%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM746^1 : 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 : n025.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 09:24:31 AM UTC 2026
% Result : Theorem 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 3 unt; 0 typ; 4 def)
% Number of atoms : 446 ( 124 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 541 ( 116 ~; 68 |; 6 &; 304 @)
% ( 4 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 77 ( 0 ^; 77 !; 0 ?; 77 :)
% 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,
z: frac ).
thf(func_def_4,type,
lessf: frac > frac > $o ).
thf(func_def_5,type,
eq: frac > frac > $o ).
thf(f132,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f61,f70,f76,f90,f101,f131]) ).
thf(f131,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f130]) ).
thf(f130,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f128,f69]) ).
thf(f69,plain,
( ( ( eq @ y @ z )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl0_4
<=> ( ( eq @ y @ z )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f128,plain,
( ( ( eq @ y @ z )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ( ( eq @ y @ z )
!= $true )
| ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f125,f60]) ).
thf(f60,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl0_2
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f125,plain,
! [X0: frac] :
( ( $true
!= ( eq @ x @ X0 ) )
| ( $true
!= ( eq @ X0 @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
! [X0: frac] :
( ( $true
!= ( eq @ x @ X0 ) )
| ( $true != $true )
| ( $true
!= ( eq @ X0 @ z ) ) ),
inference(superposition,[status(thm)],[f47,f46]) ).
thf(f46,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ X2 @ X0 ) )
| ( $true
!= ( eq @ X2 @ X1 ) )
| ( $true
!= ( eq @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( eq @ X2 @ X0 ) )
| ( $true
!= ( eq @ X2 @ X1 ) )
| ( $true
!= ( eq @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X1 @ X2 )
= $true )
| ( $true
!= ( eq @ X1 @ X0 ) )
| ( $true
!= ( eq @ X0 @ X2 ) ) ),
inference(flattening,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X1 @ X2 )
= $true )
| ( $true
!= ( eq @ X0 @ X2 ) )
| ( $true
!= ( eq @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ X1 @ X0 ) )
=> ( ( $true
= ( eq @ X0 @ X2 ) )
=> ( ( eq @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X1 @ X0 )
=> ( ( eq @ X0 @ X2 )
=> ( eq @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: frac,X1: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',satz39) ).
thf(f47,plain,
( ( eq @ x @ z )
!= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( lessf @ x @ z )
!= $true )
& ( ( eq @ x @ z )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
~ ( ( ( lessf @ x @ z )
!= $true )
=> ( ( eq @ x @ z )
= $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
~ ( ( ( lessf @ x @ z )
!= $true )
=> ( ( eq @ x @ z )
= $true ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',satz52) ).
thf(f101,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f100,f67,f54]) ).
thf(f54,definition,
( spl0_1
<=> ( ( lessf @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f100,plain,
( ( ( lessf @ x @ y )
!= $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( ( lessf @ x @ y )
!= $true )
| ( $true != $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f78,f69]) ).
thf(f78,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ z ) )
| ( $true
!= ( lessf @ x @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ z ) )
| ( $true
!= ( lessf @ x @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f48,f44]) ).
thf(f44,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( lessf @ X2 @ X0 ) )
| ( ( lessf @ X2 @ X1 )
!= $true )
| ( $true
!= ( eq @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X2 @ X1 )
!= $true )
| ( $true
= ( lessf @ X2 @ X0 ) )
| ( ( $true
!= ( lessf @ X1 @ X0 ) )
& ( $true
!= ( eq @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( lessf @ X1 @ X0 ) )
| ( ( lessf @ X1 @ X2 )
= $true )
| ( ( $true
!= ( lessf @ X0 @ X2 ) )
& ( $true
!= ( eq @ X0 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( ( lessf @ X1 @ X2 )
= $true )
| ( ( $true
!= ( lessf @ X0 @ X2 ) )
& ( $true
!= ( eq @ X0 @ X2 ) ) )
| ( $true
!= ( lessf @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( $true
= ( lessf @ X1 @ X0 ) )
=> ( ( ( $true
!= ( lessf @ X0 @ X2 ) )
=> ( $true
= ( eq @ X0 @ X2 ) ) )
=> ( ( lessf @ X1 @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( lessf @ X1 @ X0 ) )
=> ( ( ( $true
!= ( lessf @ X0 @ X2 ) )
=> ( $true
= ( eq @ X0 @ X2 ) ) )
=> ( ( lessf @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X1 @ X0 )
=> ( ( ~ ( lessf @ X0 @ X2 )
=> ( eq @ X0 @ X2 ) )
=> ( lessf @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: frac,X1: frac,X3: frac] :
( ( lessf @ X1 @ X2 )
=> ( ( ~ ( lessf @ X2 @ X3 )
=> ( eq @ X2 @ X3 ) )
=> ( lessf @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',satz51b) ).
