%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM742^1 : 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 09:24:30 AM UTC 2026
% Result : Theorem 1.69s 1.30s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 306 ( 86 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 348 ( 57 ~; 49 |; 0 &; 218 @)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 73 ( 0 ^; 73 !; 0 ?; 73 :)
% 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(f84,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f56,f65,f83]) ).
thf(f83,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f82]) ).
thf(f82,plain,
( $false
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f80,f45]) ).
thf(f45,plain,
( ( lessf @ x @ z )
!= $true ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( lessf @ x @ z )
!= $true ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ( lessf @ x @ z )
!= $true ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
~ ( lessf @ x @ z ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( lessf @ x @ z ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
lessf @ x @ z,
file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz51a) ).
thf(f80,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( lessf @ x @ z )
= $true )
| ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f77,f67]) ).
thf(f67,plain,
( ( $true
= ( eq @ y @ x ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true != $true )
| ( $true
= ( eq @ y @ x ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f40,f51]) ).
thf(f51,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl0_1
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f40,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ X1 ) )
| ( $true
= ( eq @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( eq @ X1 @ X0 ) )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( eq @ X0 @ X1 ) )
=> ( $true
= ( eq @ X1 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: frac,X2: frac] :
( ( eq @ X1 @ X2 )
=> ( eq @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz38) ).
thf(f77,plain,
! [X0: frac] :
( ( $true
!= ( eq @ y @ X0 ) )
| ( $true
= ( lessf @ X0 @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
! [X0: frac] :
( ( $true
= ( lessf @ X0 @ z ) )
| ( $true != $true )
| ( $true
!= ( eq @ y @ X0 ) ) ),
inference(superposition,[status(thm)],[f73,f46]) ).
thf(f46,plain,
( ( lessf @ y @ z )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( lessf @ y @ z )
= $true ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
lessf @ y @ z,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
lessf @ y @ z,
file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',k) ).
thf(f73,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( lessf @ X2 @ X0 ) )
| ( $true
= ( lessf @ X1 @ X0 ) )
| ( ( eq @ X2 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( lessf @ X1 @ X0 ) )
| ( ( eq @ X2 @ X1 )
!= $true )
| ( $true
!= ( lessf @ X2 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f44,f42]) ).
thf(f42,plain,
! [X0: frac] :
( $true
= ( eq @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: frac] :
( $true
= ( eq @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X1: frac] : ( eq @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz37) ).
thf(f44,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ X3 @ X2 ) )
| ( ( lessf @ X1 @ X2 )
= $true )
| ( $true
!= ( lessf @ X0 @ X3 ) )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
!= ( eq @ X0 @ X1 ) )
| ( $true
!= ( lessf @ X0 @ X3 ) )
| ( $true
!= ( eq @ X3 @ X2 ) )
| ( ( lessf @ X1 @ X2 )
= $true ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
! [X3: frac,X0: frac,X1: frac,X2: frac] :
( ( $true
!= ( eq @ X3 @ X0 ) )
| ( $true
!= ( lessf @ X3 @ X2 ) )
| ( ( eq @ X2 @ X1 )
!= $true )
| ( $true
= ( lessf @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: frac,X0: frac,X2: frac,X3: frac] :
( ( $true
= ( lessf @ X0 @ X1 ) )
| ( ( eq @ X2 @ X1 )
!= $true )
| ( $true
!= ( eq @ X3 @ X0 ) )
| ( $true
!= ( lessf @ X3 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: frac,X0: frac,X2: frac,X3: frac] :
( ( $true
= ( lessf @ X3 @ X2 ) )
=> ( ( $true
= ( eq @ X3 @ X0 ) )
=> ( ( ( eq @ X2 @ X1 )
= $true )
=> ( $true
= ( lessf @ X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( lessf @ X3 @ X2 )
=> ( ( eq @ X3 @ X0 )
=> ( ( eq @ X2 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: frac,X4: frac,X2: frac,X1: frac] :
( ( lessf @ X1 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( ( eq @ X2 @ X4 )
=> ( lessf @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz45) ).
