%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM667^1 : 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 : n010.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 09:24:11 AM UTC 2026
% Result : Theorem 1.62s 1.31s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 203 ( 77 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 227 ( 57 ~; 38 |; 3 &; 102 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
x: nat ).
thf(func_def_2,type,
y: nat ).
thf(func_def_3,type,
z: nat ).
thf(func_def_4,type,
less: nat > nat > $o ).
thf(f105,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f66,f77,f97,f104]) ).
thf(f104,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
| ~ spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f102,f42]) ).
thf(f42,plain,
( ( less @ x @ z )
!= $true ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( less @ x @ z )
!= $true )
& ( x != z ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
~ ( ( ( less @ x @ z )
!= $true )
=> ( x = z ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( ( less @ x @ z )
!= $true )
=> ( x = z ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ~ ( less @ x @ z )
=> ( x = z ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( ~ ( less @ x @ z )
=> ( x = z ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( ~ ( less @ x @ z )
=> ( x = z ) ),
file('/export/starexec/sandbox2/tmp/tmp.tdc6EbW2gW/DTF2THF_14129.p',satz17) ).
thf(f102,plain,
( ( ( less @ x @ z )
= $true )
| ~ spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f60,f65]) ).
thf(f65,plain,
( ( x = y )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl0_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f60,plain,
( ( ( less @ y @ z )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f59,definition,
( spl0_1
<=> ( ( less @ y @ z )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f97,plain,
( spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f96]) ).
thf(f96,plain,
( $false
| spl0_1
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f93,f64]) ).
thf(f64,plain,
( ( x != y )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f93,plain,
( ( x = y )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true != $true )
| ( x = y )
| spl0_1 ),
inference(superposition,[status(thm)],[f74,f40]) ).
thf(f40,plain,
( ( ( less @ x @ y )
= $true )
| ( x = y ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/tmp/tmp.tdc6EbW2gW/DTF2THF_14129.p',l) ).
thf(f74,plain,
( ( ( less @ x @ y )
!= $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f42,f71]) ).
thf(f71,plain,
( ( y = z )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( y = z )
| ( $true != $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f61,f37]) ).
thf(f37,plain,
( ( ( less @ y @ z )
= $true )
| ( y = z ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( y = z )
| ( ( less @ y @ z )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( less @ y @ z )
!= $true )
=> ( y = z ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( less @ y @ z )
!= $true )
=> ( y = z ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( ~ ( less @ y @ z )
=> ( y = z ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ~ ( less @ y @ z )
=> ( y = z ) ),
file('/export/starexec/sandbox2/tmp/tmp.tdc6EbW2gW/DTF2THF_14129.p',k) ).
thf(f61,plain,
( ( ( less @ y @ z )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f77,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f75,f59,f63]) ).
thf(f75,plain,
( ( x != y )
| spl0_1 ),
inference(superposition,[status(thm)],[f41,f71]) ).
thf(f41,plain,
x != z,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f66,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f55,f63,f59]) ).
thf(f55,plain,
( ( ( less @ y @ z )
!= $true )
| ( x = y ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( less @ y @ z )
!= $true )
| ( $true != $true )
| ( x = y ) ),
inference(superposition,[status(thm)],[f51,f40]) ).
thf(f51,plain,
! [X0: nat] :
( ( ( less @ x @ X0 )
!= $true )
| ( ( less @ X0 @ z )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: nat] :
( ( $true != $true )
| ( ( less @ X0 @ z )
!= $true )
| ( ( less @ x @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f42,f43]) ).
