%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM743^1 : 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 : 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 1.53s 1.26s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 254 ( 76 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 300 ( 52 ~; 37 |; 0 &; 192 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 0 ^; 61 !; 0 ?; 61 :)
% 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_6,type,
eq: frac > frac > $o ).
thf(f60,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f59,f39]) ).
thf(f39,plain,
( ( lessf @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( lessf @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
lessf @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
lessf @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',l) ).
thf(f59,plain,
( ( lessf @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( ( lessf @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f46,f57]) ).
thf(f57,plain,
( ( lessf @ y @ z )
= $true ),
inference(subsumption_resolution,[status(thm)],[f56,f39]) ).
thf(f56,plain,
( ( ( lessf @ y @ z )
= $true )
| ( ( lessf @ x @ y )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( lessf @ y @ z )
= $true )
| ( ( lessf @ x @ y )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f52,f37]) ).
thf(f37,plain,
( ( ( eq @ y @ z )
= $true )
| ( ( lessf @ y @ z )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( lessf @ y @ z )
= $true )
| ( ( eq @ y @ z )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( lessf @ y @ z )
!= $true )
=> ( ( eq @ y @ z )
= $true ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( lessf @ y @ z )
!= $true )
=> ( ( eq @ y @ z )
= $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',k) ).
thf(f52,plain,
! [X0: frac] :
( ( ( eq @ X0 @ z )
!= $true )
| ( ( lessf @ x @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: frac] :
( ( $true != $true )
| ( ( lessf @ x @ X0 )
!= $true )
| ( ( eq @ X0 @ z )
!= $true ) ),
inference(superposition,[status(thm)],[f45,f38]) ).
thf(f38,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: frac] : ( eq @ X1 @ X1 ),
file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',satz37) ).
thf(f45,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ x )
!= $true )
| ( ( lessf @ X1 @ X0 )
!= $true )
| ( ( eq @ X0 @ z )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ x )
!= $true )
| ( ( eq @ X0 @ z )
!= $true )
| ( $true != $true )
| ( ( lessf @ X1 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f35,f36]) ).
thf(f36,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( lessf @ X1 @ X3 )
= $true )
| ( ( eq @ X2 @ X3 )
!= $true )
| ( $true
!= ( lessf @ X0 @ X2 ) )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
!= ( lessf @ X0 @ X2 ) )
| ( $true
!= ( eq @ X0 @ X1 ) )
| ( ( eq @ X2 @ X3 )
!= $true )
| ( ( lessf @ X1 @ X3 )
= $true ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: frac,X0: frac,X3: frac,X1: frac] :
( ( ( lessf @ X2 @ X3 )
!= $true )
| ( ( eq @ X2 @ X0 )
!= $true )
| ( ( eq @ X3 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f29]) ).
thf(f29,plain,
! [X3: frac,X1: frac,X2: frac,X0: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
| ( ( eq @ X3 @ X1 )
!= $true )
| ( ( eq @ X2 @ X0 )
!= $true )
| ( ( lessf @ X2 @ X3 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X3: frac,X1: frac,X2: frac,X0: frac] :
( ( ( lessf @ X2 @ X3 )
= $true )
=> ( ( ( eq @ X2 @ X0 )
= $true )
=> ( ( ( eq @ X3 @ X1 )
= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( lessf @ X2 @ X3 )
=> ( ( eq @ X2 @ X0 )
=> ( ( eq @ X3 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: frac,X4: frac,X1: frac,X2: frac] :
( ( lessf @ X1 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( ( eq @ X2 @ X4 )
=> ( lessf @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',satz45) ).
thf(f35,plain,
( ( lessf @ x @ z )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( lessf @ x @ z )
!= $true ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ( lessf @ x @ z )
!= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( lessf @ x @ z ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( lessf @ x @ z ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
lessf @ x @ z,
file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',satz51b) ).