thf(f48,plain,
( ( lessf @ x @ z )
!= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f90,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f85,f65]) ).
thf(f65,plain,
( ( ( lessf @ y @ z )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl0_3
<=> ( ( lessf @ y @ z )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f85,plain,
( ( ( lessf @ y @ z )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true != $true )
| ( ( lessf @ y @ z )
!= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f80,f56]) ).
thf(f56,plain,
( ( ( lessf @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f80,plain,
! [X0: frac] :
( ( $true
!= ( lessf @ x @ X0 ) )
| ( $true
!= ( lessf @ X0 @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X0: frac] :
( ( $true
!= ( lessf @ x @ X0 ) )
| ( $true != $true )
| ( $true
!= ( lessf @ X0 @ z ) ) ),
inference(superposition,[status(thm)],[f48,f45]) ).
thf(f45,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( lessf @ X2 @ X0 ) )
| ( ( lessf @ X2 @ X1 )
!= $true )
| ( $true
!= ( lessf @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f76,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f75]) ).
thf(f75,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f74,f65]) ).
thf(f74,plain,
( ( ( lessf @ y @ z )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true != $true )
| ( ( lessf @ y @ z )
!= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f72,f60]) ).
thf(f72,plain,
! [X0: frac] :
( ( $true
!= ( eq @ x @ X0 ) )
| ( $true
!= ( lessf @ X0 @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true
!= ( lessf @ X0 @ z ) )
| ( $true
!= ( eq @ x @ X0 ) ) ),
inference(superposition,[status(thm)],[f48,f42]) ).
thf(f42,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( lessf @ X2 @ X1 )
= $true )
| ( $true
!= ( lessf @ X0 @ X1 ) )
| ( $true
!= ( eq @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X2 @ X1 )
= $true )
| ( $true
!= ( lessf @ X0 @ X1 ) )
| ( ( $true
!= ( lessf @ X2 @ X0 ) )
& ( $true
!= ( eq @ X2 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( ( lessf @ X2 @ X1 )
= $true )
| ( $true
!= ( lessf @ X0 @ X1 ) )
| ( ( $true
!= ( lessf @ X2 @ X0 ) )
& ( $true
!= ( eq @ X2 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( ( $true
!= ( lessf @ X2 @ X0 ) )
=> ( $true
= ( eq @ X2 @ X0 ) ) )
=> ( ( $true
= ( lessf @ X0 @ X1 ) )
=> ( ( lessf @ X2 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( $true
!= ( lessf @ X2 @ X0 ) )
=> ( $true
= ( eq @ X2 @ X0 ) ) )
=> ( ( $true
= ( lessf @ X0 @ X1 ) )
=> ( ( lessf @ X2 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ~ ( lessf @ X2 @ X0 )
=> ( eq @ X2 @ X0 ) )
=> ( ( lessf @ X0 @ X1 )
=> ( lessf @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X2: frac,X3: frac,X1: frac] :
( ( ~ ( lessf @ X1 @ X2 )
=> ( eq @ X1 @ X2 ) )
=> ( ( lessf @ X2 @ X3 )
=> ( lessf @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',satz51a) ).
thf(f70,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f50,f67,f63]) ).
thf(f50,plain,
( ( ( eq @ y @ z )
= $true )
| ( ( lessf @ y @ z )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( lessf @ y @ z )
= $true )
| ( ( eq @ y @ z )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( lessf @ y @ z )
!= $true )
=> ( ( eq @ y @ z )
= $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( lessf @ y @ z )
!= $true )
=> ( ( eq @ y @ z )
= $true ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',k) ).
thf(f61,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f49,f58,f54]) ).