thf(f65,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f63,f45]) ).
thf(f63,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true != $true )
| ( ( lessf @ x @ z )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f60,f55]) ).
thf(f55,plain,
( ( ( lessf @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl0_2
<=> ( ( lessf @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f60,plain,
! [X0: frac] :
( ( ( lessf @ X0 @ y )
!= $true )
| ( $true
= ( lessf @ X0 @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: frac] :
( ( ( lessf @ X0 @ y )
!= $true )
| ( $true
= ( lessf @ X0 @ z ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f43,f46]) ).
thf(f43,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( lessf @ X2 @ X1 ) )
| ( $true
= ( lessf @ X0 @ X1 ) )
| ( $true
!= ( lessf @ X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
!= ( lessf @ X0 @ X2 ) )
| ( $true
= ( lessf @ X0 @ X1 ) )
| ( $true
!= ( lessf @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( ( lessf @ X1 @ X2 )
!= $true )
| ( $true
= ( lessf @ X1 @ X0 ) )
| ( $true
!= ( lessf @ X2 @ X0 ) ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( lessf @ X1 @ X0 ) )
| ( $true
!= ( lessf @ X2 @ X0 ) )
| ( ( lessf @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X1 @ X2 )
= $true )
=> ( ( $true
= ( lessf @ X2 @ X0 ) )
=> ( $true
= ( lessf @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X1 @ X2 )
=> ( ( lessf @ X2 @ X0 )
=> ( lessf @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X3: frac,X1: frac,X2: frac] :
( ( lessf @ X1 @ X2 )
=> ( ( lessf @ X2 @ X3 )
=> ( lessf @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz50) ).
thf(f56,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f39,f53,f49]) ).
thf(f39,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( lessf @ x @ y )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( lessf @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',l) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM742^1 : 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
% 0.18/0.35 % Computer : n026.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 11:12:55 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : NUM742^1 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.47 % Domain : Number Theory
% 0.21/0.47 % Problem : Landau theorem 51a
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English : lessf x z
% 0.21/0.47
% 0.21/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Bro09]
% 0.21/0.47 % Names : satz51a [Lan30]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % : Without extensionality : Theorem
% 0.21/0.47 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.17 v5.5.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v4.1.0, 0.00 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.21/0.47 % Syntax : Number of formulae : 14 ( 3 unt; 6 typ; 0 def)
% 0.21/0.47 % Number of atoms : 14 ( 0 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 4 ( 1 avg)
% 0.21/0.47 % Number of connectives : 39 ( 3 ~; 0 |; 0 &; 28 @)
% 0.21/0.47 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 10 ( 6 avg)
% 0.21/0.47 % Number of types : 2 ( 1 usr)
% 0.21/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.21/0.47 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.21/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.47
% 0.21/0.47 % Comments :
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(frac_type,type,
% 0.21/0.47 frac: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(x,type,
% 0.21/0.47 x: frac ).
% 0.21/0.47
% 0.21/0.47 thf(y,type,
% 0.21/0.47 y: frac ).
% 0.21/0.47
% 0.21/0.47 thf(z,type,
% 0.21/0.47 z: frac ).
% 0.21/0.47
% 0.21/0.47 thf(lessf,type,
% 0.21/0.47 lessf: frac > frac > $o ).
% 0.21/0.47
% 0.21/0.47 thf(eq,type,
% 0.21/0.47 eq: frac > frac > $o ).
% 0.21/0.47
% 0.21/0.47 thf(l,axiom,
% 0.21/0.47 ( ~ ( lessf @ x @ y )
% 0.21/0.47 => ( eq @ x @ y ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(k,axiom,
% 0.21/0.47 lessf @ y @ z ).
% 0.21/0.47
% 0.21/0.47 thf(et,axiom,
% 0.21/0.47 ! [Xa: $o] :
% 0.21/0.47 ( ~ ~ Xa
% 0.21/0.47 => Xa ) ).
