44,plain,
( ( $true
!= ( moreis @ u0 @ z0 ) )
| ( $true
!= ( more @ y0 @ x0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $true != $true )
| ( $true
!= ( moreis @ u0 @ z0 ) )
| ( $true
!= ( more @ y0 @ x0 ) ) ),
inference(superposition,[status(thm)],[f40,f33]) ).
thf(f33,plain,
! [X2: rat,X3: rat,X0: rat,X1: rat] :
( ( $true
= ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X3 @ X0 ) ) )
| ( ( moreis @ X1 @ X0 )
!= $true )
| ( $true
!= ( more @ X2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: rat,X1: rat,X2: rat,X3: rat] :
( ( $true
= ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X3 @ X0 ) ) )
| ( ( moreis @ X1 @ X0 )
!= $true )
| ( $true
!= ( more @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
! [X3: rat,X2: rat,X1: rat,X0: rat] :
( ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) )
| ( ( moreis @ X2 @ X3 )
!= $true )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
! [X3: rat,X2: rat,X1: rat,X0: rat] :
( ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) )
| ( ( moreis @ X2 @ X3 )
!= $true )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X3: rat,X2: rat,X1: rat,X0: rat] :
( ( ( more @ X1 @ X0 )
= $true )
=> ( ( ( moreis @ X2 @ X3 )
= $true )
=> ( $true
= ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: rat,X1: rat,X2: rat,X3: rat] :
( ( more @ X1 @ X0 )
=> ( ( moreis @ X2 @ X3 )
=> ( more @ ( pl @ X1 @ X2 ) @ ( pl @ X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: rat,X0: rat,X2: rat,X3: rat] :
( ( more @ X0 @ X1 )
=> ( ( moreis @ X2 @ X3 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz99b) ).
thf(f40,plain,
( $true
!= ( more @ ( pl @ y0 @ u0 ) @ ( pl @ x0 @ z0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true != $true )
| ( $true
!= ( more @ ( pl @ y0 @ u0 ) @ ( pl @ x0 @ z0 ) ) ) ),
inference(superposition,[status(thm)],[f34,f38]) ).
thf(f38,plain,
! [X0: rat,X1: rat] :
( ( ( less @ X0 @ X1 )
= $true )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: rat,X1: rat] :
( ( ( more @ X1 @ X0 )
!= $true )
| ( ( less @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: rat,X0: rat] :
( ( ( more @ X1 @ X0 )
= $true )
=> ( ( less @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: rat,X1: rat] :
( ( more @ X1 @ X0 )
=> ( less @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: rat,X0: rat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz82) ).
thf(f34,plain,
( ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) )
!= $true ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ),
file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz99d) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM796^1 : 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
% 0.16/0.34 % Computer : n020.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 11:14:42 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : NUM796^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Number Theory
% 0.29/0.46 % Problem : Landau theorem 99d
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : less (pl x0 z0) (pl y0 u0)
% 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 : satz99d [Lan30]
% 0.29/0.46 % : satz65d [Lan30]
% 0.29/0.46 % : satz75d [Lan30]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % : Without extensionality : Theorem
% 0.29/0.46 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 17 ( 3 unt; 10 typ; 0 def)
% 0.29/0.46 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 3 ( 1 avg)
% 0.29/0.46 % Number of connectives : 37 ( 0 ~; 0 |; 0 &; 32 @)
% 0.29/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 11 ( 6 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 9 ( 9 usr; 4 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 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(z0,type,
% 0.29/0.46 z0: rat ).
% 0.29/0.46
% 0.29/0.46 thf(u0,type,
% 0.29/0.46 u0: rat ).
% 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(l,axiom,
% 0.29/0.46 less @ x0 @ y0 ).
% 0.29/0.46
% 0.29/0.46 thf(lessis,type,
% 0.29/0.46 lessis: rat > rat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(k,axiom,
% 0.29/0.46 lessis @ z0 @ u0 ).
% 0.29/0.46
% 0.29/0.46 thf(pl,type,
% 0.29/0.46 pl: rat > rat > rat ).