thf(f43,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( less @ X0 @ X1 )
= $true )
| ( $true
!= ( less @ X0 @ X2 ) )
| ( $true
!= ( less @ X2 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
!= ( less @ X2 @ X1 ) )
| ( ( X0 != X2 )
& ( $true
!= ( less @ X0 @ X2 ) ) )
| ( ( less @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( less @ X0 @ X1 )
= $true )
| ( $true
!= ( less @ X2 @ X1 ) )
| ( ( X0 != X2 )
& ( $true
!= ( less @ X0 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( $true
!= ( less @ X0 @ X2 ) )
=> ( X0 = X2 ) )
=> ( ( $true
= ( less @ X2 @ X1 ) )
=> ( ( less @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true
!= ( less @ X0 @ X2 ) )
=> ( X0 = X2 ) )
=> ( ( $true
= ( less @ X2 @ X1 ) )
=> ( ( less @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ~ ( less @ X0 @ X2 )
=> ( X0 = X2 ) )
=> ( ( less @ X2 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: nat,X3: nat,X2: nat] :
( ( ~ ( less @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( less @ X2 @ X3 )
=> ( less @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tdc6EbW2gW/DTF2THF_14129.p',satz16a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM667^1 : 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
% 0.18/0.34 % Computer : n010.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 11:09:48 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : NUM667^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Number Theory
% 0.28/0.47 % Problem : Landau theorem 17
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English : ~(less x z) -> x = z
% 0.28/0.47
% 0.28/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.28/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.28/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : satz17 [Lan30]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % : Without extensionality : Theorem
% 0.28/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 11 ( 0 unt; 5 typ; 0 def)
% 0.28/0.47 % Number of atoms : 14 ( 5 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 4 ( 2 avg)
% 0.28/0.47 % Number of connectives : 35 ( 7 ~; 0 |; 0 &; 18 @)
% 0.28/0.47 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 10 ( 7 avg)
% 0.28/0.47 % Number of types : 2 ( 1 usr)
% 0.28/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments :
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(nat_type,type,
% 0.28/0.47 nat: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(x,type,
% 0.28/0.47 x: nat ).
% 0.28/0.47
% 0.28/0.47 thf(y,type,
% 0.28/0.47 y: nat ).
% 0.28/0.47
% 0.28/0.47 thf(z,type,
% 0.28/0.47 z: nat ).
% 0.28/0.47
% 0.28/0.47 thf(less,type,
% 0.28/0.47 less: nat > nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(l,axiom,
% 0.28/0.47 ( ~ ( less @ x @ y )
% 0.28/0.47 => ( x = y ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(k,axiom,
% 0.28/0.47 ( ~ ( less @ y @ z )
% 0.28/0.47 => ( y = z ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(et,axiom,
% 0.28/0.47 ! [Xa: $o] :
% 0.28/0.47 ( ~ ~ Xa
% 0.28/0.47 => Xa ) ).
% 0.28/0.47
% 0.28/0.47 thf(satz16a,axiom,
% 0.28/0.47 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.28/0.47 ( ( ~ ( less @ Xx @ Xy )
% 0.28/0.47 => ( Xx = Xy ) )
% 0.28/0.47 => ( ( less @ Xy @ Xz )
% 0.28/0.47 => ( less @ Xx @ Xz ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(satz16b,axiom,
% 0.28/0.47 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.28/0.47 ( ( less @ Xx @ Xy )
% 0.28/0.47 => ( ( ~ ( less @ Xy @ Xz )
% 0.28/0.47 => ( Xy = Xz ) )
% 0.28/0.47 => ( less @ Xx @ Xz ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(satz17,conjecture,
% 0.28/0.47 ( ~ ( less @ x @ z )
% 0.28/0.47 => ( x = z ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.47/1.28 ---- Embedded in THF ---
% 1.47/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.28 %%% Generated on Tue Feb 24 11:09:49 EST 2026
% 1.47/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.28 %%% Logic specification used:
% 1.47/1.28 %%% thf(spec, logic, $$dhol).
% 1.47/1.28
% 1.47/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.tdc6EbW2gW/DTF2DTF14129.p
% See solution above
% 1.47/1.28 ------------------------
% 1.47/1.29 ---- Cleaned THF ---
% 1.47/1.29 thf(nat_type,type,
% 1.47/1.29 nat: $tType ).
% 1.47/1.29
% 1.47/1.29 thf(x,type,
% 1.47/1.29 x: nat ).
% 1.47/1.29
% 1.47/1.29 thf(y,type,
% 1.47/1.29 y: nat ).
% 1.47/1.29
% 1.47/1.29 thf(z,type,
% 1.47/1.29 z: nat ).
% 1.47/1.29
% 1.47/1.29 thf(less,type,
% 1.47/1.29 less: nat > nat > $o ).
% 1.47/1.29
% 1.47/1.29 thf(l,axiom,
% 1.47/1.29 ( ~ ( less @ x @ y )
% 1.47/1.29 => ( x = y ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(k,axiom,
% 1.47/1.29 ( ~ ( less @ y @ z )
% 1.47/1.29 => ( y = z ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(et,axiom,
% 1.47/1.29 ! [Xa: $o] :
% 1.47/1.29 ( ~ ~ Xa
% 1.47/1.29 => Xa ) ).