thf(f49,plain,
( ( ( lessf @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( lessf @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',l) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM746^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n025.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 11:12:43 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : NUM746^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Number Theory
% 0.28/0.46 % Problem : Landau theorem 52
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : ~(lessf x z) -> eq x z
% 0.28/0.46
% 0.28/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.28/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.28/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : satz52 [Lan30]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % : Without extensionality : Theorem
% 0.28/0.46 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 13 ( 0 unt; 6 typ; 0 def)
% 0.28/0.46 % Number of atoms : 17 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 4 ( 2 avg)
% 0.28/0.46 % Number of connectives : 53 ( 7 ~; 0 |; 0 &; 34 @)
% 0.28/0.46 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 10 ( 7 avg)
% 0.28/0.46 % Number of types : 2 ( 1 usr)
% 0.28/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments :
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(frac_type,type,
% 0.28/0.46 frac: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(x,type,
% 0.28/0.46 x: frac ).
% 0.28/0.46
% 0.28/0.46 thf(y,type,
% 0.28/0.46 y: frac ).
% 0.28/0.46
% 0.28/0.46 thf(z,type,
% 0.28/0.46 z: frac ).
% 0.28/0.46
% 0.28/0.46 thf(lessf,type,
% 0.28/0.46 lessf: frac > frac > $o ).
% 0.28/0.46
% 0.28/0.46 thf(eq,type,
% 0.28/0.46 eq: frac > frac > $o ).
% 0.28/0.46
% 0.28/0.46 thf(l,axiom,
% 0.28/0.46 ( ~ ( lessf @ x @ y )
% 0.28/0.46 => ( eq @ x @ y ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(k,axiom,
% 0.28/0.46 ( ~ ( lessf @ y @ z )
% 0.28/0.46 => ( eq @ y @ z ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(et,axiom,
% 0.28/0.46 ! [Xa: $o] :
% 0.28/0.46 ( ~ ~ Xa
% 0.28/0.46 => Xa ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz39,axiom,
% 0.28/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.28/0.46 ( ( eq @ Xx @ Xy )
% 0.28/0.46 => ( ( eq @ Xy @ Xz )
% 0.28/0.46 => ( eq @ Xx @ Xz ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz51b,axiom,
% 0.28/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.28/0.46 ( ( lessf @ Xx @ Xy )
% 0.28/0.46 => ( ( ~ ( lessf @ Xy @ Xz )
% 0.28/0.46 => ( eq @ Xy @ Xz ) )
% 0.28/0.46 => ( lessf @ Xx @ Xz ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz51a,axiom,
% 0.28/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.28/0.46 ( ( ~ ( lessf @ Xx @ Xy )
% 0.28/0.46 => ( eq @ Xx @ Xy ) )
% 0.28/0.46 => ( ( lessf @ Xy @ Xz )
% 0.28/0.46 => ( lessf @ Xx @ Xz ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz52,conjecture,
% 0.28/0.46 ( ~ ( lessf @ x @ z )
% 0.28/0.46 => ( eq @ x @ z ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 11:12:43 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2DTF19615.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(frac_type,type,
% 1.49/1.25 frac: $tType ).
% 1.49/1.25
% 1.49/1.25 thf(x,type,
% 1.49/1.25 x: frac ).
% 1.49/1.25
% 1.49/1.25 thf(y,type,
% 1.49/1.25 y: frac ).
% 1.49/1.25
% 1.49/1.25 thf(z,type,
% 1.49/1.25 z: frac ).
% 1.49/1.25
% 1.49/1.25 thf(lessf,type,
% 1.49/1.25 lessf: frac > frac > $o ).
% 1.49/1.25
% 1.49/1.25 thf(eq,type,
% 1.49/1.25 eq: frac > frac > $o ).
% 1.49/1.25
% 1.49/1.25 thf(l,axiom,
% 1.49/1.25 ( ~ ( lessf @ x @ y )
% 1.49/1.25 => ( eq @ x @ y ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(k,axiom,
% 1.49/1.25 ( ~ ( lessf @ y @ z )
% 1.49/1.25 => ( eq @ y @ z ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(et,axiom,
% 1.49/1.25 ! [Xa: $o] :
% 1.49/1.25 ( ~ ~ Xa
% 1.49/1.25 => Xa ) ).