% 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(satz82,axiom,
% 0.29/0.46 ! [Xx0: rat,Xy0: rat] :
% 0.29/0.46 ( ( more @ Xx0 @ Xy0 )
% 0.29/0.46 => ( less @ Xy0 @ Xx0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(moreis,type,
% 0.29/0.46 moreis: rat > rat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(satz99b,axiom,
% 0.29/0.46 ! [Xx0: rat,Xy0: rat,Xz0: rat,Xu0: rat] :
% 0.29/0.46 ( ( more @ Xx0 @ Xy0 )
% 0.29/0.46 => ( ( moreis @ Xz0 @ Xu0 )
% 0.29/0.46 => ( more @ ( pl @ Xx0 @ Xz0 ) @ ( pl @ Xy0 @ Xu0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz83,axiom,
% 0.29/0.46 ! [Xx0: rat,Xy0: rat] :
% 0.29/0.46 ( ( less @ Xx0 @ Xy0 )
% 0.29/0.46 => ( more @ Xy0 @ Xx0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz85,axiom,
% 0.29/0.46 ! [Xx0: rat,Xy0: rat] :
% 0.29/0.46 ( ( lessis @ Xx0 @ Xy0 )
% 0.29/0.46 => ( moreis @ Xy0 @ Xx0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz99d,conjecture,
% 0.29/0.46 less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 11:14:43 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2DTF18494.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.28 thf(rat_type,type,
% 1.46/1.28 rat: $tType ).
% 1.46/1.28
% 1.46/1.28 thf(x0,type,
% 1.46/1.28 x0: rat ).
% 1.46/1.28
% 1.46/1.28 thf(y0,type,
% 1.46/1.28 y0: rat ).
% 1.46/1.28
% 1.46/1.28 thf(z0,type,
% 1.46/1.28 z0: rat ).
% 1.46/1.28
% 1.46/1.28 thf(u0,type,
% 1.46/1.28 u0: rat ).
% 1.46/1.28
% 1.46/1.28 thf(less,type,
% 1.46/1.28 less: rat > rat > $o ).
% 1.46/1.28
% 1.46/1.28 thf(l,axiom,
% 1.46/1.28 less @ x0 @ y0 ).
% 1.46/1.28
% 1.46/1.28 thf(lessis,type,
% 1.46/1.28 lessis: rat > rat > $o ).
% 1.46/1.28
% 1.46/1.28 thf(k,axiom,
% 1.46/1.28 lessis @ z0 @ u0 ).
% 1.46/1.28
% 1.46/1.28 thf(pl,type,
% 1.46/1.28 pl: rat > rat > rat ).
% 1.46/1.28
% 1.46/1.28 thf(more,type,
% 1.46/1.28 more: rat > rat > $o ).
% 1.46/1.28
% 1.46/1.28 thf(satz82,axiom,
% 1.46/1.28 ! [Xx0: rat,Xy0: rat] :
% 1.46/1.28 ( ( more @ Xx0 @ Xy0 )
% 1.46/1.28 => ( less @ Xy0 @ Xx0 ) ) ).
% 1.46/1.28
% 1.46/1.28 thf(moreis,type,
% 1.46/1.28 moreis: rat > rat > $o ).
% 1.46/1.28
% 1.46/1.28 thf(satz99b,axiom,
% 1.46/1.28 ! [Xx0: rat,Xy0: rat,Xz0: rat,Xu0: rat] :
% 1.46/1.28 ( ( more @ Xx0 @ Xy0 )
% 1.46/1.28 => ( ( moreis @ Xz0 @ Xu0 )
% 1.46/1.28 => ( more @ ( pl @ Xx0 @ Xz0 ) @ ( pl @ Xy0 @ Xu0 ) ) ) ) ).
% 1.46/1.28
% 1.46/1.28 thf(satz83,axiom,
% 1.46/1.28 ! [Xx0: rat,Xy0: rat] :
% 1.46/1.28 ( ( less @ Xx0 @ Xy0 )
% 1.46/1.28 => ( more @ Xy0 @ Xx0 ) ) ).
% 1.46/1.28
% 1.46/1.28 thf(satz85,axiom,
% 1.46/1.28 ! [Xx0: rat,Xy0: rat] :
% 1.46/1.28 ( ( lessis @ Xx0 @ Xy0 )
% 1.46/1.28 => ( moreis @ Xy0 @ Xx0 ) ) ).
% 1.46/1.28
% 1.46/1.28 thf(satz99d,conjecture,
% 1.46/1.28 less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) ).
% 1.46/1.28 ------------------------
% 1.63/1.30 % (18772)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18494 for (2999ds/18Mi)
% 1.63/1.30 % (18771)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_18494 for (2999ds/275Mi)
% 1.63/1.30 % (18771)First to succeed.
% 1.63/1.30 % (18772)Also succeeded, but the first one will report.
% 1.63/1.30 % (18771)Refutation found. Thanks to Tanya!
% 1.63/1.30 % SZS status Theorem for DTF2THF_18494
% 1.63/1.30 % SZS output start Proof for DTF2THF_18494
% 1.63/1.30 thf(type_def_5, type, rat: $tType).