thf(f46,plain,
! [X0: frac] :
( ( $true
!= ( lessf @ X0 @ z ) )
| ( ( lessf @ x @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: frac] :
( ( ( lessf @ x @ X0 )
!= $true )
| ( $true != $true )
| ( $true
!= ( lessf @ X0 @ z ) ) ),
inference(superposition,[status(thm)],[f35,f41]) ).
thf(f41,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( lessf @ X2 @ X0 )
= $true )
| ( ( lessf @ X2 @ X1 )
!= $true )
| ( ( lessf @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X2 @ X0 )
= $true )
| ( ( lessf @ X1 @ X0 )
!= $true )
| ( ( lessf @ X2 @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( ( lessf @ X1 @ X0 )
= $true )
| ( ( lessf @ X2 @ X0 )
!= $true )
| ( ( lessf @ X1 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( ( lessf @ X1 @ X0 )
= $true )
| ( ( lessf @ X2 @ X0 )
!= $true )
| ( ( lessf @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( ( lessf @ X1 @ X2 )
= $true )
=> ( ( ( lessf @ X2 @ X0 )
= $true )
=> ( ( lessf @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,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/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',satz50) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM743^1 : 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
% 0.17/0.34 % Computer : n026.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:12:55 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : NUM743^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Number Theory
% 0.20/0.46 % Problem : Landau theorem 51b
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : lessf x z
% 0.20/0.46
% 0.20/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : satz51b [Lan30]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % : Without extensionality : Theorem
% 0.20/0.46 % 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 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 13 ( 3 unt; 6 typ; 0 def)
% 0.20/0.46 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.20/0.46 % Number of connectives : 34 ( 3 ~; 0 |; 0 &; 24 @)
% 0.20/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 10 ( 5 avg)
% 0.20/0.46 % Number of types : 2 ( 1 usr)
% 0.20/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.20/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(frac_type,type,
% 0.20/0.46 frac: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(x,type,
% 0.20/0.46 x: frac ).
% 0.20/0.46
% 0.20/0.46 thf(y,type,
% 0.20/0.46 y: frac ).
% 0.20/0.46
% 0.20/0.46 thf(z,type,
% 0.20/0.46 z: frac ).
% 0.20/0.46
% 0.20/0.46 thf(lessf,type,
% 0.20/0.46 lessf: frac > frac > $o ).
% 0.20/0.46
% 0.20/0.46 thf(l,axiom,
% 0.20/0.46 lessf @ x @ y ).
% 0.20/0.46
% 0.20/0.46 thf(eq,type,
% 0.20/0.46 eq: frac > frac > $o ).
% 0.20/0.46
% 0.20/0.46 thf(k,axiom,
% 0.20/0.46 ( ~ ( lessf @ y @ z )
% 0.20/0.46 => ( eq @ y @ z ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(et,axiom,
% 0.20/0.46 ! [Xa: $o] :
% 0.20/0.46 ( ~ ~ Xa
% 0.20/0.46 => Xa ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz45,axiom,
% 0.20/0.46 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.20/0.46 ( ( lessf @ Xx @ Xy )
% 0.20/0.46 => ( ( eq @ Xx @ Xz )
% 0.20/0.46 => ( ( eq @ Xy @ Xu )
% 0.20/0.46 => ( lessf @ Xz @ Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz37,axiom,
% 0.20/0.46 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz50,axiom,
% 0.20/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.20/0.46 ( ( lessf @ Xx @ Xy )
% 0.20/0.46 => ( ( lessf @ Xy @ Xz )
% 0.20/0.46 => ( lessf @ Xx @ Xz ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz51b,conjecture,
% 0.20/0.46 lessf @ x @ z ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.53/1.24 ---- Embedded in THF ---
% 1.53/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.24 %%% Generated on Tue Feb 24 11:12:56 EST 2026
% 1.53/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.24 %%% Logic specification used:
% 1.53/1.24 %%% thf(spec, logic, $$dhol).
% 1.53/1.24
% 1.53/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2DTF31317.p
% See solution above
% 1.53/1.24 ------------------------
% 1.53/1.25 ---- Cleaned THF ---
% 1.53/1.25 thf(frac_type,type,
% 1.53/1.25 frac: $tType ).