% 1.49/1.25
% 1.49/1.25 thf(satz39,axiom,
% 1.49/1.25 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.49/1.25 ( ( eq @ Xx @ Xy )
% 1.49/1.25 => ( ( eq @ Xy @ Xz )
% 1.49/1.25 => ( eq @ Xx @ Xz ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(satz51b,axiom,
% 1.49/1.25 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.49/1.25 ( ( lessf @ Xx @ Xy )
% 1.49/1.25 => ( ( ~ ( lessf @ Xy @ Xz )
% 1.49/1.25 => ( eq @ Xy @ Xz ) )
% 1.49/1.25 => ( lessf @ Xx @ Xz ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(satz51a,axiom,
% 1.49/1.25 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.49/1.25 ( ( ~ ( lessf @ Xx @ Xy )
% 1.49/1.25 => ( eq @ Xx @ Xy ) )
% 1.49/1.25 => ( ( lessf @ Xy @ Xz )
% 1.49/1.25 => ( lessf @ Xx @ Xz ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(satz52,conjecture,
% 1.49/1.25 ( ~ ( lessf @ x @ z )
% 1.49/1.25 => ( eq @ x @ z ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.27 % (19888)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19615 for (3000ds/183Mi)
% 1.49/1.27 % (19889)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_19615 for (3000ds/4Mi)
% 1.49/1.28 % (19891)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19615 for (3000ds/2Mi)
% 1.49/1.28 % (19890)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_19615 for (3000ds/27Mi)
% 1.49/1.28 % (19892)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_19615 for (3000ds/2Mi)
% 1.49/1.28 % (19894)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19615 for (3000ds/18Mi)
% 1.49/1.28 % (19893)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_19615 for (3000ds/275Mi)
% 1.49/1.28 % (19889)Instruction limit reached!
% 1.49/1.28 % (19889)------------------------------
% 1.49/1.28 % (19889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (19889)Termination reason: Unknown
% 1.49/1.28 % (19889)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (19889)Memory used [KB]: 5500
% 1.49/1.28 % (19889)Time elapsed: 0.004 s
% 1.49/1.28 % (19889)Instructions burned: 4 (million)
% 1.49/1.28 % (19889)------------------------------
% 1.49/1.28 % (19889)------------------------------
% 1.49/1.28 % (19891)Instruction limit reached!
% 1.49/1.28 % (19891)------------------------------
% 1.49/1.28 % (19891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (19891)Termination reason: Unknown
% 1.49/1.28 % (19891)Termination phase: Property scanning
% 1.49/1.28
% 1.49/1.28 % (19891)Memory used [KB]: 895
% 1.49/1.28 % (19891)Time elapsed: 0.003 s
% 1.49/1.28 % (19891)Instructions burned: 2 (million)
% 1.49/1.28 % (19891)------------------------------
% 1.49/1.28 % (19891)------------------------------
% 1.49/1.28 % (19892)Instruction limit reached!
% 1.49/1.28 % (19892)------------------------------
% 1.49/1.28 % (19892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (19892)Termination reason: Unknown
% 1.49/1.28 % (19892)Termination phase: Property scanning
% 1.49/1.28
% 1.49/1.28 % (19892)Memory used [KB]: 895
% 1.49/1.28 % (19892)Time elapsed: 0.003 s
% 1.49/1.28 % (19892)Instructions burned: 2 (million)
% 1.49/1.28 % (19892)------------------------------
% 1.49/1.28 % (19892)------------------------------
% 1.49/1.28 % (19888)First to succeed.
% 1.49/1.28 % (19888)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Theorem for DTF2THF_19615
% 1.49/1.28 % SZS output start Proof for DTF2THF_19615
% 1.49/1.28 thf(type_def_5, type, frac: $tType).
% 1.49/1.28 thf(func_def_0, type, frac: $tType).
% 1.49/1.28 thf(func_def_1, type, x: frac).
% 1.49/1.28 thf(func_def_2, type, y: frac).
% 1.49/1.28 thf(func_def_3, type, z: frac).
% 1.49/1.28 thf(func_def_4, type, lessf: frac > frac > $o).
% 1.49/1.28 thf(func_def_5, type, eq: frac > frac > $o).
% 1.49/1.28 thf(f132,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(avatar_sat_refutation,[status(thm)],[f61,f70,f76,f90,f101,f131])).
% 1.49/1.28 thf(f131,plain,(
% 1.49/1.28 ~spl0_2 | ~spl0_4),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f130])).
% 1.49/1.28 thf(f130,plain,(
% 1.49/1.28 $false | (~spl0_2 | ~spl0_4)),
% 1.49/1.28 inference(subsumption_resolution,[status(thm)],[f128,f69])).
