%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM740^1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:24:29 AM UTC 2026
% Result : Theorem 1.61s 1.32s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 155 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 182 ( 34 ~; 18 |; 1 &; 112 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% 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,
moref: frac > frac > $o ).
thf(func_def_4,type,
eq: frac > frac > $o ).
thf(func_def_6,type,
lessf: frac > frac > $o ).
thf(f44,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f35,f39,f43]) ).
thf(f43,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f41,f25]) ).
thf(f25,plain,
( ( lessf @ y @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( eq @ y @ x )
!= $true )
& ( ( lessf @ y @ x )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( ( lessf @ y @ x )
!= $true )
=> ( ( eq @ y @ x )
= $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( ( lessf @ y @ x )
!= $true )
=> ( ( eq @ y @ x )
= $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ~ ( lessf @ y @ x )
=> ( eq @ y @ x ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( ~ ( lessf @ y @ x )
=> ( eq @ y @ x ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( ~ ( lessf @ y @ x )
=> ( eq @ y @ x ) ),
file('/export/starexec/sandbox2/tmp/tmp.eIC6VchqvY/DTF2THF_11147.p',satz48) ).
thf(f41,plain,
( ( ( lessf @ y @ x )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true != $true )
| ( ( lessf @ y @ x )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f22,f30]) ).
thf(f30,plain,
( ( ( moref @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl0_1
<=> ( ( moref @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f22,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( lessf @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( lessf @ X1 @ X0 )
= $true ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: frac,X0: frac] :
( ( $true
!= ( moref @ X1 @ X0 ) )
| ( ( lessf @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( moref @ X1 @ X0 ) )
=> ( ( lessf @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: frac,X1: frac] :
( ( moref @ X1 @ X0 )
=> ( lessf @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: frac,X0: frac] :
( ( moref @ X0 @ X1 )
=> ( lessf @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.eIC6VchqvY/DTF2THF_11147.p',satz42) ).
thf(f39,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f37,f26]) ).
thf(f26,plain,
( ( eq @ y @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f37,plain,
( ( ( eq @ y @ x )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( eq @ y @ x )
= $true )
| ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f23,f34]) ).
thf(f34,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl0_2
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f23,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( eq @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.eIC6VchqvY/DTF2THF_11147.p',satz38) ).
thf(f35,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f32,f28]) ).
thf(f24,plain,
( ( ( moref @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( moref @ x @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/tmp/tmp.eIC6VchqvY/DTF2THF_11147.p',m) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM740^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n020.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 11:12:42 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.25/0.48 ---- Original DTF file ---
% 0.25/0.48 thf(spec,logic,$$dhol).
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 % File : NUM740^1 : TPTP v9.2.1. Released v3.7.0.
% 0.25/0.48 % Domain : Number Theory
% 0.25/0.48 % Problem : Landau theorem 48
% 0.25/0.48 % Version : Especial.
% 0.25/0.48 % English : ~(lessf y x) -> eq y x
% 0.25/0.48
% 0.25/0.48 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.25/0.48 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.25/0.48 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.25/0.48 % Source : [Bro09]
% 0.25/0.48 % Names : satz48 [Lan30]
% 0.25/0.48
% 0.25/0.48 % Status : Theorem
% 0.25/0.48 % : Without extensionality : Theorem
% 0.25/0.48 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.25/0.48 % Syntax : Number of formulae : 10 ( 0 unt; 6 typ; 0 def)
% 0.25/0.48 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.25/0.48 % Maximal formula atoms : 2 ( 2 avg)
% 0.25/0.48 % Number of connectives : 22 ( 2 ~; 0 |; 0 &; 16 @)
% 0.25/0.48 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.25/0.48 % Maximal formula depth : 6 ( 6 avg)
% 0.25/0.48 % Number of types : 2 ( 1 usr)
% 0.25/0.48 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.25/0.48 % Number of symbols : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.25/0.48 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.25/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.25/0.48
% 0.25/0.48 % Comments :
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 thf(frac_type,type,
% 0.25/0.48 frac: $tType ).
