%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM770^1 : 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 : n006.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 09:24:40 AM UTC 2026
% Result : Theorem 1.49s 1.29s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 135 ( 39 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 234 ( 20 ~; 15 |; 0 &; 190 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% 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,
v: frac ).
thf(func_def_4,type,
moref: frac > frac > $o ).
thf(func_def_6,type,
eq: frac > frac > $o ).
thf(func_def_7,type,
pf: frac > frac > frac ).
thf(func_def_8,type,
mf: frac > frac > frac ).
thf(f38,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f36,f24]) ).
thf(f24,plain,
( ( eq @ v @ ( mf @ x @ y ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( eq @ v @ ( mf @ x @ y ) )
!= $true ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( eq @ v @ ( mf @ x @ y ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( eq @ v @ ( mf @ x @ y ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( eq @ v @ ( mf @ x @ y ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
eq @ v @ ( mf @ x @ y ),
file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',satz67e) ).
thf(f36,plain,
( ( eq @ v @ ( mf @ x @ y ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true != $true )
| ( ( eq @ v @ ( mf @ x @ y ) )
= $true ) ),
inference(superposition,[status(thm)],[f33,f29]) ).
thf(f29,plain,
( $true
= ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true
= ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f27,f26]) ).
thf(f26,plain,
( ( moref @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( moref @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
moref @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
moref @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',m) ).
thf(f27,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: frac,X1: frac] :
( ( moref @ X0 @ X1 )
=> ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: frac,X1: frac] :
( ( moref @ X0 @ X1 )
=> ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',satz67c) ).
thf(f33,plain,
! [X0: frac] :
( ( ( eq @ ( pf @ y @ X0 ) @ x )
!= $true )
| ( ( eq @ v @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: frac] :
( ( ( eq @ v @ X0 )
= $true )
| ( $true != $true )
| ( ( eq @ ( pf @ y @ X0 ) @ x )
!= $true ) ),
inference(superposition,[status(thm)],[f23,f25]) ).
thf(f25,plain,
( ( eq @ ( pf @ y @ v ) @ x )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( eq @ ( pf @ y @ v ) @ x )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
eq @ ( pf @ y @ v ) @ x,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
eq @ ( pf @ y @ v ) @ x,
file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',e) ).
thf(f23,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X0 @ X3 ) @ X1 )
!= $true )
| ( ( eq @ ( pf @ X0 @ X2 ) @ X1 )
!= $true )
| ( ( eq @ X3 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ ( pf @ X0 @ X3 ) @ X1 )
!= $true )
| ( ( eq @ X3 @ X2 )
= $true )
| ( ( eq @ ( pf @ X0 @ X2 ) @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
! [X3: frac,X2: frac,X1: frac,X0: frac] :
( ( ( eq @ ( pf @ X3 @ X0 ) @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true )
| ( ( eq @ ( pf @ X3 @ X1 ) @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: frac,X1: frac,X3: frac,X0: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
| ( ( eq @ ( pf @ X3 @ X1 ) @ X2 )
!= $true )
| ( ( eq @ ( pf @ X3 @ X0 ) @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: frac,X1: frac,X3: frac,X0: frac] :
( ( ( eq @ ( pf @ X3 @ X0 ) @ X2 )
= $true )
=> ( ( ( eq @ ( pf @ X3 @ X1 ) @ X2 )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ ( pf @ X3 @ X0 ) @ X2 )
=> ( ( eq @ ( pf @ X3 @ X1 ) @ X2 )
=> ( eq @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( eq @ ( pf @ X1 @ X2 ) @ X0 )
=> ( ( eq @ ( pf @ X1 @ X3 ) @ X0 )
=> ( eq @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',satz67b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM770^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 11:13:45 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : NUM770^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.45 % Domain : Number Theory
% 0.29/0.45 % Problem : Landau theorem 67e
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English : eq v (mf x y)
% 0.29/0.45
% 0.29/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.29/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.29/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : satz67e [Lan30]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % : Without extensionality : Theorem
% 0.29/0.45 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.29/0.45 % Syntax : Number of formulae : 13 ( 3 unt; 8 typ; 0 def)
% 0.29/0.45 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 3 ( 1 avg)
% 0.29/0.45 % Number of connectives : 31 ( 0 ~; 0 |; 0 &; 28 @)
% 0.29/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 11 ( 6 avg)
% 0.29/0.45 % Number of types : 2 ( 1 usr)
% 0.29/0.45 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.29/0.45 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.29/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.45
% 0.29/0.45 % Comments :
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(frac_type,type,
% 0.29/0.45 frac: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(x,type,
% 0.29/0.45 x: frac ).
% 0.29/0.45
% 0.29/0.45 thf(y,type,
% 0.29/0.45 y: frac ).