% 1.63/1.30 thf(func_def_0, type, rat: $tType).
% 1.63/1.30 thf(func_def_1, type, x0: rat).
% 1.63/1.30 thf(func_def_2, type, y0: rat).
% 1.63/1.30 thf(func_def_3, type, z0: rat).
% 1.63/1.30 thf(func_def_4, type, u0: rat).
% 1.63/1.30 thf(func_def_5, type, less: rat > rat > $o).
% 1.63/1.30 thf(func_def_7, type, lessis: rat > rat > $o).
% 1.63/1.30 thf(func_def_8, type, pl: rat > rat > rat).
% 1.63/1.30 thf(func_def_9, type, more: rat > rat > $o).
% 1.63/1.30 thf(func_def_10, type, moreis: rat > rat > $o).
% 1.63/1.30 thf(f62,plain,(
% 1.63/1.30 $false),
% 1.63/1.30 inference(avatar_sat_refutation,[status(thm)],[f53,f57,f61])).
% 1.63/1.30 thf(f61,plain,(
% 1.63/1.30 spl0_2),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 1.63/1.30 thf(f60,plain,(
% 1.63/1.30 $false | spl0_2),
% 1.63/1.30 inference(subsumption_resolution,[status(thm)],[f59,f32])).
% 1.63/1.30 thf(f32,plain,(
% 1.63/1.30 ((less @ x0 @ y0) = $true)),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.30 thf(f13,plain,(
% 1.63/1.30 ((less @ x0 @ y0) = $true)),
% 1.63/1.30 inference(fool_elimination,[status(thm)],[f12])).
% 1.63/1.30 thf(f12,plain,(
% 1.63/1.30 (less @ x0 @ y0)),
% 1.63/1.30 inference(rectify,[status(thm)],[f1])).
% 1.63/1.30 thf(f1,axiom,(
% 1.63/1.30 (less @ x0 @ y0)),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',l)).
% 1.63/1.30 thf(f59,plain,(
% 1.63/1.30 ((less @ x0 @ y0) != $true) | spl0_2),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.63/1.30 thf(f58,plain,(
% 1.63/1.30 ($true != $true) | ((less @ x0 @ y0) != $true) | spl0_2),
% 1.63/1.30 inference(superposition,[status(thm)],[f52,f35])).
% 1.63/1.30 thf(f35,plain,(
% 1.63/1.30 ( ! [X0 : rat,X1 : rat] : (((more @ X1 @ X0) = $true) | ((less @ X0 @ X1) != $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f25])).
% 1.63/1.30 thf(f25,plain,(
% 1.63/1.30 ! [X0 : rat,X1 : rat] : (((more @ X1 @ X0) = $true) | ((less @ X0 @ X1) != $true))),
% 1.63/1.30 inference(ennf_transformation,[status(thm)],[f23])).
% 1.63/1.30 thf(f23,plain,(
% 1.63/1.30 ! [X1 : rat,X0 : rat] : (((less @ X0 @ X1) = $true) => ((more @ X1 @ X0) = $true))),
% 1.63/1.30 inference(fool_elimination,[status(thm)],[f22])).
% 1.63/1.30 thf(f22,plain,(
% 1.63/1.30 ! [X0 : rat,X1 : rat] : ((less @ X0 @ X1) => (more @ X1 @ X0))),
% 1.63/1.30 inference(rectify,[status(thm)],[f5])).
% 1.63/1.30 thf(f5,axiom,(
% 1.63/1.30 ! [X0 : rat,X1 : rat] : ((less @ X0 @ X1) => (more @ X1 @ X0))),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz83)).
% 1.63/1.30 thf(f52,plain,(
% 1.63/1.30 ($true != (more @ y0 @ x0)) | spl0_2),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.63/1.30 thf(f50,definition,(
% 1.63/1.30 spl0_2 <=> ($true = (more @ y0 @ x0))),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.63/1.30 thf(f57,plain,(
% 1.63/1.30 spl0_1),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.63/1.30 thf(f56,plain,(
% 1.63/1.30 $false | spl0_1),
% 1.63/1.30 inference(subsumption_resolution,[status(thm)],[f55,f36])).
% 1.63/1.30 thf(f36,plain,(
% 1.63/1.30 ((lessis @ z0 @ u0) = $true)),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.30 thf(f11,plain,(
% 1.63/1.30 ((lessis @ z0 @ u0) = $true)),
% 1.63/1.30 inference(fool_elimination,[status(thm)],[f10])).
% 1.63/1.30 thf(f10,plain,(
% 1.63/1.30 (lessis @ z0 @ u0)),
% 1.63/1.30 inference(rectify,[status(thm)],[f2])).
