%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM756^1 : 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 : n027.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 09:24:35 AM UTC 2026
% Result : Theorem 1.65s 1.31s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 327 ( 93 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 490 ( 81 ~; 43 |; 4 &; 326 @)
% ( 2 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 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,
eq: frac > frac > $o ).
thf(func_def_5,type,
pf: frac > frac > frac ).
thf(func_def_7,type,
lessf: frac > frac > $o ).
thf(func_def_8,type,
moref: frac > frac > $o ).
thf(func_def_9,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f90,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f68,f77,f88]) ).
thf(f88,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f42,f63]) ).
thf(f63,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl0_1
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f42,plain,
( ( eq @ x @ y )
!= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( eq @ x @ y )
!= $true ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ( eq @ x @ y )
!= $true ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( eq @ x @ y ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( eq @ x @ y ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
eq @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz63b) ).
thf(f77,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f76]) ).
thf(f76,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f47,f70]) ).
thf(f70,plain,
( ! [X0: frac] :
( $true
= ( lessf @ ( pf @ x @ X0 ) @ ( pf @ y @ X0 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( $true
= ( lessf @ ( pf @ x @ X0 ) @ ( pf @ y @ X0 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f43,f67]) ).
thf(f67,plain,
( ( ( lessf @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl0_2
<=> ( ( lessf @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f43,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( lessf @ X0 @ X2 ) )
| ( $true
= ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( lessf @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( $true
= ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
=> ( $true
= ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X0 @ X1 )
=> ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: frac,X2: frac,X3: frac] :
( ( lessf @ X1 @ X2 )
=> ( lessf @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz62c) ).
thf(f47,plain,
( $true
!= ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true
!= ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f40,f41]) ).
thf(f41,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',e) ).
thf(f40,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ X1 ) )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: frac,X1: frac] :
( ( ( $true
!= ( eq @ X0 @ X1 ) )
| ( ( lessf @ X0 @ X1 )
!= $true ) )
& ( ( $true
!= ( moref @ X0 @ X1 ) )
| ( $true
!= ( eq @ X0 @ X1 ) ) )
& ( ( ( lessf @ X0 @ X1 )
!= $true )
| ( $true
!= ( moref @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: frac,X0: frac] :
( ( ( $true
!= ( eq @ X0 @ X1 ) )
| ( ( lessf @ X0 @ X1 )
!= $true ) )
& ( ( ( lessf @ X0 @ X1 )
!= $true )
| ( $true
!= ( moref @ X0 @ X1 ) ) )
& ( ( $true
!= ( moref @ X0 @ X1 ) )
| ( $true
!= ( eq @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: frac,X0: frac] :
~ ( ( ( $true
= ( eq @ X0 @ X1 ) )
=> ( $true
!= ( moref @ X0 @ X1 ) ) )
=> ( ( ( $true
= ( moref @ X0 @ X1 ) )
=> ( ( lessf @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( lessf @ X0 @ X1 )
= $true )
=> ( $true
!= ( eq @ X0 @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
~ ( ( ( $true
= ( eq @ X0 @ X1 ) )
=> ( $true
!= ( moref @ X0 @ X1 ) ) )
=> ~ ~ ( ( ( $true
= ( moref @ X0 @ X1 ) )
=> ( ( lessf @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( lessf @ X0 @ X1 )
= $true )
=> ( $true
!= ( eq @ X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: frac,X1: frac] :
~ ( ( ( eq @ X0 @ X1 )
=> ~ ( moref @ X0 @ X1 ) )
=> ~ ~ ( ( ( moref @ X0 @ X1 )
=> ~ ( lessf @ X0 @ X1 ) )
=> ~ ( ( lessf @ X0 @ X1 )
=> ~ ( eq @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: frac,X2: frac] :
~ ( ( ( eq @ X1 @ X2 )
=> ~ ( moref @ X1 @ X2 ) )
=> ~ ~ ( ( ( moref @ X1 @ X2 )
=> ~ ( lessf @ X1 @ X2 ) )
=> ~ ( ( lessf @ X1 @ X2 )
=> ~ ( eq @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz41b) ).