% 0.29/0.45
% 0.29/0.45 thf(v,type,
% 0.29/0.45 v: frac ).
% 0.29/0.45
% 0.29/0.45 thf(moref,type,
% 0.29/0.45 moref: frac > frac > $o ).
% 0.29/0.45
% 0.29/0.45 thf(m,axiom,
% 0.29/0.45 moref @ x @ y ).
% 0.29/0.45
% 0.29/0.45 thf(eq,type,
% 0.29/0.45 eq: frac > frac > $o ).
% 0.29/0.45
% 0.29/0.45 thf(pf,type,
% 0.29/0.45 pf: frac > frac > frac ).
% 0.29/0.45
% 0.29/0.45 thf(e,axiom,
% 0.29/0.45 eq @ ( pf @ y @ v ) @ x ).
% 0.29/0.45
% 0.29/0.45 thf(mf,type,
% 0.29/0.45 mf: frac > frac > frac ).
% 0.29/0.45
% 0.29/0.45 thf(satz67b,axiom,
% 0.29/0.45 ! [Xx: frac,Xy: frac,Xv: frac,Xw: frac] :
% 0.29/0.45 ( ( eq @ ( pf @ Xy @ Xv ) @ Xx )
% 0.29/0.45 => ( ( eq @ ( pf @ Xy @ Xw ) @ Xx )
% 0.29/0.45 => ( eq @ Xv @ Xw ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(satz67c,axiom,
% 0.29/0.45 ! [Xx: frac,Xy: frac] :
% 0.29/0.45 ( ( moref @ Xx @ Xy )
% 0.29/0.45 => ( eq @ ( pf @ Xy @ ( mf @ Xx @ Xy ) ) @ Xx ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(satz67e,conjecture,
% 0.29/0.45 eq @ v @ ( mf @ x @ y ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.49/1.26 ---- Embedded in THF ---
% 1.49/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.26 %%% Generated on Tue Feb 24 11:13:46 EST 2026
% 1.49/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.26 %%% Logic specification used:
% 1.49/1.26 %%% thf(spec, logic, $$dhol).
% 1.49/1.26
% 1.49/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2DTF10373.p
% See solution above
% 1.49/1.26 ------------------------
% 1.49/1.27 ---- Cleaned THF ---
% 1.49/1.27 thf(frac_type,type,
% 1.49/1.27 frac: $tType ).
% 1.49/1.27
% 1.49/1.27 thf(x,type,
% 1.49/1.27 x: frac ).
% 1.49/1.27
% 1.49/1.27 thf(y,type,
% 1.49/1.27 y: frac ).
% 1.49/1.27
% 1.49/1.27 thf(v,type,
% 1.49/1.27 v: frac ).
% 1.49/1.27
% 1.49/1.27 thf(moref,type,
% 1.49/1.27 moref: frac > frac > $o ).
% 1.49/1.27
% 1.49/1.27 thf(m,axiom,
% 1.49/1.27 moref @ x @ y ).
% 1.49/1.27
% 1.49/1.27 thf(eq,type,
% 1.49/1.27 eq: frac > frac > $o ).
% 1.49/1.27
% 1.49/1.27 thf(pf,type,
% 1.49/1.27 pf: frac > frac > frac ).
% 1.49/1.27
% 1.49/1.27 thf(e,axiom,
% 1.49/1.27 eq @ ( pf @ y @ v ) @ x ).
% 1.49/1.27
% 1.49/1.27 thf(mf,type,
% 1.49/1.27 mf: frac > frac > frac ).
% 1.49/1.27
% 1.49/1.27 thf(satz67b,axiom,
% 1.49/1.27 ! [Xx: frac,Xy: frac,Xv: frac,Xw: frac] :
% 1.49/1.27 ( ( eq @ ( pf @ Xy @ Xv ) @ Xx )
% 1.49/1.27 => ( ( eq @ ( pf @ Xy @ Xw ) @ Xx )
% 1.49/1.27 => ( eq @ Xv @ Xw ) ) ) ).
% 1.49/1.27
% 1.49/1.27 thf(satz67c,axiom,
% 1.49/1.27 ! [Xx: frac,Xy: frac] :
% 1.49/1.27 ( ( moref @ Xx @ Xy )
% 1.49/1.27 => ( eq @ ( pf @ Xy @ ( mf @ Xx @ Xy ) ) @ Xx ) ) ).
% 1.49/1.27
% 1.49/1.27 thf(satz67e,conjecture,
% 1.49/1.27 eq @ v @ ( mf @ x @ y ) ).
% 1.49/1.27 ------------------------
% 1.49/1.28 % (10477)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10373 for (3000ds/18Mi)
% 1.49/1.28 % (10471)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10373 for (3000ds/183Mi)
% 1.49/1.29 % (10477)First to succeed.