% 1.53/1.25
% 1.53/1.25 thf(x,type,
% 1.53/1.25 x: frac ).
% 1.53/1.25
% 1.53/1.25 thf(y,type,
% 1.53/1.25 y: frac ).
% 1.53/1.25
% 1.53/1.25 thf(z,type,
% 1.53/1.25 z: frac ).
% 1.53/1.25
% 1.53/1.25 thf(lessf,type,
% 1.53/1.25 lessf: frac > frac > $o ).
% 1.53/1.25
% 1.53/1.25 thf(l,axiom,
% 1.53/1.25 lessf @ x @ y ).
% 1.53/1.25
% 1.53/1.25 thf(eq,type,
% 1.53/1.25 eq: frac > frac > $o ).
% 1.53/1.25
% 1.53/1.25 thf(k,axiom,
% 1.53/1.25 ( ~ ( lessf @ y @ z )
% 1.53/1.25 => ( eq @ y @ z ) ) ).
% 1.53/1.25
% 1.53/1.25 thf(et,axiom,
% 1.53/1.25 ! [Xa: $o] :
% 1.53/1.25 ( ~ ~ Xa
% 1.53/1.25 => Xa ) ).
% 1.53/1.25
% 1.53/1.25 thf(satz45,axiom,
% 1.53/1.25 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.53/1.25 ( ( lessf @ Xx @ Xy )
% 1.53/1.25 => ( ( eq @ Xx @ Xz )
% 1.53/1.25 => ( ( eq @ Xy @ Xu )
% 1.53/1.25 => ( lessf @ Xz @ Xu ) ) ) ) ).
% 1.53/1.25
% 1.53/1.25 thf(satz37,axiom,
% 1.53/1.25 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 1.53/1.25
% 1.53/1.25 thf(satz50,axiom,
% 1.53/1.25 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.53/1.25 ( ( lessf @ Xx @ Xy )
% 1.53/1.25 => ( ( lessf @ Xy @ Xz )
% 1.53/1.25 => ( lessf @ Xx @ Xz ) ) ) ).
% 1.53/1.25
% 1.53/1.25 thf(satz51b,conjecture,
% 1.53/1.25 lessf @ x @ z ).
% 1.53/1.25 ------------------------
% 1.53/1.26 % (31473)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_31317 for (3000ds/275Mi)
% 1.53/1.26 % (31474)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31317 for (3000ds/18Mi)
% 1.53/1.26 % (31473)First to succeed.
% 1.53/1.26 % (31474)Also succeeded, but the first one will report.
% 1.53/1.26 % (31473)Refutation found. Thanks to Tanya!
% 1.53/1.26 % SZS status Theorem for DTF2THF_31317
% 1.53/1.26 % SZS output start Proof for DTF2THF_31317
% 1.53/1.26 thf(type_def_5, type, frac: $tType).
% 1.53/1.26 thf(func_def_0, type, frac: $tType).
% 1.53/1.26 thf(func_def_1, type, x: frac).
% 1.53/1.26 thf(func_def_2, type, y: frac).
% 1.53/1.26 thf(func_def_3, type, z: frac).
% 1.53/1.26 thf(func_def_4, type, lessf: frac > frac > $o).
% 1.53/1.26 thf(func_def_6, type, eq: frac > frac > $o).
% 1.53/1.26 thf(f60,plain,(
% 1.53/1.26 $false),
% 1.53/1.26 inference(subsumption_resolution,[status(thm)],[f59,f39])).
% 1.53/1.26 thf(f39,plain,(
% 1.53/1.26 ((lessf @ x @ y) = $true)),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f19])).
% 1.53/1.26 thf(f19,plain,(
% 1.53/1.26 ((lessf @ x @ y) = $true)),
% 1.53/1.26 inference(fool_elimination,[status(thm)],[f18])).
% 1.53/1.26 thf(f18,plain,(
% 1.53/1.26 (lessf @ x @ y)),
% 1.53/1.26 inference(rectify,[status(thm)],[f1])).