% 0.21/0.47
% 0.21/0.47 thf(satz45,axiom,
% 0.21/0.47 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.21/0.47 ( ( lessf @ Xx @ Xy )
% 0.21/0.47 => ( ( eq @ Xx @ Xz )
% 0.21/0.47 => ( ( eq @ Xy @ Xu )
% 0.21/0.47 => ( lessf @ Xz @ Xu ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(satz38,axiom,
% 0.21/0.47 ! [Xx: frac,Xy: frac] :
% 0.21/0.47 ( ( eq @ Xx @ Xy )
% 0.21/0.47 => ( eq @ Xy @ Xx ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(satz50,axiom,
% 0.21/0.47 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.21/0.47 ( ( lessf @ Xx @ Xy )
% 0.21/0.47 => ( ( lessf @ Xy @ Xz )
% 0.21/0.47 => ( lessf @ Xx @ Xz ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(satz37,axiom,
% 0.21/0.47 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.21/0.47
% 0.21/0.47 thf(satz51a,conjecture,
% 0.21/0.47 lessf @ x @ z ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.51/1.27 ---- Embedded in THF ---
% 1.51/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.27 %%% Generated on Tue Feb 24 11:12:56 EST 2026
% 1.51/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.27 %%% Logic specification used:
% 1.51/1.27 %%% thf(spec, logic, $$dhol).
% 1.51/1.27
% 1.51/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2DTF31263.p
% See solution above
% 1.51/1.27 ------------------------
% 1.51/1.28 ---- Cleaned THF ---
% 1.51/1.28 thf(frac_type,type,
% 1.51/1.28 frac: $tType ).
% 1.51/1.28
% 1.51/1.28 thf(x,type,
% 1.51/1.28 x: frac ).
% 1.51/1.28
% 1.51/1.28 thf(y,type,
% 1.51/1.28 y: frac ).
% 1.51/1.28
% 1.51/1.28 thf(z,type,
% 1.51/1.28 z: frac ).
% 1.51/1.28
% 1.51/1.28 thf(lessf,type,
% 1.51/1.28 lessf: frac > frac > $o ).
% 1.51/1.28
% 1.51/1.28 thf(eq,type,
% 1.51/1.28 eq: frac > frac > $o ).
% 1.51/1.28
% 1.51/1.28 thf(l,axiom,
% 1.51/1.28 ( ~ ( lessf @ x @ y )
% 1.51/1.28 => ( eq @ x @ y ) ) ).
% 1.51/1.28
% 1.51/1.28 thf(k,axiom,
% 1.51/1.28 lessf @ y @ z ).
% 1.51/1.28
% 1.51/1.28 thf(et,axiom,
% 1.51/1.28 ! [Xa: $o] :
% 1.51/1.28 ( ~ ~ Xa
% 1.51/1.28 => Xa ) ).
% 1.51/1.28
% 1.51/1.28 thf(satz45,axiom,
% 1.51/1.28 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.51/1.28 ( ( lessf @ Xx @ Xy )
% 1.51/1.28 => ( ( eq @ Xx @ Xz )
% 1.51/1.28 => ( ( eq @ Xy @ Xu )
% 1.51/1.28 => ( lessf @ Xz @ Xu ) ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf(satz38,axiom,
% 1.51/1.28 ! [Xx: frac,Xy: frac] :
% 1.51/1.28 ( ( eq @ Xx @ Xy )
% 1.51/1.28 => ( eq @ Xy @ Xx ) ) ).
% 1.51/1.28
% 1.51/1.28 thf(satz50,axiom,
% 1.51/1.28 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.51/1.28 ( ( lessf @ Xx @ Xy )
% 1.51/1.28 => ( ( lessf @ Xy @ Xz )
% 1.51/1.28 => ( lessf @ Xx @ Xz ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf(satz37,axiom,
% 1.51/1.28 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 1.51/1.28
% 1.51/1.28 thf(satz51a,conjecture,
% 1.51/1.28 lessf @ x @ z ).