% 1.49/1.28 thf(f69,plain,(
% 1.49/1.28 ((eq @ y @ z) = $true) | ~spl0_4),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.49/1.28 thf(f67,definition,(
% 1.49/1.28 spl0_4 <=> ((eq @ y @ z) = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.49/1.28 thf(f128,plain,(
% 1.49/1.28 ((eq @ y @ z) != $true) | ~spl0_2),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.49/1.28 thf(f126,plain,(
% 1.49/1.28 ((eq @ y @ z) != $true) | ($true != $true) | ~spl0_2),
% 1.49/1.28 inference(superposition,[status(thm)],[f125,f60])).
% 1.49/1.28 thf(f60,plain,(
% 1.49/1.28 ((eq @ x @ y) = $true) | ~spl0_2),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.49/1.28 thf(f58,definition,(
% 1.49/1.28 spl0_2 <=> ((eq @ x @ y) = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.49/1.28 thf(f125,plain,(
% 1.49/1.28 ( ! [X0 : frac] : (($true != (eq @ x @ X0)) | ($true != (eq @ X0 @ z))) )),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.49/1.28 thf(f120,plain,(
% 1.49/1.28 ( ! [X0 : frac] : (($true != (eq @ x @ X0)) | ($true != $true) | ($true != (eq @ X0 @ z))) )),
% 1.49/1.28 inference(superposition,[status(thm)],[f47,f46])).
% 1.49/1.28 thf(f46,plain,(
% 1.49/1.28 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (eq @ X2 @ X0)) | ($true != (eq @ X2 @ X1)) | ($true != (eq @ X1 @ X0))) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f41])).
% 1.49/1.28 thf(f41,plain,(
% 1.49/1.28 ! [X0 : frac,X1 : frac,X2 : frac] : (($true = (eq @ X2 @ X0)) | ($true != (eq @ X2 @ X1)) | ($true != (eq @ X1 @ X0)))),
% 1.49/1.28 inference(rectify,[status(thm)],[f32])).
% 1.49/1.28 thf(f32,plain,(
% 1.49/1.28 ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X1 @ X2) = $true) | ($true != (eq @ X1 @ X0)) | ($true != (eq @ X0 @ X2)))),
% 1.49/1.28 inference(flattening,[status(thm)],[f31])).
% 1.49/1.28 thf(f31,plain,(
% 1.49/1.28 ! [X2 : frac,X0 : frac,X1 : frac] : ((((eq @ X1 @ X2) = $true) | ($true != (eq @ X0 @ X2))) | ($true != (eq @ X1 @ X0)))),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f17])).
% 1.49/1.28 thf(f17,plain,(
% 1.49/1.28 ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (eq @ X1 @ X0)) => (($true = (eq @ X0 @ X2)) => ((eq @ X1 @ X2) = $true)))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f16])).
% 1.49/1.28 thf(f16,plain,(
% 1.49/1.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X1 @ X0) => ((eq @ X0 @ X2) => (eq @ X1 @ X2)))),
% 1.49/1.28 inference(rectify,[status(thm)],[f4])).
% 1.49/1.28 thf(f4,axiom,(
% 1.49/1.28 ! [X2 : frac,X1 : frac,X3 : frac] : ((eq @ X1 @ X2) => ((eq @ X2 @ X3) => (eq @ X1 @ X3)))),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',satz39)).
% 1.49/1.28 thf(f47,plain,(
% 1.49/1.28 ((eq @ x @ z) != $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f30])).
% 1.49/1.28 thf(f30,plain,(
% 1.49/1.28 ((lessf @ x @ z) != $true) & ((eq @ x @ z) != $true)),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f28])).
% 1.49/1.28 thf(f28,plain,(
% 1.49/1.28 ~(((lessf @ x @ z) != $true) => ((eq @ x @ z) = $true))),
% 1.49/1.28 inference(flattening,[status(thm)],[f21])).
% 1.49/1.28 thf(f21,plain,(
% 1.49/1.28 ~(~((lessf @ x @ z) = $true) => ((eq @ x @ z) = $true))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f20])).
% 1.49/1.28 thf(f20,plain,(
% 1.49/1.28 ~(~(lessf @ x @ z) => (eq @ x @ z))),
% 1.49/1.28 inference(rectify,[status(thm)],[f8])).