thf(f68,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f59,f65,f61]) ).
thf(f59,plain,
( ( ( lessf @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( eq @ x @ y )
= $true )
| ( $true != $true )
| ( ( lessf @ x @ y )
= $true ) ),
inference(superposition,[status(thm)],[f56,f41]) ).
thf(f56,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
= ( lessf @ X0 @ X2 ) )
| ( ( eq @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true != $true )
| ( ( eq @ X0 @ X2 )
= $true )
| ( $true
= ( lessf @ X0 @ X2 ) ) ),
inference(superposition,[status(thm)],[f39,f51]) ).
thf(f51,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) )
| ( ( lessf @ X0 @ X1 )
= $true )
| ( $true
= ( eq @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) )
| ( $true != $true )
| ( $true
= ( eq @ X0 @ X1 ) )
| ( ( lessf @ X0 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f44,f37]) ).
thf(f37,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( moref @ X0 @ X1 ) )
| ( ( lessf @ X0 @ X1 )
= $true )
| ( $true
= ( eq @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( moref @ X0 @ X1 ) )
| ( $true
= ( eq @ X0 @ X1 ) )
| ( ( lessf @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: frac,X0: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
| ( $true
= ( moref @ X0 @ X1 ) )
| ( $true
= ( eq @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: frac,X0: frac] :
( ( $true
!= ( eq @ X0 @ X1 ) )
=> ( ( $true
!= ( moref @ X0 @ X1 ) )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ X1 ) )
=> ( ( $true
!= ( moref @ X0 @ X1 ) )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: frac,X1: frac] :
( ~ ( eq @ X0 @ X1 )
=> ( ~ ( moref @ X0 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: frac,X2: frac] :
( ~ ( eq @ X1 @ X2 )
=> ( ~ ( moref @ X1 @ X2 )
=> ( lessf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz41a) ).
thf(f44,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( moref @ X1 @ X0 )
!= $true )
| ( $true
= ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X2 ) ) )
| ( ( moref @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: frac,X1: frac,X0: frac] :
( ( ( moref @ X1 @ X0 )
= $true )
=> ( $true
= ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X1 @ X0 )
=> ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X2: frac,X1: frac,X3: frac] :
( ( moref @ X1 @ X2 )
=> ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz62a) ).
thf(f39,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( moref @ X0 @ X1 ) )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM756^1 : 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
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 11:13:22 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 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 : NUM756^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Number Theory
% 0.28/0.46 % Problem : Landau theorem 63b
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : eq x y
% 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 : satz63b [Lan30]
% 0.28/0.46 % : satz73b [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 v5.5.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 15 ( 2 unt; 8 typ; 0 def)
% 0.28/0.46 % Number of atoms : 15 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 6 ( 2 avg)
% 0.28/0.46 % Number of connectives : 63 ( 11 ~; 0 |; 0 &; 42 @)
% 0.28/0.46 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 13 ( 7 avg)
% 0.28/0.46 % Number of types : 2 ( 1 usr)
% 0.28/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 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(eq,type,
% 0.28/0.46 eq: frac > frac > $o ).
% 0.28/0.46
% 0.28/0.46 thf(pf,type,
% 0.28/0.46 pf: frac > frac > frac ).
% 0.28/0.46
% 0.28/0.46 thf(e,axiom,
% 0.28/0.46 eq @ ( pf @ x @ z ) @ ( pf @ 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(lessf,type,
% 0.28/0.46 lessf: frac > frac > $o ).
% 0.28/0.46
% 0.28/0.46 thf(moref,type,
% 0.28/0.46 moref: frac > frac > $o ).