% 1.53/1.26 thf(f1,axiom,(
% 1.53/1.26 (lessf @ x @ y)),
% 1.53/1.26 file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',l)).
% 1.53/1.26 thf(f59,plain,(
% 1.53/1.26 ((lessf @ x @ y) != $true)),
% 1.53/1.26 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.53/1.26 thf(f58,plain,(
% 1.53/1.26 ($true != $true) | ((lessf @ x @ y) != $true)),
% 1.53/1.26 inference(superposition,[status(thm)],[f46,f57])).
% 1.53/1.26 thf(f57,plain,(
% 1.53/1.26 ((lessf @ y @ z) = $true)),
% 1.53/1.26 inference(subsumption_resolution,[status(thm)],[f56,f39])).
% 1.53/1.26 thf(f56,plain,(
% 1.53/1.26 ((lessf @ y @ z) = $true) | ((lessf @ x @ y) != $true)),
% 1.53/1.26 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.53/1.26 thf(f53,plain,(
% 1.53/1.26 ((lessf @ y @ z) = $true) | ((lessf @ x @ y) != $true) | ($true != $true)),
% 1.53/1.26 inference(superposition,[status(thm)],[f52,f37])).
% 1.53/1.26 thf(f37,plain,(
% 1.53/1.26 ((eq @ y @ z) = $true) | ((lessf @ y @ z) = $true)),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f31])).
% 1.53/1.26 thf(f31,plain,(
% 1.53/1.26 ((lessf @ y @ z) = $true) | ((eq @ y @ z) = $true)),
% 1.53/1.26 inference(ennf_transformation,[status(thm)],[f26])).
% 1.53/1.26 thf(f26,plain,(
% 1.53/1.26 ((lessf @ y @ z) != $true) => ((eq @ y @ z) = $true)),
% 1.53/1.26 inference(flattening,[status(thm)],[f17])).
% 1.53/1.26 thf(f17,plain,(
% 1.53/1.26 ~((lessf @ y @ z) = $true) => ((eq @ y @ z) = $true)),
% 1.53/1.26 inference(fool_elimination,[status(thm)],[f16])).
% 1.53/1.26 thf(f16,plain,(
% 1.53/1.26 ~(lessf @ y @ z) => (eq @ y @ z)),
% 1.53/1.26 inference(rectify,[status(thm)],[f2])).
% 1.53/1.26 thf(f2,axiom,(
% 1.53/1.26 ~(lessf @ y @ z) => (eq @ y @ z)),
% 1.53/1.26 file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',k)).
% 1.53/1.26 thf(f52,plain,(
% 1.53/1.26 ( ! [X0 : frac] : (((eq @ X0 @ z) != $true) | ((lessf @ x @ X0) != $true)) )),
% 1.53/1.26 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.53/1.26 thf(f51,plain,(
% 1.53/1.26 ( ! [X0 : frac] : (($true != $true) | ((lessf @ x @ X0) != $true) | ((eq @ X0 @ z) != $true)) )),
% 1.53/1.26 inference(superposition,[status(thm)],[f45,f38])).
% 1.53/1.26 thf(f38,plain,(
% 1.53/1.26 ( ! [X0 : frac] : (((eq @ X0 @ X0) = $true)) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f21])).
% 1.53/1.26 thf(f21,plain,(
% 1.53/1.26 ! [X0 : frac] : ((eq @ X0 @ X0) = $true)),
% 1.53/1.26 inference(fool_elimination,[status(thm)],[f20])).
% 1.53/1.26 thf(f20,plain,(
% 1.53/1.26 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.53/1.26 inference(rectify,[status(thm)],[f5])).
% 1.53/1.26 thf(f5,axiom,(
% 1.53/1.26 ! [X1 : frac] : (eq @ X1 @ X1)),
% 1.53/1.26 file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',satz37)).