% 0.25/0.48
% 0.25/0.48 thf(x,type,
% 0.25/0.48 x: frac ).
% 0.25/0.48
% 0.25/0.48 thf(y,type,
% 0.25/0.48 y: frac ).
% 0.25/0.48
% 0.25/0.48 thf(moref,type,
% 0.25/0.48 moref: frac > frac > $o ).
% 0.25/0.48
% 0.25/0.48 thf(eq,type,
% 0.25/0.48 eq: frac > frac > $o ).
% 0.25/0.48
% 0.25/0.48 thf(m,axiom,
% 0.25/0.48 ( ~ ( moref @ x @ y )
% 0.25/0.48 => ( eq @ x @ y ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(lessf,type,
% 0.25/0.48 lessf: frac > frac > $o ).
% 0.25/0.48
% 0.25/0.48 thf(satz38,axiom,
% 0.25/0.48 ! [Xx: frac,Xy: frac] :
% 0.25/0.48 ( ( eq @ Xx @ Xy )
% 0.25/0.48 => ( eq @ Xy @ Xx ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(satz42,axiom,
% 0.25/0.48 ! [Xx: frac,Xy: frac] :
% 0.25/0.48 ( ( moref @ Xx @ Xy )
% 0.25/0.48 => ( lessf @ Xy @ Xx ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(satz48,conjecture,
% 0.25/0.48 ( ~ ( lessf @ y @ x )
% 0.25/0.48 => ( eq @ y @ x ) ) ).
% 0.25/0.48
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 ------------------------
% 1.41/1.28 ---- Embedded in THF ---
% 1.41/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.41/1.28 %%% Generated on Tue Feb 24 11:12:43 EST 2026
% 1.41/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.41/1.28 %%% Logic specification used:
% 1.41/1.28 %%% thf(spec, logic, $$dhol).
% 1.41/1.28
% 1.41/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.eIC6VchqvY/DTF2DTF11147.p
% See solution above
% 1.41/1.28 ------------------------
% 1.41/1.29 ---- Cleaned THF ---
% 1.41/1.29 thf(frac_type,type,
% 1.41/1.29 frac: $tType ).
% 1.41/1.29
% 1.41/1.29 thf(x,type,
% 1.41/1.29 x: frac ).
% 1.41/1.29
% 1.41/1.29 thf(y,type,
% 1.41/1.29 y: frac ).
% 1.41/1.29
% 1.41/1.29 thf(moref,type,
% 1.41/1.29 moref: frac > frac > $o ).
% 1.41/1.29
% 1.41/1.29 thf(eq,type,
% 1.41/1.29 eq: frac > frac > $o ).
% 1.41/1.29
% 1.41/1.29 thf(m,axiom,
% 1.41/1.29 ( ~ ( moref @ x @ y )
% 1.41/1.29 => ( eq @ x @ y ) ) ).
% 1.41/1.29
% 1.41/1.29 thf(lessf,type,
% 1.41/1.29 lessf: frac > frac > $o ).
% 1.41/1.29
% 1.41/1.29 thf(satz38,axiom,
% 1.41/1.29 ! [Xx: frac,Xy: frac] :
% 1.41/1.29 ( ( eq @ Xx @ Xy )
% 1.41/1.29 => ( eq @ Xy @ Xx ) ) ).
% 1.41/1.29
% 1.41/1.29 thf(satz42,axiom,
% 1.41/1.29 ! [Xx: frac,Xy: frac] :
% 1.41/1.29 ( ( moref @ Xx @ Xy )
% 1.41/1.29 => ( lessf @ Xy @ Xx ) ) ).
% 1.41/1.29
% 1.41/1.29 thf(satz48,conjecture,
% 1.41/1.29 ( ~ ( lessf @ y @ x )
% 1.41/1.29 => ( eq @ y @ x ) ) ).