% 1.49/1.28 thf(f8,negated_conjecture,(
% 1.49/1.28 ~(~(lessf @ x @ z) => (eq @ x @ z))),
% 1.49/1.28 inference(negated_conjecture,[status(cth)],[f7])).
% 1.49/1.28 thf(f7,conjecture,(
% 1.49/1.28 ~(lessf @ x @ z) => (eq @ x @ z)),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',satz52)).
% 1.49/1.28 thf(f101,plain,(
% 1.49/1.28 ~spl0_1 | ~spl0_4),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f100,f67,f54])).
% 1.49/1.28 thf(f54,definition,(
% 1.49/1.28 spl0_1 <=> ((lessf @ x @ y) = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.49/1.28 thf(f100,plain,(
% 1.49/1.28 ((lessf @ x @ y) != $true) | ~spl0_4),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.49/1.28 thf(f99,plain,(
% 1.49/1.28 ((lessf @ x @ y) != $true) | ($true != $true) | ~spl0_4),
% 1.49/1.28 inference(superposition,[status(thm)],[f78,f69])).
% 1.49/1.28 thf(f78,plain,(
% 1.49/1.28 ( ! [X0 : frac] : (($true != (eq @ X0 @ z)) | ($true != (lessf @ x @ X0))) )),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.49/1.28 thf(f77,plain,(
% 1.49/1.28 ( ! [X0 : frac] : (($true != (eq @ X0 @ z)) | ($true != (lessf @ x @ X0)) | ($true != $true)) )),
% 1.49/1.28 inference(superposition,[status(thm)],[f48,f44])).
% 1.49/1.28 thf(f44,plain,(
% 1.49/1.28 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (lessf @ X2 @ X0)) | ((lessf @ X2 @ X1) != $true) | ($true != (eq @ X1 @ X0))) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f40])).
% 1.49/1.28 thf(f40,plain,(
% 1.49/1.28 ! [X0 : frac,X1 : frac,X2 : frac] : (((lessf @ X2 @ X1) != $true) | ($true = (lessf @ X2 @ X0)) | (($true != (lessf @ X1 @ X0)) & ($true != (eq @ X1 @ X0))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f38])).
% 1.49/1.28 thf(f38,plain,(
% 1.49/1.28 ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (lessf @ X1 @ X0)) | ((lessf @ X1 @ X2) = $true) | (($true != (lessf @ X0 @ X2)) & ($true != (eq @ X0 @ X2))))),
% 1.49/1.28 inference(flattening,[status(thm)],[f37])).
% 1.49/1.28 thf(f37,plain,(
% 1.49/1.28 ! [X0 : frac,X2 : frac,X1 : frac] : ((((lessf @ X1 @ X2) = $true) | (($true != (lessf @ X0 @ X2)) & ($true != (eq @ X0 @ X2)))) | ($true != (lessf @ X1 @ X0)))),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f25])).
% 1.49/1.28 thf(f25,plain,(
% 1.49/1.28 ! [X0 : frac,X2 : frac,X1 : frac] : (($true = (lessf @ X1 @ X0)) => ((($true != (lessf @ X0 @ X2)) => ($true = (eq @ X0 @ X2))) => ((lessf @ X1 @ X2) = $true)))),
% 1.49/1.28 inference(flattening,[status(thm)],[f13])).
% 1.49/1.28 thf(f13,plain,(
% 1.49/1.28 ! [X0 : frac,X1 : frac,X2 : frac] : (($true = (lessf @ X1 @ X0)) => ((~($true = (lessf @ X0 @ X2)) => ($true = (eq @ X0 @ X2))) => ((lessf @ X1 @ X2) = $true)))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f12])).
% 1.49/1.28 thf(f12,plain,(
% 1.49/1.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X1 @ X0) => ((~(lessf @ X0 @ X2) => (eq @ X0 @ X2)) => (lessf @ X1 @ X2)))),
% 1.49/1.28 inference(rectify,[status(thm)],[f5])).
% 1.49/1.28 thf(f5,axiom,(
% 1.49/1.28 ! [X2 : frac,X1 : frac,X3 : frac] : ((lessf @ X1 @ X2) => ((~(lessf @ X2 @ X3) => (eq @ X2 @ X3)) => (lessf @ X1 @ X3)))),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',satz51b)).
% 1.49/1.28 thf(f48,plain,(
% 1.49/1.28 ((lessf @ x @ z) != $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f30])).