% 0.28/0.46
% 0.28/0.46 thf(satz41b,axiom,
% 0.28/0.46 ! [Xx: frac,Xy: frac] :
% 0.28/0.46 ~ ( ( ( eq @ Xx @ Xy )
% 0.28/0.46 => ~ ( moref @ Xx @ Xy ) )
% 0.28/0.46 => ~ ~ ( ( ( moref @ Xx @ Xy )
% 0.28/0.46 => ~ ( lessf @ Xx @ Xy ) )
% 0.28/0.46 => ~ ( ( lessf @ Xx @ Xy )
% 0.28/0.46 => ~ ( eq @ Xx @ Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz62c,axiom,
% 0.28/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.28/0.46 ( ( lessf @ Xx @ Xy )
% 0.28/0.46 => ( lessf @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz41a,axiom,
% 0.28/0.46 ! [Xx: frac,Xy: frac] :
% 0.28/0.46 ( ~ ( eq @ Xx @ Xy )
% 0.28/0.46 => ( ~ ( moref @ Xx @ Xy )
% 0.28/0.46 => ( lessf @ Xx @ Xy ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz62a,axiom,
% 0.28/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.28/0.46 ( ( moref @ Xx @ Xy )
% 0.28/0.46 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz63b,conjecture,
% 0.28/0.46 eq @ x @ y ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.50/1.28 ---- Embedded in THF ---
% 1.50/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.28 %%% Generated on Tue Feb 24 11:13:23 EST 2026
% 1.50/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.28 %%% Logic specification used:
% 1.50/1.28 %%% thf(spec, logic, $$dhol).
% 1.50/1.28
% 1.50/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2DTF26018.p
% See solution above
% 1.50/1.28 ------------------------
% 1.50/1.29 ---- Cleaned THF ---
% 1.50/1.29 thf(frac_type,type,
% 1.50/1.29 frac: $tType ).
% 1.50/1.29
% 1.50/1.29 thf(x,type,
% 1.50/1.29 x: frac ).
% 1.50/1.29
% 1.50/1.29 thf(y,type,
% 1.50/1.29 y: frac ).
% 1.50/1.29
% 1.50/1.29 thf(z,type,
% 1.50/1.29 z: frac ).
% 1.50/1.29
% 1.50/1.29 thf(eq,type,
% 1.50/1.29 eq: frac > frac > $o ).
% 1.50/1.29
% 1.50/1.29 thf(pf,type,
% 1.50/1.29 pf: frac > frac > frac ).
% 1.50/1.29
% 1.50/1.29 thf(e,axiom,
% 1.50/1.29 eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ).
% 1.50/1.29
% 1.50/1.29 thf(et,axiom,
% 1.50/1.29 ! [Xa: $o] :
% 1.50/1.29 ( ~ ~ Xa
% 1.50/1.29 => Xa ) ).
% 1.50/1.29
% 1.50/1.29 thf(lessf,type,
% 1.50/1.29 lessf: frac > frac > $o ).
% 1.50/1.29
% 1.50/1.29 thf(moref,type,
% 1.50/1.29 moref: frac > frac > $o ).
% 1.50/1.29
% 1.50/1.29 thf(satz41b,axiom,
% 1.50/1.29 ! [Xx: frac,Xy: frac] :
% 1.50/1.29 ~ ( ( ( eq @ Xx @ Xy )
% 1.50/1.29 => ~ ( moref @ Xx @ Xy ) )
% 1.50/1.29 => ~ ~ ( ( ( moref @ Xx @ Xy )
% 1.50/1.29 => ~ ( lessf @ Xx @ Xy ) )
% 1.50/1.29 => ~ ( ( lessf @ Xx @ Xy )
% 1.50/1.29 => ~ ( eq @ Xx @ Xy ) ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(satz62c,axiom,
% 1.50/1.29 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.50/1.29 ( ( lessf @ Xx @ Xy )
% 1.50/1.29 => ( lessf @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(satz41a,axiom,
% 1.50/1.29 ! [Xx: frac,Xy: frac] :
% 1.50/1.29 ( ~ ( eq @ Xx @ Xy )
% 1.50/1.29 => ( ~ ( moref @ Xx @ Xy )
% 1.50/1.29 => ( lessf @ Xx @ Xy ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(satz62a,axiom,
% 1.50/1.29 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.50/1.29 ( ( moref @ Xx @ Xy )
% 1.50/1.29 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(satz63b,conjecture,
% 1.50/1.29 eq @ x @ y ).