% 1.41/1.29 ------------------------
% 1.61/1.31 % (11244)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11147 for (3000ds/183Mi)
% 1.61/1.31 % (11250)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11147 for (3000ds/18Mi)
% 1.61/1.31 % (11245)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_11147 for (3000ds/4Mi)
% 1.61/1.31 % (11248)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_11147 for (3000ds/2Mi)
% 1.61/1.32 % (11250)First to succeed.
% 1.61/1.32 % (11248)Instruction limit reached!
% 1.61/1.32 % (11248)------------------------------
% 1.61/1.32 % (11248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (11248)Termination reason: Unknown
% 1.61/1.32 % (11248)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (11248)Memory used [KB]: 5500
% 1.61/1.32 % (11248)Time elapsed: 0.002 s
% 1.61/1.32 % (11248)Instructions burned: 3 (million)
% 1.61/1.32 % (11248)------------------------------
% 1.61/1.32 % (11248)------------------------------
% 1.61/1.32 % (11245)Instruction limit reached!
% 1.61/1.32 % (11245)------------------------------
% 1.61/1.32 % (11245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (11245)Termination reason: Unknown
% 1.61/1.32 % (11245)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (11245)Memory used [KB]: 5500
% 1.61/1.32 % (11245)Time elapsed: 0.005 s
% 1.61/1.32 % (11245)Instructions burned: 4 (million)
% 1.61/1.32 % (11245)------------------------------
% 1.61/1.32 % (11245)------------------------------
% 1.61/1.32 % (11249)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_11147 for (3000ds/275Mi)
% 1.61/1.32 % (11244)Also succeeded, but the first one will report.
% 1.61/1.32 % (11250)Refutation found. Thanks to Tanya!
% 1.61/1.32 % SZS status Theorem for DTF2THF_11147
% 1.61/1.32 % SZS output start Proof for DTF2THF_11147
% 1.61/1.32 thf(type_def_5, type, frac: $tType).
% 1.61/1.32 thf(func_def_0, type, frac: $tType).
% 1.61/1.32 thf(func_def_1, type, x: frac).
% 1.61/1.32 thf(func_def_2, type, y: frac).
% 1.61/1.32 thf(func_def_3, type, moref: frac > frac > $o).
% 1.61/1.32 thf(func_def_4, type, eq: frac > frac > $o).
% 1.61/1.32 thf(func_def_6, type, lessf: frac > frac > $o).
% 1.61/1.32 thf(f44,plain,(
% 1.61/1.32 $false),
% 1.61/1.32 inference(avatar_sat_refutation,[status(thm)],[f35,f39,f43])).
% 1.61/1.32 thf(f43,plain,(
% 1.61/1.32 ~spl0_1),
% 1.61/1.32 inference(avatar_contradiction_clause,[status(thm)],[f42])).
% 1.61/1.32 thf(f42,plain,(
% 1.61/1.32 $false | ~spl0_1),
% 1.61/1.32 inference(subsumption_resolution,[status(thm)],[f41,f25])).
% 1.61/1.32 thf(f25,plain,(
% 1.61/1.32 ((lessf @ y @ x) != $true)),
% 1.61/1.32 inference(cnf_transformation,[status(thm)],[f19])).
% 1.61/1.32 thf(f19,plain,(
% 1.61/1.32 ((eq @ y @ x) != $true) & ((lessf @ y @ x) != $true)),
% 1.61/1.32 inference(ennf_transformation,[status(thm)],[f15])).
% 1.61/1.32 thf(f15,plain,(
% 1.61/1.32 ~(((lessf @ y @ x) != $true) => ((eq @ y @ x) = $true))),
% 1.61/1.32 inference(flattening,[status(thm)],[f10])).
% 1.61/1.32 thf(f10,plain,(
% 1.61/1.32 ~(~((lessf @ y @ x) = $true) => ((eq @ y @ x) = $true))),
% 1.61/1.32 inference(fool_elimination,[status(thm)],[f9])).
% 1.61/1.32 thf(f9,plain,(
% 1.61/1.32 ~(~(lessf @ y @ x) => (eq @ y @ x))),
% 1.61/1.32 inference(rectify,[status(thm)],[f5])).