% 1.49/1.28 thf(f90,plain,(
% 1.49/1.28 ~spl0_1 | ~spl0_3),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f89])).
% 1.49/1.28 thf(f89,plain,(
% 1.49/1.28 $false | (~spl0_1 | ~spl0_3)),
% 1.49/1.28 inference(subsumption_resolution,[status(thm)],[f85,f65])).
% 1.49/1.28 thf(f65,plain,(
% 1.49/1.28 ((lessf @ y @ z) = $true) | ~spl0_3),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.49/1.28 thf(f63,definition,(
% 1.49/1.28 spl0_3 <=> ((lessf @ y @ z) = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.49/1.28 thf(f85,plain,(
% 1.49/1.28 ((lessf @ y @ z) != $true) | ~spl0_1),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.49/1.28 thf(f81,plain,(
% 1.49/1.28 ($true != $true) | ((lessf @ y @ z) != $true) | ~spl0_1),
% 1.49/1.28 inference(superposition,[status(thm)],[f80,f56])).
% 1.49/1.28 thf(f56,plain,(
% 1.49/1.28 ((lessf @ x @ y) = $true) | ~spl0_1),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.49/1.28 thf(f80,plain,(
% 1.49/1.28 ( ! [X0 : frac] : (($true != (lessf @ x @ X0)) | ($true != (lessf @ X0 @ z))) )),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.49/1.28 thf(f79,plain,(
% 1.49/1.28 ( ! [X0 : frac] : (($true != (lessf @ x @ X0)) | ($true != $true) | ($true != (lessf @ X0 @ z))) )),
% 1.49/1.28 inference(superposition,[status(thm)],[f48,f45])).
% 1.49/1.28 thf(f45,plain,(
% 1.49/1.28 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (lessf @ X2 @ X0)) | ((lessf @ X2 @ X1) != $true) | ($true != (lessf @ X1 @ X0))) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f40])).
% 1.49/1.28 thf(f76,plain,(
% 1.49/1.28 ~spl0_2 | ~spl0_3),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f75])).
% 1.49/1.28 thf(f75,plain,(
% 1.49/1.28 $false | (~spl0_2 | ~spl0_3)),
% 1.49/1.28 inference(subsumption_resolution,[status(thm)],[f74,f65])).
% 1.49/1.28 thf(f74,plain,(
% 1.49/1.28 ((lessf @ y @ z) != $true) | ~spl0_2),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.49/1.28 thf(f73,plain,(
% 1.49/1.28 ($true != $true) | ((lessf @ y @ z) != $true) | ~spl0_2),
% 1.49/1.28 inference(superposition,[status(thm)],[f72,f60])).
% 1.49/1.28 thf(f72,plain,(
% 1.49/1.28 ( ! [X0 : frac] : (($true != (eq @ x @ X0)) | ($true != (lessf @ X0 @ z))) )),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.49/1.28 thf(f71,plain,(
% 1.49/1.28 ( ! [X0 : frac] : (($true != $true) | ($true != (lessf @ X0 @ z)) | ($true != (eq @ x @ X0))) )),
% 1.49/1.28 inference(superposition,[status(thm)],[f48,f42])).
% 1.49/1.28 thf(f42,plain,(
% 1.49/1.28 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((lessf @ X2 @ X1) = $true) | ($true != (lessf @ X0 @ X1)) | ($true != (eq @ X2 @ X0))) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f34])).
% 1.49/1.28 thf(f34,plain,(
% 1.49/1.28 ! [X0 : frac,X1 : frac,X2 : frac] : (((lessf @ X2 @ X1) = $true) | ($true != (lessf @ X0 @ X1)) | (($true != (lessf @ X2 @ X0)) & ($true != (eq @ X2 @ X0))))),
% 1.49/1.28 inference(flattening,[status(thm)],[f33])).
% 1.49/1.28 thf(f33,plain,(
% 1.49/1.28 ! [X1 : frac,X0 : frac,X2 : frac] : ((((lessf @ X2 @ X1) = $true) | ($true != (lessf @ X0 @ X1))) | (($true != (lessf @ X2 @ X0)) & ($true != (eq @ X2 @ X0))))),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f26])).
% 1.49/1.28 thf(f26,plain,(
% 1.49/1.28 ! [X1 : frac,X0 : frac,X2 : frac] : ((($true != (lessf @ X2 @ X0)) => ($true = (eq @ X2 @ X0))) => (($true = (lessf @ X0 @ X1)) => ((lessf @ X2 @ X1) = $true)))),
% 1.49/1.28 inference(flattening,[status(thm)],[f15])).