% 1.49/1.29 % (10471)Also succeeded, but the first one will report.
% 1.49/1.29 % (10477)Refutation found. Thanks to Tanya!
% 1.49/1.29 % SZS status Theorem for DTF2THF_10373
% 1.49/1.29 % SZS output start Proof for DTF2THF_10373
% 1.49/1.29 thf(type_def_5, type, frac: $tType).
% 1.49/1.29 thf(func_def_0, type, frac: $tType).
% 1.49/1.29 thf(func_def_1, type, x: frac).
% 1.49/1.29 thf(func_def_2, type, y: frac).
% 1.49/1.29 thf(func_def_3, type, v: frac).
% 1.49/1.29 thf(func_def_4, type, moref: frac > frac > $o).
% 1.49/1.29 thf(func_def_6, type, eq: frac > frac > $o).
% 1.49/1.29 thf(func_def_7, type, pf: frac > frac > frac).
% 1.49/1.29 thf(func_def_8, type, mf: frac > frac > frac).
% 1.49/1.29 thf(f38,plain,(
% 1.49/1.29 $false),
% 1.49/1.29 inference(subsumption_resolution,[status(thm)],[f36,f24])).
% 1.49/1.29 thf(f24,plain,(
% 1.49/1.29 ((eq @ v @ (mf @ x @ y)) != $true)),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.49/1.29 thf(f18,plain,(
% 1.49/1.29 ((eq @ v @ (mf @ x @ y)) != $true)),
% 1.49/1.29 inference(flattening,[status(thm)],[f9])).
% 1.49/1.29 thf(f9,plain,(
% 1.49/1.29 ~((eq @ v @ (mf @ x @ y)) = $true)),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.49/1.29 thf(f8,plain,(
% 1.49/1.29 ~(eq @ v @ (mf @ x @ y))),
% 1.49/1.29 inference(rectify,[status(thm)],[f6])).
% 1.49/1.29 thf(f6,negated_conjecture,(
% 1.49/1.29 ~(eq @ v @ (mf @ x @ y))),
% 1.49/1.29 inference(negated_conjecture,[status(cth)],[f5])).
% 1.49/1.29 thf(f5,conjecture,(
% 1.49/1.29 (eq @ v @ (mf @ x @ y))),
% 1.49/1.29 file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',satz67e)).
% 1.49/1.29 thf(f36,plain,(
% 1.49/1.29 ((eq @ v @ (mf @ x @ y)) = $true)),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.49/1.29 thf(f35,plain,(
% 1.49/1.29 ($true != $true) | ((eq @ v @ (mf @ x @ y)) = $true)),
% 1.49/1.29 inference(superposition,[status(thm)],[f33,f29])).
% 1.49/1.29 thf(f29,plain,(
% 1.49/1.29 ($true = (eq @ (pf @ y @ (mf @ x @ y)) @ x))),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.49/1.29 thf(f28,plain,(
% 1.49/1.29 ($true = (eq @ (pf @ y @ (mf @ x @ y)) @ x)) | ($true != $true)),
% 1.49/1.29 inference(superposition,[status(thm)],[f27,f26])).
% 1.49/1.29 thf(f26,plain,(
% 1.49/1.29 ((moref @ x @ y) = $true)),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.49/1.29 thf(f17,plain,(
% 1.49/1.29 ((moref @ x @ y) = $true)),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f16])).
% 1.49/1.29 thf(f16,plain,(
% 1.49/1.29 (moref @ x @ y)),
% 1.49/1.29 inference(rectify,[status(thm)],[f1])).
% 1.49/1.29 thf(f1,axiom,(
% 1.49/1.29 (moref @ x @ y)),
% 1.49/1.29 file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',m)).
% 1.49/1.29 thf(f27,plain,(
% 1.49/1.29 ( ! [X0 : frac,X1 : frac] : (((moref @ X0 @ X1) != $true) | ((eq @ (pf @ X1 @ (mf @ X0 @ X1)) @ X0) = $true)) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f21])).
% 1.49/1.29 thf(f21,plain,(
% 1.49/1.29 ! [X0 : frac,X1 : frac] : (((eq @ (pf @ X1 @ (mf @ X0 @ X1)) @ X0) = $true) | ((moref @ X0 @ X1) != $true))),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f15])).
% 1.49/1.29 thf(f15,plain,(
% 1.49/1.29 ! [X0 : frac,X1 : frac] : (((moref @ X0 @ X1) = $true) => ((eq @ (pf @ X1 @ (mf @ X0 @ X1)) @ X0) = $true))),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f14])).
% 1.49/1.29 thf(f14,plain,(
% 1.49/1.29 ! [X0 : frac,X1 : frac] : ((moref @ X0 @ X1) => (eq @ (pf @ X1 @ (mf @ X0 @ X1)) @ X0))),
% 1.49/1.29 inference(rectify,[status(thm)],[f4])).