% 1.50/1.29 ------------------------
% 1.65/1.30 % (26187)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26018 for (3000ds/2Mi)
% 1.65/1.30 % (26185)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_26018 for (3000ds/4Mi)
% 1.65/1.30 % (26187)Instruction limit reached!
% 1.65/1.30 % (26187)------------------------------
% 1.65/1.30 % (26187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (26187)Termination reason: Unknown
% 1.65/1.30 % (26187)Termination phase: Saturation
% 1.65/1.30
% 1.65/1.30 % (26187)Memory used [KB]: 1023
% 1.65/1.30 % (26187)Time elapsed: 0.002 s
% 1.65/1.30 % (26187)Instructions burned: 2 (million)
% 1.65/1.30 % (26187)------------------------------
% 1.65/1.30 % (26187)------------------------------
% 1.65/1.30 % (26189)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_26018 for (3000ds/275Mi)
% 1.65/1.30 % (26185)Instruction limit reached!
% 1.65/1.30 % (26185)------------------------------
% 1.65/1.30 % (26185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (26185)Termination reason: Unknown
% 1.65/1.30 % (26185)Termination phase: Saturation
% 1.65/1.30
% 1.65/1.30 % (26185)Memory used [KB]: 5500
% 1.65/1.30 % (26185)Time elapsed: 0.003 s
% 1.65/1.30 % (26185)Instructions burned: 5 (million)
% 1.65/1.30 % (26185)------------------------------
% 1.65/1.30 % (26185)------------------------------
% 1.65/1.30 % (26189)Refutation not found, incomplete strategy
% 1.65/1.30 % (26189)------------------------------
% 1.65/1.30 % (26189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (26189)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.30
% 1.65/1.30
% 1.65/1.30 % (26189)Memory used [KB]: 5500
% 1.65/1.30 % (26189)Time elapsed: 0.002 s
% 1.65/1.30 % (26189)Instructions burned: 2 (million)
% 1.65/1.30 % (26189)------------------------------
% 1.65/1.30 % (26189)------------------------------
% 1.65/1.30 % (26186)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_26018 for (3000ds/27Mi)
% 1.65/1.31 % (26188)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_26018 for (3000ds/2Mi)
% 1.65/1.31 % (26184)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26018 for (3000ds/183Mi)
% 1.65/1.31 % (26190)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26018 for (3000ds/18Mi)
% 1.65/1.31 % (26188)Instruction limit reached!
% 1.65/1.31 % (26188)------------------------------
% 1.65/1.31 % (26188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (26188)Termination reason: Unknown
% 1.65/1.31 % (26188)Termination phase: Saturation
% 1.65/1.31
% 1.65/1.31 % (26188)Memory used [KB]: 1023
% 1.65/1.31 % (26188)Time elapsed: 0.003 s
% 1.65/1.31 % (26188)Instructions burned: 3 (million)
% 1.65/1.31 % (26188)------------------------------
% 1.65/1.31 % (26188)------------------------------
% 1.65/1.31 % (26186)First to succeed.
% 1.65/1.31 % (26191)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26018 for (2999ds/3Mi)
% 1.65/1.31 % (26186)Refutation found. Thanks to Tanya!
% 1.65/1.31 % SZS status Theorem for DTF2THF_26018
% 1.65/1.31 % SZS output start Proof for DTF2THF_26018
% 1.65/1.31 thf(type_def_5, type, frac: $tType).