% 1.51/1.28 ------------------------
% 1.51/1.29 % (31458)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31263 for (3000ds/18Mi)
% 1.51/1.29 % (31456)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_31263 for (3000ds/2Mi)
% 1.51/1.30 % (31456)Instruction limit reached!
% 1.51/1.30 % (31456)------------------------------
% 1.51/1.30 % (31456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.30 % (31456)Termination reason: Unknown
% 1.51/1.30 % (31456)Termination phase: Saturation
% 1.51/1.30
% 1.51/1.30 % (31456)Memory used [KB]: 1023
% 1.51/1.30 % (31456)Time elapsed: 0.002 s
% 1.51/1.30 % (31456)Instructions burned: 2 (million)
% 1.51/1.30 % (31456)------------------------------
% 1.51/1.30 % (31456)------------------------------
% 1.69/1.30 % (31457)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_31263 for (3000ds/275Mi)
% 1.69/1.30 % (31458)First to succeed.
% 1.69/1.30 % (31458)Refutation found. Thanks to Tanya!
% 1.69/1.30 % SZS status Theorem for DTF2THF_31263
% 1.69/1.30 % SZS output start Proof for DTF2THF_31263
% 1.69/1.30 thf(type_def_5, type, frac: $tType).
% 1.69/1.30 thf(func_def_0, type, frac: $tType).
% 1.69/1.30 thf(func_def_1, type, x: frac).
% 1.69/1.30 thf(func_def_2, type, y: frac).
% 1.69/1.30 thf(func_def_3, type, z: frac).
% 1.69/1.30 thf(func_def_4, type, lessf: frac > frac > $o).
% 1.69/1.30 thf(func_def_5, type, eq: frac > frac > $o).
% 1.69/1.30 thf(f84,plain,(
% 1.69/1.30 $false),
% 1.69/1.30 inference(avatar_sat_refutation,[status(thm)],[f56,f65,f83])).
% 1.69/1.30 thf(f83,plain,(
% 1.69/1.30 ~spl0_1),
% 1.69/1.30 inference(avatar_contradiction_clause,[status(thm)],[f82])).
% 1.69/1.30 thf(f82,plain,(
% 1.69/1.30 $false | ~spl0_1),
% 1.69/1.30 inference(subsumption_resolution,[status(thm)],[f80,f45])).
% 1.69/1.30 thf(f45,plain,(
% 1.69/1.30 ((lessf @ x @ z) != $true)),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.69/1.30 thf(f28,plain,(
% 1.69/1.30 ((lessf @ x @ z) != $true)),
% 1.69/1.30 inference(flattening,[status(thm)],[f24])).
% 1.69/1.30 thf(f24,plain,(
% 1.69/1.30 ~((lessf @ x @ z) = $true)),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f23])).
% 1.69/1.30 thf(f23,plain,(
% 1.69/1.30 ~(lessf @ x @ z)),
% 1.69/1.30 inference(rectify,[status(thm)],[f9])).
% 1.69/1.30 thf(f9,negated_conjecture,(
% 1.69/1.30 ~(lessf @ x @ z)),
% 1.69/1.30 inference(negated_conjecture,[status(cth)],[f8])).
% 1.69/1.30 thf(f8,conjecture,(
% 1.69/1.30 (lessf @ x @ z)),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz51a)).
% 1.69/1.30 thf(f80,plain,(
% 1.69/1.30 ((lessf @ x @ z) = $true) | ~spl0_1),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.69/1.30 thf(f78,plain,(
% 1.69/1.30 ((lessf @ x @ z) = $true) | ($true != $true) | ~spl0_1),
% 1.69/1.30 inference(superposition,[status(thm)],[f77,f67])).
% 1.69/1.30 thf(f67,plain,(
% 1.69/1.30 ($true = (eq @ y @ x)) | ~spl0_1),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.69/1.30 thf(f66,plain,(
% 1.69/1.30 ($true != $true) | ($true = (eq @ y @ x)) | ~spl0_1),
% 1.69/1.30 inference(superposition,[status(thm)],[f40,f51])).