% 1.53/1.26 thf(f45,plain,(
% 1.53/1.26 ( ! [X0 : frac,X1 : frac] : (((eq @ X1 @ x) != $true) | ((lessf @ X1 @ X0) != $true) | ((eq @ X0 @ z) != $true)) )),
% 1.53/1.26 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.53/1.26 thf(f43,plain,(
% 1.53/1.26 ( ! [X0 : frac,X1 : frac] : (((eq @ X1 @ x) != $true) | ((eq @ X0 @ z) != $true) | ($true != $true) | ((lessf @ X1 @ X0) != $true)) )),
% 1.53/1.26 inference(superposition,[status(thm)],[f35,f36])).
% 1.53/1.26 thf(f36,plain,(
% 1.53/1.26 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((lessf @ X1 @ X3) = $true) | ((eq @ X2 @ X3) != $true) | ($true != (lessf @ X0 @ X2)) | ($true != (eq @ X0 @ X1))) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f33])).
% 1.53/1.26 thf(f33,plain,(
% 1.53/1.26 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true != (lessf @ X0 @ X2)) | ($true != (eq @ X0 @ X1)) | ((eq @ X2 @ X3) != $true) | ((lessf @ X1 @ X3) = $true))),
% 1.53/1.26 inference(rectify,[status(thm)],[f30])).
% 1.53/1.26 thf(f30,plain,(
% 1.53/1.26 ! [X2 : frac,X0 : frac,X3 : frac,X1 : frac] : (((lessf @ X2 @ X3) != $true) | ((eq @ X2 @ X0) != $true) | ((eq @ X3 @ X1) != $true) | ((lessf @ X0 @ X1) = $true))),
% 1.53/1.26 inference(flattening,[status(thm)],[f29])).
% 1.53/1.26 thf(f29,plain,(
% 1.53/1.26 ! [X3 : frac,X1 : frac,X2 : frac,X0 : frac] : (((((lessf @ X0 @ X1) = $true) | ((eq @ X3 @ X1) != $true)) | ((eq @ X2 @ X0) != $true)) | ((lessf @ X2 @ X3) != $true))),
% 1.53/1.26 inference(ennf_transformation,[status(thm)],[f11])).
% 1.53/1.26 thf(f11,plain,(
% 1.53/1.26 ! [X3 : frac,X1 : frac,X2 : frac,X0 : frac] : (((lessf @ X2 @ X3) = $true) => (((eq @ X2 @ X0) = $true) => (((eq @ X3 @ X1) = $true) => ((lessf @ X0 @ X1) = $true))))),
% 1.53/1.26 inference(fool_elimination,[status(thm)],[f10])).
% 1.53/1.26 thf(f10,plain,(
% 1.53/1.26 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((lessf @ X2 @ X3) => ((eq @ X2 @ X0) => ((eq @ X3 @ X1) => (lessf @ X0 @ X1))))),
% 1.53/1.26 inference(rectify,[status(thm)],[f4])).
% 1.53/1.26 thf(f4,axiom,(
% 1.53/1.26 ! [X3 : frac,X4 : frac,X1 : frac,X2 : frac] : ((lessf @ X1 @ X2) => ((eq @ X1 @ X3) => ((eq @ X2 @ X4) => (lessf @ X3 @ X4))))),
% 1.53/1.26 file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',satz45)).
% 1.53/1.26 thf(f35,plain,(
% 1.53/1.26 ((lessf @ x @ z) != $true)),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f24])).
% 1.53/1.26 thf(f24,plain,(
% 1.53/1.26 ((lessf @ x @ z) != $true)),
% 1.53/1.26 inference(flattening,[status(thm)],[f13])).
% 1.53/1.26 thf(f13,plain,(
% 1.53/1.26 ~((lessf @ x @ z) = $true)),
% 1.53/1.26 inference(fool_elimination,[status(thm)],[f12])).
% 1.53/1.26 thf(f12,plain,(
% 1.53/1.26 ~(lessf @ x @ z)),
% 1.53/1.26 inference(rectify,[status(thm)],[f8])).