% 1.65/1.31 thf(func_def_0, type, frac: $tType).
% 1.65/1.31 thf(func_def_1, type, x: frac).
% 1.65/1.31 thf(func_def_2, type, y: frac).
% 1.65/1.31 thf(func_def_3, type, z: frac).
% 1.65/1.31 thf(func_def_4, type, eq: frac > frac > $o).
% 1.65/1.31 thf(func_def_5, type, pf: frac > frac > frac).
% 1.65/1.31 thf(func_def_7, type, lessf: frac > frac > $o).
% 1.65/1.31 thf(func_def_8, type, moref: frac > frac > $o).
% 1.65/1.31 thf(func_def_9, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.65/1.31 thf(f90,plain,(
% 1.65/1.31 $false),
% 1.65/1.31 inference(avatar_sat_refutation,[status(thm)],[f68,f77,f88])).
% 1.65/1.31 thf(f88,plain,(
% 1.65/1.31 ~spl0_1),
% 1.65/1.31 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.65/1.31 thf(f87,plain,(
% 1.65/1.31 $false | ~spl0_1),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.65/1.31 thf(f84,plain,(
% 1.65/1.31 ($true != $true) | ~spl0_1),
% 1.65/1.31 inference(superposition,[status(thm)],[f42,f63])).
% 1.65/1.31 thf(f63,plain,(
% 1.65/1.31 ((eq @ x @ y) = $true) | ~spl0_1),
% 1.65/1.31 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.65/1.31 thf(f61,definition,(
% 1.65/1.31 spl0_1 <=> ((eq @ x @ y) = $true)),
% 1.65/1.31 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.65/1.31 thf(f42,plain,(
% 1.65/1.31 ((eq @ x @ y) != $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f26])).
% 1.65/1.31 thf(f26,plain,(
% 1.65/1.31 ((eq @ x @ y) != $true)),
% 1.65/1.31 inference(flattening,[status(thm)],[f19])).
% 1.65/1.31 thf(f19,plain,(
% 1.65/1.31 ~((eq @ x @ y) = $true)),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f18])).
% 1.65/1.31 thf(f18,plain,(
% 1.65/1.31 ~(eq @ x @ y)),
% 1.65/1.31 inference(rectify,[status(thm)],[f8])).
% 1.65/1.31 thf(f8,negated_conjecture,(
% 1.65/1.31 ~(eq @ x @ y)),
% 1.65/1.31 inference(negated_conjecture,[status(cth)],[f7])).
% 1.65/1.31 thf(f7,conjecture,(
% 1.65/1.31 (eq @ x @ y)),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz63b)).
% 1.65/1.31 thf(f77,plain,(
% 1.65/1.31 ~spl0_2),
% 1.65/1.31 inference(avatar_contradiction_clause,[status(thm)],[f76])).
% 1.65/1.31 thf(f76,plain,(
% 1.65/1.31 $false | ~spl0_2),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.65/1.31 thf(f71,plain,(
% 1.65/1.31 ($true != $true) | ~spl0_2),
% 1.65/1.31 inference(superposition,[status(thm)],[f47,f70])).
% 1.65/1.31 thf(f70,plain,(
% 1.65/1.31 ( ! [X0 : frac] : (($true = (lessf @ (pf @ x @ X0) @ (pf @ y @ X0)))) ) | ~spl0_2),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.65/1.31 thf(f69,plain,(
% 1.65/1.31 ( ! [X0 : frac] : (($true != $true) | ($true = (lessf @ (pf @ x @ X0) @ (pf @ y @ X0)))) ) | ~spl0_2),
% 1.65/1.31 inference(superposition,[status(thm)],[f43,f67])).