% 1.61/1.32 thf(f5,negated_conjecture,(
% 1.61/1.32 ~(~(lessf @ y @ x) => (eq @ y @ x))),
% 1.61/1.32 inference(negated_conjecture,[status(cth)],[f4])).
% 1.61/1.32 thf(f4,conjecture,(
% 1.61/1.32 ~(lessf @ y @ x) => (eq @ y @ x)),
% 1.61/1.32 file('/export/starexec/sandbox2/tmp/tmp.eIC6VchqvY/DTF2THF_11147.p',satz48)).
% 1.61/1.32 thf(f41,plain,(
% 1.61/1.32 ((lessf @ y @ x) = $true) | ~spl0_1),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.61/1.32 thf(f40,plain,(
% 1.61/1.32 ($true != $true) | ((lessf @ y @ x) = $true) | ~spl0_1),
% 1.61/1.32 inference(superposition,[status(thm)],[f22,f30])).
% 1.61/1.32 thf(f30,plain,(
% 1.61/1.32 ((moref @ x @ y) = $true) | ~spl0_1),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.61/1.32 thf(f28,definition,(
% 1.61/1.32 spl0_1 <=> ((moref @ x @ y) = $true)),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.61/1.32 thf(f22,plain,(
% 1.61/1.32 ( ! [X0 : frac,X1 : frac] : (((moref @ X0 @ X1) != $true) | ((lessf @ X1 @ X0) = $true)) )),
% 1.61/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.61/1.32 thf(f21,plain,(
% 1.61/1.32 ! [X0 : frac,X1 : frac] : (((moref @ X0 @ X1) != $true) | ((lessf @ X1 @ X0) = $true))),
% 1.61/1.32 inference(rectify,[status(thm)],[f20])).
% 1.61/1.32 thf(f20,plain,(
% 1.61/1.32 ! [X1 : frac,X0 : frac] : (($true != (moref @ X1 @ X0)) | ((lessf @ X0 @ X1) = $true))),
% 1.61/1.32 inference(ennf_transformation,[status(thm)],[f8])).
% 1.61/1.32 thf(f8,plain,(
% 1.61/1.32 ! [X0 : frac,X1 : frac] : (($true = (moref @ X1 @ X0)) => ((lessf @ X0 @ X1) = $true))),
% 1.61/1.32 inference(fool_elimination,[status(thm)],[f7])).
% 1.61/1.32 thf(f7,plain,(
% 1.61/1.32 ! [X0 : frac,X1 : frac] : ((moref @ X1 @ X0) => (lessf @ X0 @ X1))),
% 1.61/1.32 inference(rectify,[status(thm)],[f3])).
% 1.61/1.32 thf(f3,axiom,(
% 1.61/1.32 ! [X1 : frac,X0 : frac] : ((moref @ X0 @ X1) => (lessf @ X1 @ X0))),
% 1.61/1.32 file('/export/starexec/sandbox2/tmp/tmp.eIC6VchqvY/DTF2THF_11147.p',satz42)).
% 1.61/1.32 thf(f39,plain,(
% 1.61/1.32 ~spl0_2),
% 1.61/1.32 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.61/1.32 thf(f38,plain,(
% 1.61/1.32 $false | ~spl0_2),
% 1.61/1.32 inference(subsumption_resolution,[status(thm)],[f37,f26])).
% 1.61/1.32 thf(f26,plain,(
% 1.61/1.32 ((eq @ y @ x) != $true)),
% 1.61/1.32 inference(cnf_transformation,[status(thm)],[f19])).
% 1.61/1.32 thf(f37,plain,(
% 1.61/1.32 ((eq @ y @ x) = $true) | ~spl0_2),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.61/1.32 thf(f36,plain,(
% 1.61/1.32 ((eq @ y @ x) = $true) | ($true != $true) | ~spl0_2),
% 1.61/1.32 inference(superposition,[status(thm)],[f23,f34])).