% 1.49/1.28 thf(f15,plain,(
% 1.49/1.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((~($true = (lessf @ X2 @ X0)) => ($true = (eq @ X2 @ X0))) => (($true = (lessf @ X0 @ X1)) => ((lessf @ X2 @ X1) = $true)))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f14])).
% 1.49/1.28 thf(f14,plain,(
% 1.49/1.28 ! [X0 : frac,X1 : frac,X2 : frac] : ((~(lessf @ X2 @ X0) => (eq @ X2 @ X0)) => ((lessf @ X0 @ X1) => (lessf @ X2 @ X1)))),
% 1.49/1.28 inference(rectify,[status(thm)],[f6])).
% 1.49/1.28 thf(f6,axiom,(
% 1.49/1.28 ! [X2 : frac,X3 : frac,X1 : frac] : ((~(lessf @ X1 @ X2) => (eq @ X1 @ X2)) => ((lessf @ X2 @ X3) => (lessf @ X1 @ X3)))),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',satz51a)).
% 1.49/1.28 thf(f70,plain,(
% 1.49/1.28 spl0_3 | spl0_4),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f50,f67,f63])).
% 1.49/1.28 thf(f50,plain,(
% 1.49/1.28 ((eq @ y @ z) = $true) | ((lessf @ y @ z) = $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f36])).
% 1.49/1.28 thf(f36,plain,(
% 1.49/1.28 ((lessf @ y @ z) = $true) | ((eq @ y @ z) = $true)),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f29])).
% 1.49/1.28 thf(f29,plain,(
% 1.49/1.28 ((lessf @ y @ z) != $true) => ((eq @ y @ z) = $true)),
% 1.49/1.28 inference(flattening,[status(thm)],[f23])).
% 1.49/1.28 thf(f23,plain,(
% 1.49/1.28 ~((lessf @ y @ z) = $true) => ((eq @ y @ z) = $true)),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f22])).
% 1.49/1.28 thf(f22,plain,(
% 1.49/1.28 ~(lessf @ y @ z) => (eq @ y @ z)),
% 1.49/1.28 inference(rectify,[status(thm)],[f2])).
% 1.49/1.28 thf(f2,axiom,(
% 1.49/1.28 ~(lessf @ y @ z) => (eq @ y @ z)),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',k)).
% 1.49/1.28 thf(f61,plain,(
% 1.49/1.28 spl0_1 | spl0_2),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f49,f58,f54])).
% 1.49/1.28 thf(f49,plain,(
% 1.49/1.28 ((lessf @ x @ y) = $true) | ((eq @ x @ y) = $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f39])).
% 1.49/1.28 thf(f39,plain,(
% 1.49/1.28 ((lessf @ x @ y) = $true) | ((eq @ x @ y) = $true)),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f24])).
% 1.49/1.28 thf(f24,plain,(
% 1.49/1.28 ((lessf @ x @ y) != $true) => ((eq @ x @ y) = $true)),
% 1.49/1.28 inference(flattening,[status(thm)],[f11])).
% 1.49/1.28 thf(f11,plain,(
% 1.49/1.28 ~((lessf @ x @ y) = $true) => ((eq @ x @ y) = $true)),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f10])).
% 1.49/1.28 thf(f10,plain,(
% 1.49/1.28 ~(lessf @ x @ y) => (eq @ x @ y)),
% 1.49/1.28 inference(rectify,[status(thm)],[f1])).
% 1.49/1.28 thf(f1,axiom,(
% 1.49/1.28 ~(lessf @ x @ y) => (eq @ x @ y)),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.8OjmDhArjC/DTF2THF_19615.p',l)).
% 1.49/1.28 % SZS output end Proof for DTF2THF_19615
% 1.49/1.28 % (19888)------------------------------
% 1.49/1.28 % (19888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (19888)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (19888)Memory used [KB]: 5500
% 1.49/1.28 % (19888)Time elapsed: 0.008 s
% 1.49/1.28 % (19888)Instructions burned: 13 (million)
% 1.49/1.28 % (19888)------------------------------
% 1.49/1.28 % (19888)------------------------------
% 1.49/1.28 % (19887)Success in time 0.022 s
%------------------------------------------------------------------------------