% 1.65/1.31 thf(f67,plain,(
% 1.65/1.31 ((lessf @ x @ y) = $true) | ~spl0_2),
% 1.65/1.31 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.65/1.31 thf(f65,definition,(
% 1.65/1.31 spl0_2 <=> ((lessf @ x @ y) = $true)),
% 1.65/1.31 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.65/1.31 thf(f43,plain,(
% 1.65/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (lessf @ X0 @ X2)) | ($true = (lessf @ (pf @ X0 @ X1) @ (pf @ X2 @ X1)))) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f35])).
% 1.65/1.31 thf(f35,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : (($true = (lessf @ (pf @ X0 @ X1) @ (pf @ X2 @ X1))) | ($true != (lessf @ X0 @ X2)))),
% 1.65/1.31 inference(rectify,[status(thm)],[f30])).
% 1.65/1.31 thf(f30,plain,(
% 1.65/1.31 ! [X0 : frac,X2 : frac,X1 : frac] : (($true = (lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) | ((lessf @ X0 @ X1) != $true))),
% 1.65/1.31 inference(ennf_transformation,[status(thm)],[f13])).
% 1.65/1.31 thf(f13,plain,(
% 1.65/1.31 ! [X1 : frac,X0 : frac,X2 : frac] : (((lessf @ X0 @ X1) = $true) => ($true = (lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f12])).
% 1.65/1.31 thf(f12,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X0 @ X1) => (lessf @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 1.65/1.31 inference(rectify,[status(thm)],[f4])).
% 1.65/1.31 thf(f4,axiom,(
% 1.65/1.31 ! [X1 : frac,X2 : frac,X3 : frac] : ((lessf @ X1 @ X2) => (lessf @ (pf @ X1 @ X3) @ (pf @ X2 @ X3)))),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz62c)).
% 1.65/1.31 thf(f47,plain,(
% 1.65/1.31 ($true != (lessf @ (pf @ x @ z) @ (pf @ y @ z)))),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.65/1.31 thf(f46,plain,(
% 1.65/1.31 ($true != (lessf @ (pf @ x @ z) @ (pf @ y @ z))) | ($true != $true)),
% 1.65/1.31 inference(superposition,[status(thm)],[f40,f41])).
% 1.65/1.31 thf(f41,plain,(
% 1.65/1.31 ((eq @ (pf @ x @ z) @ (pf @ y @ z)) = $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.31 thf(f15,plain,(
% 1.65/1.31 ((eq @ (pf @ x @ z) @ (pf @ y @ z)) = $true)),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f14])).
% 1.65/1.31 thf(f14,plain,(
% 1.65/1.31 (eq @ (pf @ x @ z) @ (pf @ y @ z))),
% 1.65/1.31 inference(rectify,[status(thm)],[f1])).
% 1.65/1.31 thf(f1,axiom,(
% 1.65/1.31 (eq @ (pf @ x @ z) @ (pf @ y @ z))),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',e)).
% 1.65/1.31 thf(f40,plain,(
% 1.65/1.31 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ X0 @ X1)) | ((lessf @ X0 @ X1) != $true)) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f34])).
% 1.65/1.31 thf(f34,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac] : ((($true != (eq @ X0 @ X1)) | ((lessf @ X0 @ X1) != $true)) & (($true != (moref @ X0 @ X1)) | ($true != (eq @ X0 @ X1))) & (((lessf @ X0 @ X1) != $true) | ($true != (moref @ X0 @ X1))))),
% 1.65/1.31 inference(flattening,[status(thm)],[f33])).
% 1.65/1.31 thf(f33,plain,(
% 1.65/1.31 ! [X1 : frac,X0 : frac] : (((($true != (eq @ X0 @ X1)) | ((lessf @ X0 @ X1) != $true)) & (((lessf @ X0 @ X1) != $true) | ($true != (moref @ X0 @ X1)))) & (($true != (moref @ X0 @ X1)) | ($true != (eq @ X0 @ X1))))),
% 1.65/1.31 inference(ennf_transformation,[status(thm)],[f27])).