% 1.61/1.32 thf(f34,plain,(
% 1.61/1.32 ((eq @ x @ y) = $true) | ~spl0_2),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.61/1.32 thf(f32,definition,(
% 1.61/1.32 spl0_2 <=> ((eq @ x @ y) = $true)),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.61/1.32 thf(f23,plain,(
% 1.61/1.32 ( ! [X0 : frac,X1 : frac] : (((eq @ X0 @ X1) != $true) | ((eq @ X1 @ X0) = $true)) )),
% 1.61/1.32 inference(cnf_transformation,[status(thm)],[f18])).
% 1.61/1.32 thf(f18,plain,(
% 1.61/1.32 ! [X0 : frac,X1 : frac] : (((eq @ X1 @ X0) = $true) | ((eq @ X0 @ X1) != $true))),
% 1.61/1.32 inference(ennf_transformation,[status(thm)],[f14])).
% 1.61/1.32 thf(f14,plain,(
% 1.61/1.32 ! [X0 : frac,X1 : frac] : (((eq @ X0 @ X1) = $true) => ((eq @ X1 @ X0) = $true))),
% 1.61/1.32 inference(fool_elimination,[status(thm)],[f13])).
% 1.61/1.32 thf(f13,plain,(
% 1.61/1.32 ! [X0 : frac,X1 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 1.61/1.32 inference(rectify,[status(thm)],[f2])).
% 1.61/1.32 thf(f2,axiom,(
% 1.61/1.32 ! [X0 : frac,X1 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 1.61/1.32 file('/export/starexec/sandbox2/tmp/tmp.eIC6VchqvY/DTF2THF_11147.p',satz38)).
% 1.61/1.32 thf(f35,plain,(
% 1.61/1.32 spl0_1 | spl0_2),
% 1.61/1.32 inference(avatar_split_clause,[status(thm)],[f24,f32,f28])).
% 1.61/1.32 thf(f24,plain,(
% 1.61/1.32 ((moref @ x @ y) = $true) | ((eq @ x @ y) = $true)),
% 1.61/1.32 inference(cnf_transformation,[status(thm)],[f17])).
% 1.61/1.32 thf(f17,plain,(
% 1.61/1.32 ((eq @ x @ y) = $true) | ((moref @ x @ y) = $true)),
% 1.61/1.32 inference(ennf_transformation,[status(thm)],[f16])).
% 1.61/1.32 thf(f16,plain,(
% 1.61/1.32 ((moref @ x @ y) != $true) => ((eq @ x @ y) = $true)),
% 1.61/1.32 inference(flattening,[status(thm)],[f12])).
% 1.61/1.32 thf(f12,plain,(
% 1.61/1.32 ~((moref @ x @ y) = $true) => ((eq @ x @ y) = $true)),
% 1.61/1.32 inference(fool_elimination,[status(thm)],[f11])).
% 1.61/1.32 thf(f11,plain,(
% 1.61/1.32 ~(moref @ x @ y) => (eq @ x @ y)),
% 1.61/1.32 inference(rectify,[status(thm)],[f1])).
% 1.61/1.32 thf(f1,axiom,(
% 1.61/1.32 ~(moref @ x @ y) => (eq @ x @ y)),
% 1.61/1.32 file('/export/starexec/sandbox2/tmp/tmp.eIC6VchqvY/DTF2THF_11147.p',m)).
% 1.61/1.32 % SZS output end Proof for DTF2THF_11147
% 1.61/1.32 % (11250)------------------------------
% 1.61/1.32 % (11250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (11250)Termination reason: Refutation
% 1.61/1.32
% 1.61/1.32 % (11250)Memory used [KB]: 5500
% 1.61/1.32 % (11250)Time elapsed: 0.004 s
% 1.61/1.32 % (11250)Instructions burned: 2 (million)
% 1.61/1.32 % (11250)------------------------------
% 1.61/1.32 % (11250)------------------------------
% 1.61/1.32 % (11243)Success in time 0.023 s
%------------------------------------------------------------------------------