% 1.69/1.30 thf(f51,plain,(
% 1.69/1.30 ((eq @ x @ y) = $true) | ~spl0_1),
% 1.69/1.30 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.69/1.30 thf(f49,definition,(
% 1.69/1.30 spl0_1 <=> ((eq @ x @ y) = $true)),
% 1.69/1.30 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.69/1.30 thf(f40,plain,(
% 1.69/1.30 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ X0 @ X1)) | ($true = (eq @ X1 @ X0))) )),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f33])).
% 1.69/1.30 thf(f33,plain,(
% 1.69/1.30 ! [X0 : frac,X1 : frac] : (($true = (eq @ X1 @ X0)) | ($true != (eq @ X0 @ X1)))),
% 1.69/1.30 inference(ennf_transformation,[status(thm)],[f22])).
% 1.69/1.30 thf(f22,plain,(
% 1.69/1.30 ! [X0 : frac,X1 : frac] : (($true = (eq @ X0 @ X1)) => ($true = (eq @ X1 @ X0)))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f21])).
% 1.69/1.30 thf(f21,plain,(
% 1.69/1.30 ! [X0 : frac,X1 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 1.69/1.30 inference(rectify,[status(thm)],[f5])).
% 1.69/1.30 thf(f5,axiom,(
% 1.69/1.30 ! [X1 : frac,X2 : frac] : ((eq @ X1 @ X2) => (eq @ X2 @ X1))),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz38)).
% 1.69/1.30 thf(f77,plain,(
% 1.69/1.30 ( ! [X0 : frac] : (($true != (eq @ y @ X0)) | ($true = (lessf @ X0 @ z))) )),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.69/1.30 thf(f76,plain,(
% 1.69/1.30 ( ! [X0 : frac] : (($true = (lessf @ X0 @ z)) | ($true != $true) | ($true != (eq @ y @ X0))) )),
% 1.69/1.30 inference(superposition,[status(thm)],[f73,f46])).
% 1.69/1.30 thf(f46,plain,(
% 1.69/1.30 ((lessf @ y @ z) = $true)),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.69/1.30 thf(f16,plain,(
% 1.69/1.30 ((lessf @ y @ z) = $true)),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f15])).
% 1.69/1.30 thf(f15,plain,(
% 1.69/1.30 (lessf @ y @ z)),
% 1.69/1.30 inference(rectify,[status(thm)],[f2])).
% 1.69/1.30 thf(f2,axiom,(
% 1.69/1.30 (lessf @ y @ z)),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',k)).
% 1.69/1.30 thf(f73,plain,(
% 1.69/1.30 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (lessf @ X2 @ X0)) | ($true = (lessf @ X1 @ X0)) | ((eq @ X2 @ X1) != $true)) )),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.69/1.30 thf(f70,plain,(
% 1.69/1.30 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (lessf @ X1 @ X0)) | ((eq @ X2 @ X1) != $true) | ($true != (lessf @ X2 @ X0)) | ($true != $true)) )),
% 1.69/1.30 inference(superposition,[status(thm)],[f44,f42])).
% 1.69/1.30 thf(f42,plain,(
% 1.69/1.30 ( ! [X0 : frac] : (($true = (eq @ X0 @ X0))) )),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.30 thf(f14,plain,(
% 1.69/1.30 ! [X0 : frac] : ($true = (eq @ X0 @ X0))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f13])).
% 1.69/1.30 thf(f13,plain,(
% 1.69/1.30 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.69/1.30 inference(rectify,[status(thm)],[f7])).
% 1.69/1.30 thf(f7,axiom,(
% 1.69/1.30 ! [X1 : frac] : (eq @ X1 @ X1)),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz37)).
% 1.69/1.30 thf(f44,plain,(
% 1.69/1.30 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != (eq @ X3 @ X2)) | ((lessf @ X1 @ X2) = $true) | ($true != (lessf @ X0 @ X3)) | ($true != (eq @ X0 @ X1))) )),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f38])).