% 1.65/1.31 thf(f27,plain,(
% 1.65/1.31 ! [X1 : frac,X0 : frac] : ~((($true = (eq @ X0 @ X1)) => ($true != (moref @ X0 @ X1))) => ((($true = (moref @ X0 @ X1)) => ((lessf @ X0 @ X1) != $true)) => ~(((lessf @ X0 @ X1) = $true) => ($true != (eq @ X0 @ X1)))))),
% 1.65/1.31 inference(flattening,[status(thm)],[f21])).
% 1.65/1.31 thf(f21,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac] : ~((($true = (eq @ X0 @ X1)) => ~($true = (moref @ X0 @ X1))) => ~~((($true = (moref @ X0 @ X1)) => ~((lessf @ X0 @ X1) = $true)) => ~(((lessf @ X0 @ X1) = $true) => ~($true = (eq @ X0 @ X1)))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f20])).
% 1.65/1.31 thf(f20,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac] : ~(((eq @ X0 @ X1) => ~(moref @ X0 @ X1)) => ~~(((moref @ X0 @ X1) => ~(lessf @ X0 @ X1)) => ~((lessf @ X0 @ X1) => ~(eq @ X0 @ X1))))),
% 1.65/1.31 inference(rectify,[status(thm)],[f3])).
% 1.65/1.31 thf(f3,axiom,(
% 1.65/1.31 ! [X1 : frac,X2 : frac] : ~(((eq @ X1 @ X2) => ~(moref @ X1 @ X2)) => ~~(((moref @ X1 @ X2) => ~(lessf @ X1 @ X2)) => ~((lessf @ X1 @ X2) => ~(eq @ X1 @ X2))))),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz41b)).
% 1.65/1.31 thf(f68,plain,(
% 1.65/1.31 spl0_1 | spl0_2),
% 1.65/1.31 inference(avatar_split_clause,[status(thm)],[f59,f65,f61])).
% 1.65/1.31 thf(f59,plain,(
% 1.65/1.31 ((lessf @ x @ y) = $true) | ((eq @ x @ y) = $true)),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.65/1.31 thf(f58,plain,(
% 1.65/1.31 ((eq @ x @ y) = $true) | ($true != $true) | ((lessf @ x @ y) = $true)),
% 1.65/1.31 inference(superposition,[status(thm)],[f56,f41])).
% 1.65/1.31 thf(f56,plain,(
% 1.65/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (eq @ (pf @ X0 @ X1) @ (pf @ X2 @ X1))) | ($true = (lessf @ X0 @ X2)) | ((eq @ X0 @ X2) = $true)) )),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.65/1.31 thf(f53,plain,(
% 1.65/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (eq @ (pf @ X0 @ X1) @ (pf @ X2 @ X1))) | ($true != $true) | ((eq @ X0 @ X2) = $true) | ($true = (lessf @ X0 @ X2))) )),
% 1.65/1.31 inference(superposition,[status(thm)],[f39,f51])).
% 1.65/1.31 thf(f51,plain,(
% 1.65/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) | ((lessf @ X0 @ X1) = $true) | ($true = (eq @ X0 @ X1))) )),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.65/1.31 thf(f50,plain,(
% 1.65/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) | ($true != $true) | ($true = (eq @ X0 @ X1)) | ((lessf @ X0 @ X1) = $true)) )),
% 1.65/1.31 inference(superposition,[status(thm)],[f44,f37])).
% 1.65/1.31 thf(f37,plain,(
% 1.65/1.31 ( ! [X0 : frac,X1 : frac] : (($true = (moref @ X0 @ X1)) | ((lessf @ X0 @ X1) = $true) | ($true = (eq @ X0 @ X1))) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f29])).
% 1.65/1.31 thf(f29,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac] : (($true = (moref @ X0 @ X1)) | ($true = (eq @ X0 @ X1)) | ((lessf @ X0 @ X1) = $true))),
% 1.65/1.31 inference(flattening,[status(thm)],[f28])).