% 1.63/1.30 thf(f2,axiom,(
% 1.63/1.30 (lessis @ z0 @ u0)),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',k)).
% 1.63/1.30 thf(f55,plain,(
% 1.63/1.30 ((lessis @ z0 @ u0) != $true) | spl0_1),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.63/1.30 thf(f54,plain,(
% 1.63/1.30 ((lessis @ z0 @ u0) != $true) | ($true != $true) | spl0_1),
% 1.63/1.30 inference(superposition,[status(thm)],[f48,f37])).
% 1.63/1.30 thf(f37,plain,(
% 1.63/1.30 ( ! [X0 : rat,X1 : rat] : (((moreis @ X1 @ X0) = $true) | ((lessis @ X0 @ X1) != $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f31])).
% 1.63/1.30 thf(f31,plain,(
% 1.63/1.30 ! [X0 : rat,X1 : rat] : (((moreis @ X1 @ X0) = $true) | ((lessis @ X0 @ X1) != $true))),
% 1.63/1.30 inference(rectify,[status(thm)],[f26])).
% 1.63/1.30 thf(f26,plain,(
% 1.63/1.30 ! [X1 : rat,X0 : rat] : (($true = (moreis @ X0 @ X1)) | ((lessis @ X1 @ X0) != $true))),
% 1.63/1.30 inference(ennf_transformation,[status(thm)],[f17])).
% 1.63/1.30 thf(f17,plain,(
% 1.63/1.30 ! [X0 : rat,X1 : rat] : (((lessis @ X1 @ X0) = $true) => ($true = (moreis @ X0 @ X1)))),
% 1.63/1.30 inference(fool_elimination,[status(thm)],[f16])).
% 1.63/1.30 thf(f16,plain,(
% 1.63/1.30 ! [X0 : rat,X1 : rat] : ((lessis @ X1 @ X0) => (moreis @ X0 @ X1))),
% 1.63/1.30 inference(rectify,[status(thm)],[f6])).
% 1.63/1.30 thf(f6,axiom,(
% 1.63/1.30 ! [X1 : rat,X0 : rat] : ((lessis @ X0 @ X1) => (moreis @ X1 @ X0))),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz85)).
% 1.63/1.30 thf(f48,plain,(
% 1.63/1.30 ($true != (moreis @ u0 @ z0)) | spl0_1),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.63/1.30 thf(f46,definition,(
% 1.63/1.30 spl0_1 <=> ($true = (moreis @ u0 @ z0))),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.63/1.30 thf(f53,plain,(
% 1.63/1.30 ~spl0_1 | ~spl0_2),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f44,f50,f46])).
% 1.63/1.30 thf(f44,plain,(
% 1.63/1.30 ($true != (moreis @ u0 @ z0)) | ($true != (more @ y0 @ x0))),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.63/1.30 thf(f41,plain,(
% 1.63/1.30 ($true != $true) | ($true != (moreis @ u0 @ z0)) | ($true != (more @ y0 @ x0))),
% 1.63/1.30 inference(superposition,[status(thm)],[f40,f33])).
% 1.63/1.30 thf(f33,plain,(
% 1.63/1.30 ( ! [X2 : rat,X3 : rat,X0 : rat,X1 : rat] : (($true = (more @ (pl @ X2 @ X1) @ (pl @ X3 @ X0))) | ((moreis @ X1 @ X0) != $true) | ($true != (more @ X2 @ X3))) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f30])).
% 1.63/1.30 thf(f30,plain,(
% 1.63/1.30 ! [X0 : rat,X1 : rat,X2 : rat,X3 : rat] : (($true = (more @ (pl @ X2 @ X1) @ (pl @ X3 @ X0))) | ((moreis @ X1 @ X0) != $true) | ($true != (more @ X2 @ X3)))),
% 1.63/1.30 inference(rectify,[status(thm)],[f28])).
% 1.63/1.30 thf(f28,plain,(
% 1.63/1.30 ! [X3 : rat,X2 : rat,X1 : rat,X0 : rat] : (($true = (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3))) | ((moreis @ X2 @ X3) != $true) | ((more @ X1 @ X0) != $true))),
% 1.63/1.30 inference(flattening,[status(thm)],[f27])).
% 1.63/1.30 thf(f27,plain,(
% 1.63/1.30 ! [X3 : rat,X2 : rat,X1 : rat,X0 : rat] : ((($true = (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3))) | ((moreis @ X2 @ X3) != $true)) | ((more @ X1 @ X0) != $true))),
% 1.63/1.30 inference(ennf_transformation,[status(thm)],[f21])).