% 1.69/1.30 thf(f38,plain,(
% 1.69/1.30 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true != (eq @ X0 @ X1)) | ($true != (lessf @ X0 @ X3)) | ($true != (eq @ X3 @ X2)) | ((lessf @ X1 @ X2) = $true))),
% 1.69/1.30 inference(rectify,[status(thm)],[f36])).
% 1.69/1.30 thf(f36,plain,(
% 1.69/1.30 ! [X3 : frac,X0 : frac,X1 : frac,X2 : frac] : (($true != (eq @ X3 @ X0)) | ($true != (lessf @ X3 @ X2)) | ((eq @ X2 @ X1) != $true) | ($true = (lessf @ X0 @ X1)))),
% 1.69/1.30 inference(flattening,[status(thm)],[f35])).
% 1.69/1.30 thf(f35,plain,(
% 1.69/1.30 ! [X1 : frac,X0 : frac,X2 : frac,X3 : frac] : (((($true = (lessf @ X0 @ X1)) | ((eq @ X2 @ X1) != $true)) | ($true != (eq @ X3 @ X0))) | ($true != (lessf @ X3 @ X2)))),
% 1.69/1.30 inference(ennf_transformation,[status(thm)],[f12])).
% 1.69/1.30 thf(f12,plain,(
% 1.69/1.30 ! [X1 : frac,X0 : frac,X2 : frac,X3 : frac] : (($true = (lessf @ X3 @ X2)) => (($true = (eq @ X3 @ X0)) => (((eq @ X2 @ X1) = $true) => ($true = (lessf @ X0 @ X1)))))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f11])).
% 1.69/1.30 thf(f11,plain,(
% 1.69/1.30 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((lessf @ X3 @ X2) => ((eq @ X3 @ X0) => ((eq @ X2 @ X1) => (lessf @ X0 @ X1))))),
% 1.69/1.30 inference(rectify,[status(thm)],[f4])).
% 1.69/1.30 thf(f4,axiom,(
% 1.69/1.30 ! [X3 : frac,X4 : frac,X2 : frac,X1 : frac] : ((lessf @ X1 @ X2) => ((eq @ X1 @ X3) => ((eq @ X2 @ X4) => (lessf @ X3 @ X4))))),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz45)).
% 1.69/1.30 thf(f65,plain,(
% 1.69/1.30 ~spl0_2),
% 1.69/1.30 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.69/1.30 thf(f64,plain,(
% 1.69/1.30 $false | ~spl0_2),
% 1.69/1.30 inference(subsumption_resolution,[status(thm)],[f63,f45])).
% 1.69/1.30 thf(f63,plain,(
% 1.69/1.30 ((lessf @ x @ z) = $true) | ~spl0_2),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.69/1.30 thf(f62,plain,(
% 1.69/1.30 ($true != $true) | ((lessf @ x @ z) = $true) | ~spl0_2),
% 1.69/1.30 inference(superposition,[status(thm)],[f60,f55])).
% 1.69/1.30 thf(f55,plain,(
% 1.69/1.30 ((lessf @ x @ y) = $true) | ~spl0_2),
% 1.69/1.30 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.69/1.30 thf(f53,definition,(
% 1.69/1.30 spl0_2 <=> ((lessf @ x @ y) = $true)),
% 1.69/1.30 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.69/1.30 thf(f60,plain,(
% 1.69/1.30 ( ! [X0 : frac] : (((lessf @ X0 @ y) != $true) | ($true = (lessf @ X0 @ z))) )),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.69/1.30 thf(f58,plain,(
% 1.69/1.30 ( ! [X0 : frac] : (((lessf @ X0 @ y) != $true) | ($true = (lessf @ X0 @ z)) | ($true != $true)) )),
% 1.69/1.30 inference(superposition,[status(thm)],[f43,f46])).
% 1.69/1.30 thf(f43,plain,(
% 1.69/1.30 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (lessf @ X2 @ X1)) | ($true = (lessf @ X0 @ X1)) | ($true != (lessf @ X0 @ X2))) )),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.30 thf(f37,plain,(
% 1.69/1.30 ! [X0 : frac,X1 : frac,X2 : frac] : (($true != (lessf @ X0 @ X2)) | ($true = (lessf @ X0 @ X1)) | ($true != (lessf @ X2 @ X1)))),
% 1.69/1.30 inference(rectify,[status(thm)],[f31])).