% 1.65/1.31 thf(f28,plain,(
% 1.65/1.31 ! [X1 : frac,X0 : frac] : ((((lessf @ X0 @ X1) = $true) | ($true = (moref @ X0 @ X1))) | ($true = (eq @ X0 @ X1)))),
% 1.65/1.31 inference(ennf_transformation,[status(thm)],[f25])).
% 1.65/1.31 thf(f25,plain,(
% 1.65/1.31 ! [X1 : frac,X0 : frac] : (($true != (eq @ X0 @ X1)) => (($true != (moref @ X0 @ X1)) => ((lessf @ X0 @ X1) = $true)))),
% 1.65/1.31 inference(flattening,[status(thm)],[f17])).
% 1.65/1.31 thf(f17,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac] : (~($true = (eq @ X0 @ X1)) => (~($true = (moref @ X0 @ X1)) => ((lessf @ X0 @ X1) = $true)))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f16])).
% 1.65/1.31 thf(f16,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac] : (~(eq @ X0 @ X1) => (~(moref @ X0 @ X1) => (lessf @ X0 @ X1)))),
% 1.65/1.31 inference(rectify,[status(thm)],[f5])).
% 1.65/1.31 thf(f5,axiom,(
% 1.65/1.31 ! [X1 : frac,X2 : frac] : (~(eq @ X1 @ X2) => (~(moref @ X1 @ X2) => (lessf @ X1 @ X2)))),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz41a)).
% 1.65/1.31 thf(f44,plain,(
% 1.65/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((moref @ X1 @ X0) != $true) | ($true = (moref @ (pf @ X1 @ X2) @ (pf @ X0 @ X2)))) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f31])).
% 1.65/1.31 thf(f31,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : (($true = (moref @ (pf @ X1 @ X2) @ (pf @ X0 @ X2))) | ((moref @ X1 @ X0) != $true))),
% 1.65/1.31 inference(ennf_transformation,[status(thm)],[f23])).
% 1.65/1.31 thf(f23,plain,(
% 1.65/1.31 ! [X2 : frac,X1 : frac,X0 : frac] : (((moref @ X1 @ X0) = $true) => ($true = (moref @ (pf @ X1 @ X2) @ (pf @ X0 @ X2))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f22])).
% 1.65/1.31 thf(f22,plain,(
% 1.65/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X1 @ X0) => (moref @ (pf @ X1 @ X2) @ (pf @ X0 @ X2)))),
% 1.65/1.31 inference(rectify,[status(thm)],[f6])).
% 1.65/1.31 thf(f6,axiom,(
% 1.65/1.31 ! [X2 : frac,X1 : frac,X3 : frac] : ((moref @ X1 @ X2) => (moref @ (pf @ X1 @ X3) @ (pf @ X2 @ X3)))),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.odWEo0ZJmb/DTF2THF_26018.p',satz62a)).
% 1.65/1.31 thf(f39,plain,(
% 1.65/1.31 ( ! [X0 : frac,X1 : frac] : (($true != (moref @ X0 @ X1)) | ($true != (eq @ X0 @ X1))) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f34])).
% 1.65/1.31 % SZS output end Proof for DTF2THF_26018
% 1.65/1.31 % (26186)------------------------------
% 1.65/1.31 % (26186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (26186)Termination reason: Refutation
% 1.65/1.31
% 1.65/1.31 % (26186)Memory used [KB]: 5628
% 1.65/1.31 % (26186)Time elapsed: 0.007 s
% 1.65/1.31 % (26186)Instructions burned: 10 (million)
% 1.65/1.31 % (26186)------------------------------
% 1.65/1.31 % (26186)------------------------------
% 1.65/1.31 % (26183)Success in time 0.018 s
%------------------------------------------------------------------------------