% 1.63/1.30 thf(f21,plain,(
% 1.63/1.30 ! [X3 : rat,X2 : rat,X1 : rat,X0 : rat] : (((more @ X1 @ X0) = $true) => (((moreis @ X2 @ X3) = $true) => ($true = (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3)))))),
% 1.63/1.30 inference(fool_elimination,[status(thm)],[f20])).
% 1.63/1.30 thf(f20,plain,(
% 1.63/1.30 ! [X0 : rat,X1 : rat,X2 : rat,X3 : rat] : ((more @ X1 @ X0) => ((moreis @ X2 @ X3) => (more @ (pl @ X1 @ X2) @ (pl @ X0 @ X3))))),
% 1.63/1.30 inference(rectify,[status(thm)],[f4])).
% 1.63/1.30 thf(f4,axiom,(
% 1.63/1.30 ! [X1 : rat,X0 : rat,X2 : rat,X3 : rat] : ((more @ X0 @ X1) => ((moreis @ X2 @ X3) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))))),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz99b)).
% 1.63/1.30 thf(f40,plain,(
% 1.63/1.30 ($true != (more @ (pl @ y0 @ u0) @ (pl @ x0 @ z0)))),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.63/1.30 thf(f39,plain,(
% 1.63/1.30 ($true != $true) | ($true != (more @ (pl @ y0 @ u0) @ (pl @ x0 @ z0)))),
% 1.63/1.30 inference(superposition,[status(thm)],[f34,f38])).
% 1.63/1.30 thf(f38,plain,(
% 1.63/1.30 ( ! [X0 : rat,X1 : rat] : (((less @ X0 @ X1) = $true) | ((more @ X1 @ X0) != $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f29])).
% 1.63/1.30 thf(f29,plain,(
% 1.63/1.30 ! [X0 : rat,X1 : rat] : (((more @ X1 @ X0) != $true) | ((less @ X0 @ X1) = $true))),
% 1.63/1.30 inference(ennf_transformation,[status(thm)],[f15])).
% 1.63/1.30 thf(f15,plain,(
% 1.63/1.30 ! [X1 : rat,X0 : rat] : (((more @ X1 @ X0) = $true) => ((less @ X0 @ X1) = $true))),
% 1.63/1.30 inference(fool_elimination,[status(thm)],[f14])).
% 1.63/1.30 thf(f14,plain,(
% 1.63/1.30 ! [X0 : rat,X1 : rat] : ((more @ X1 @ X0) => (less @ X0 @ X1))),
% 1.63/1.30 inference(rectify,[status(thm)],[f3])).
% 1.63/1.30 thf(f3,axiom,(
% 1.63/1.30 ! [X1 : rat,X0 : rat] : ((more @ X0 @ X1) => (less @ X1 @ X0))),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz82)).
% 1.63/1.30 thf(f34,plain,(
% 1.63/1.30 ((less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0)) != $true)),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.30 thf(f24,plain,(
% 1.63/1.30 ((less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0)) != $true)),
% 1.63/1.30 inference(flattening,[status(thm)],[f19])).
% 1.63/1.30 thf(f19,plain,(
% 1.63/1.30 ~((less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0)) = $true)),
% 1.63/1.30 inference(fool_elimination,[status(thm)],[f18])).
% 1.63/1.30 thf(f18,plain,(
% 1.63/1.30 ~(less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))),
% 1.63/1.30 inference(rectify,[status(thm)],[f8])).
% 1.63/1.30 thf(f8,negated_conjecture,(
% 1.63/1.30 ~(less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))),
% 1.63/1.30 inference(negated_conjecture,[status(cth)],[f7])).
% 1.63/1.30 thf(f7,conjecture,(
% 1.63/1.30 (less @ (pl @ x0 @ z0) @ (pl @ y0 @ u0))),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.XyTJnrwSGl/DTF2THF_18494.p',satz99d)).
% 1.63/1.30 % SZS output end Proof for DTF2THF_18494
% 1.63/1.30 % (18771)------------------------------
% 1.63/1.30 % (18771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (18771)Termination reason: Refutation
% 1.63/1.30
% 1.63/1.30 % (18771)Memory used [KB]: 5500
% 1.63/1.30 % (18771)Time elapsed: 0.004 s
% 1.63/1.30 % (18771)Instructions burned: 3 (million)
% 1.63/1.30 % (18771)------------------------------
% 1.63/1.30 % (18771)------------------------------
% 1.63/1.30 % (18765)Success in time 0.015 s
%------------------------------------------------------------------------------