% 1.49/1.29 thf(f4,axiom,(
% 1.49/1.29 ! [X0 : frac,X1 : frac] : ((moref @ X0 @ X1) => (eq @ (pf @ X1 @ (mf @ X0 @ X1)) @ X0))),
% 1.49/1.29 file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',satz67c)).
% 1.49/1.29 thf(f33,plain,(
% 1.49/1.29 ( ! [X0 : frac] : (((eq @ (pf @ y @ X0) @ x) != $true) | ((eq @ v @ X0) = $true)) )),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.49/1.29 thf(f30,plain,(
% 1.49/1.29 ( ! [X0 : frac] : (((eq @ v @ X0) = $true) | ($true != $true) | ((eq @ (pf @ y @ X0) @ x) != $true)) )),
% 1.49/1.29 inference(superposition,[status(thm)],[f23,f25])).
% 1.49/1.29 thf(f25,plain,(
% 1.49/1.29 ((eq @ (pf @ y @ v) @ x) = $true)),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.29 thf(f11,plain,(
% 1.49/1.29 ((eq @ (pf @ y @ v) @ x) = $true)),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.49/1.29 thf(f10,plain,(
% 1.49/1.29 (eq @ (pf @ y @ v) @ x)),
% 1.49/1.29 inference(rectify,[status(thm)],[f2])).
% 1.49/1.29 thf(f2,axiom,(
% 1.49/1.29 (eq @ (pf @ y @ v) @ x)),
% 1.49/1.29 file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',e)).
% 1.49/1.29 thf(f23,plain,(
% 1.49/1.29 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((eq @ (pf @ X0 @ X3) @ X1) != $true) | ((eq @ (pf @ X0 @ X2) @ X1) != $true) | ((eq @ X3 @ X2) = $true)) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f22])).
% 1.49/1.29 thf(f22,plain,(
% 1.49/1.29 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((eq @ (pf @ X0 @ X3) @ X1) != $true) | ((eq @ X3 @ X2) = $true) | ((eq @ (pf @ X0 @ X2) @ X1) != $true))),
% 1.49/1.29 inference(rectify,[status(thm)],[f20])).
% 1.49/1.29 thf(f20,plain,(
% 1.49/1.29 ! [X3 : frac,X2 : frac,X1 : frac,X0 : frac] : (((eq @ (pf @ X3 @ X0) @ X2) != $true) | ((eq @ X0 @ X1) = $true) | ((eq @ (pf @ X3 @ X1) @ X2) != $true))),
% 1.49/1.29 inference(flattening,[status(thm)],[f19])).
% 1.49/1.29 thf(f19,plain,(
% 1.49/1.29 ! [X2 : frac,X1 : frac,X3 : frac,X0 : frac] : ((((eq @ X0 @ X1) = $true) | ((eq @ (pf @ X3 @ X1) @ X2) != $true)) | ((eq @ (pf @ X3 @ X0) @ X2) != $true))),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f13])).
% 1.49/1.29 thf(f13,plain,(
% 1.49/1.29 ! [X2 : frac,X1 : frac,X3 : frac,X0 : frac] : (((eq @ (pf @ X3 @ X0) @ X2) = $true) => (((eq @ (pf @ X3 @ X1) @ X2) = $true) => ((eq @ X0 @ X1) = $true)))),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f12])).
% 1.49/1.29 thf(f12,plain,(
% 1.49/1.29 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ (pf @ X3 @ X0) @ X2) => ((eq @ (pf @ X3 @ X1) @ X2) => (eq @ X0 @ X1)))),
% 1.49/1.29 inference(rectify,[status(thm)],[f3])).
% 1.49/1.29 thf(f3,axiom,(
% 1.49/1.29 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((eq @ (pf @ X1 @ X2) @ X0) => ((eq @ (pf @ X1 @ X3) @ X0) => (eq @ X2 @ X3)))),
% 1.49/1.29 file('/export/starexec/sandbox2/tmp/tmp.974TdJDsQt/DTF2THF_10373.p',satz67b)).
% 1.49/1.29 % SZS output end Proof for DTF2THF_10373
% 1.49/1.29 % (10477)------------------------------
% 1.49/1.29 % (10477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (10477)Termination reason: Refutation
% 1.49/1.29
% 1.49/1.29 % (10477)Memory used [KB]: 5500
% 1.49/1.29 % (10477)Time elapsed: 0.003 s
% 1.49/1.29 % (10477)Instructions burned: 4 (million)
% 1.49/1.29 % (10477)------------------------------
% 1.49/1.29 % (10477)------------------------------
% 1.49/1.29 % (10470)Success in time 0.004 s
%------------------------------------------------------------------------------