% 1.53/1.26 thf(f8,negated_conjecture,(
% 1.53/1.26 ~(lessf @ x @ z)),
% 1.53/1.26 inference(negated_conjecture,[status(cth)],[f7])).
% 1.53/1.26 thf(f7,conjecture,(
% 1.53/1.26 (lessf @ x @ z)),
% 1.53/1.26 file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',satz51b)).
% 1.53/1.26 thf(f46,plain,(
% 1.53/1.26 ( ! [X0 : frac] : (($true != (lessf @ X0 @ z)) | ((lessf @ x @ X0) != $true)) )),
% 1.53/1.26 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.53/1.26 thf(f44,plain,(
% 1.53/1.26 ( ! [X0 : frac] : (((lessf @ x @ X0) != $true) | ($true != $true) | ($true != (lessf @ X0 @ z))) )),
% 1.53/1.26 inference(superposition,[status(thm)],[f35,f41])).
% 1.53/1.26 thf(f41,plain,(
% 1.53/1.26 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((lessf @ X2 @ X0) = $true) | ((lessf @ X2 @ X1) != $true) | ((lessf @ X1 @ X0) != $true)) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f34])).
% 1.53/1.26 thf(f34,plain,(
% 1.53/1.26 ! [X0 : frac,X1 : frac,X2 : frac] : (((lessf @ X2 @ X0) = $true) | ((lessf @ X1 @ X0) != $true) | ((lessf @ X2 @ X1) != $true))),
% 1.53/1.26 inference(rectify,[status(thm)],[f28])).
% 1.53/1.26 thf(f28,plain,(
% 1.53/1.26 ! [X0 : frac,X2 : frac,X1 : frac] : (((lessf @ X1 @ X0) = $true) | ((lessf @ X2 @ X0) != $true) | ((lessf @ X1 @ X2) != $true))),
% 1.53/1.26 inference(flattening,[status(thm)],[f27])).
% 1.53/1.26 thf(f27,plain,(
% 1.53/1.26 ! [X0 : frac,X2 : frac,X1 : frac] : ((((lessf @ X1 @ X0) = $true) | ((lessf @ X2 @ X0) != $true)) | ((lessf @ X1 @ X2) != $true))),
% 1.53/1.26 inference(ennf_transformation,[status(thm)],[f15])).
% 1.53/1.26 thf(f15,plain,(
% 1.53/1.26 ! [X0 : frac,X2 : frac,X1 : frac] : (((lessf @ X1 @ X2) = $true) => (((lessf @ X2 @ X0) = $true) => ((lessf @ X1 @ X0) = $true)))),
% 1.53/1.26 inference(fool_elimination,[status(thm)],[f14])).
% 1.53/1.26 thf(f14,plain,(
% 1.53/1.26 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X1 @ X2) => ((lessf @ X2 @ X0) => (lessf @ X1 @ X0)))),
% 1.53/1.26 inference(rectify,[status(thm)],[f6])).
% 1.53/1.26 thf(f6,axiom,(
% 1.53/1.26 ! [X3 : frac,X1 : frac,X2 : frac] : ((lessf @ X1 @ X2) => ((lessf @ X2 @ X3) => (lessf @ X1 @ X3)))),
% 1.53/1.26 file('/export/starexec/sandbox2/tmp/tmp.0DPLUJMIBx/DTF2THF_31317.p',satz50)).
% 1.53/1.26 % SZS output end Proof for DTF2THF_31317
% 1.53/1.26 % (31473)------------------------------
% 1.53/1.26 % (31473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.26 % (31473)Termination reason: Refutation
% 1.53/1.26
% 1.53/1.26 % (31473)Memory used [KB]: 5500
% 1.53/1.26 % (31473)Time elapsed: 0.005 s
% 1.53/1.26 % (31473)Instructions burned: 4 (million)
% 1.53/1.26 % (31473)------------------------------
% 1.53/1.26 % (31473)------------------------------
% 1.53/1.26 % (31467)Success in time 0.014 s
%------------------------------------------------------------------------------