% 1.69/1.30 thf(f31,plain,(
% 1.69/1.30 ! [X1 : frac,X0 : frac,X2 : frac] : (((lessf @ X1 @ X2) != $true) | ($true = (lessf @ X1 @ X0)) | ($true != (lessf @ X2 @ X0)))),
% 1.69/1.30 inference(flattening,[status(thm)],[f30])).
% 1.69/1.30 thf(f30,plain,(
% 1.69/1.30 ! [X0 : frac,X1 : frac,X2 : frac] : ((($true = (lessf @ X1 @ X0)) | ($true != (lessf @ X2 @ X0))) | ((lessf @ X1 @ X2) != $true))),
% 1.69/1.30 inference(ennf_transformation,[status(thm)],[f18])).
% 1.69/1.30 thf(f18,plain,(
% 1.69/1.30 ! [X0 : frac,X1 : frac,X2 : frac] : (((lessf @ X1 @ X2) = $true) => (($true = (lessf @ X2 @ X0)) => ($true = (lessf @ X1 @ X0))))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f17])).
% 1.69/1.30 thf(f17,plain,(
% 1.69/1.30 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X1 @ X2) => ((lessf @ X2 @ X0) => (lessf @ X1 @ X0)))),
% 1.69/1.30 inference(rectify,[status(thm)],[f6])).
% 1.69/1.30 thf(f6,axiom,(
% 1.69/1.30 ! [X3 : frac,X1 : frac,X2 : frac] : ((lessf @ X1 @ X2) => ((lessf @ X2 @ X3) => (lessf @ X1 @ X3)))),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',satz50)).
% 1.69/1.30 thf(f56,plain,(
% 1.69/1.30 spl0_1 | spl0_2),
% 1.69/1.30 inference(avatar_split_clause,[status(thm)],[f39,f53,f49])).
% 1.69/1.30 thf(f39,plain,(
% 1.69/1.30 ((eq @ x @ y) = $true) | ((lessf @ x @ y) = $true)),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f32])).
% 1.69/1.30 thf(f32,plain,(
% 1.69/1.30 ((lessf @ x @ y) = $true) | ((eq @ x @ y) = $true)),
% 1.69/1.30 inference(ennf_transformation,[status(thm)],[f29])).
% 1.69/1.30 thf(f29,plain,(
% 1.69/1.30 ((lessf @ x @ y) != $true) => ((eq @ x @ y) = $true)),
% 1.69/1.30 inference(flattening,[status(thm)],[f26])).
% 1.69/1.30 thf(f26,plain,(
% 1.69/1.30 ~((lessf @ x @ y) = $true) => ((eq @ x @ y) = $true)),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f25])).
% 1.69/1.30 thf(f25,plain,(
% 1.69/1.30 ~(lessf @ x @ y) => (eq @ x @ y)),
% 1.69/1.30 inference(rectify,[status(thm)],[f1])).
% 1.69/1.30 thf(f1,axiom,(
% 1.69/1.30 ~(lessf @ x @ y) => (eq @ x @ y)),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CkDt5iynAI/DTF2THF_31263.p',l)).
% 1.69/1.30 % SZS output end Proof for DTF2THF_31263
% 1.69/1.30 % (31458)------------------------------
% 1.69/1.30 % (31458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (31458)Termination reason: Refutation
% 1.69/1.30
% 1.69/1.30 % (31458)Memory used [KB]: 5500
% 1.69/1.30 % (31458)Time elapsed: 0.005 s
% 1.69/1.30 % (31458)Instructions burned: 7 (million)
% 1.69/1.30 % (31458)------------------------------
% 1.69/1.30 % (31458)------------------------------
% 1.69/1.30 % (31451)Success in time 0.006 s
%------------------------------------------------------------------------------