% 1.47/1.29
% 1.47/1.29 thf(satz16a,axiom,
% 1.47/1.29 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.47/1.29 ( ( ~ ( less @ Xx @ Xy )
% 1.47/1.29 => ( Xx = Xy ) )
% 1.47/1.29 => ( ( less @ Xy @ Xz )
% 1.47/1.29 => ( less @ Xx @ Xz ) ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(satz16b,axiom,
% 1.47/1.29 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.47/1.29 ( ( less @ Xx @ Xy )
% 1.47/1.29 => ( ( ~ ( less @ Xy @ Xz )
% 1.47/1.29 => ( Xy = Xz ) )
% 1.47/1.29 => ( less @ Xx @ Xz ) ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(satz17,conjecture,
% 1.47/1.29 ( ~ ( less @ x @ z )
% 1.47/1.29 => ( x = z ) ) ).
% 1.47/1.29 ------------------------
% 1.62/1.31 % (14405)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_14129 for (2999ds/275Mi)
% 1.62/1.31 % (14405)First to succeed.
% 1.62/1.31 % (14405)Refutation found. Thanks to Tanya!
% 1.62/1.31 % SZS status Theorem for DTF2THF_14129
% 1.62/1.31 % SZS output start Proof for DTF2THF_14129
% 1.62/1.31 thf(type_def_5, type, nat: $tType).
% 1.62/1.31 thf(func_def_0, type, nat: $tType).
% 1.62/1.31 thf(func_def_1, type, x: nat).
% 1.62/1.31 thf(func_def_2, type, y: nat).
% 1.62/1.31 thf(func_def_3, type, z: nat).
% 1.62/1.31 thf(func_def_4, type, less: nat > nat > $o).
% 1.62/1.31 thf(f105,plain,(
% 1.62/1.31 $false),
% 1.62/1.31 inference(avatar_sat_refutation,[status(thm)],[f66,f77,f97,f104])).
% 1.62/1.31 thf(f104,plain,(
% 1.62/1.31 ~spl0_1 | ~spl0_2),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f103])).
% 1.62/1.31 thf(f103,plain,(
% 1.62/1.31 $false | (~spl0_1 | ~spl0_2)),
% 1.62/1.31 inference(subsumption_resolution,[status(thm)],[f102,f42])).
% 1.62/1.31 thf(f42,plain,(
% 1.62/1.31 ((less @ x @ z) != $true)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.62/1.31 thf(f27,plain,(
% 1.62/1.31 ((less @ x @ z) != $true) & (x != z)),
% 1.62/1.31 inference(ennf_transformation,[status(thm)],[f21])).
% 1.62/1.31 thf(f21,plain,(
% 1.62/1.31 ~(((less @ x @ z) != $true) => (x = z))),
% 1.62/1.31 inference(flattening,[status(thm)],[f10])).
% 1.62/1.31 thf(f10,plain,(
% 1.62/1.31 ~(~((less @ x @ z) = $true) => (x = z))),
% 1.62/1.31 inference(fool_elimination,[status(thm)],[f9])).
% 1.62/1.31 thf(f9,plain,(
% 1.62/1.31 ~(~(less @ x @ z) => (x = z))),
% 1.62/1.31 inference(rectify,[status(thm)],[f7])).
% 1.62/1.31 thf(f7,negated_conjecture,(
% 1.62/1.31 ~(~(less @ x @ z) => (x = z))),
% 1.62/1.31 inference(negated_conjecture,[status(cth)],[f6])).
% 1.62/1.31 thf(f6,conjecture,(
% 1.62/1.31 ~(less @ x @ z) => (x = z)),
% 1.62/1.31 file('/export/starexec/sandbox2/tmp/tmp.tdc6EbW2gW/DTF2THF_14129.p',satz17)).
% 1.62/1.31 thf(f102,plain,(
% 1.62/1.31 ((less @ x @ z) = $true) | (~spl0_1 | ~spl0_2)),
% 1.62/1.31 inference(forward_demodulation,[status(thm)],[f60,f65])).
% 1.62/1.31 thf(f65,plain,(
% 1.62/1.31 (x = y) | ~spl0_2),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.62/1.31 thf(f63,definition,(
% 1.62/1.31 spl0_2 <=> (x = y)),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.62/1.31 thf(f60,plain,(
% 1.62/1.31 ((less @ y @ z) = $true) | ~spl0_1),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.62/1.31 thf(f59,definition,(
% 1.62/1.31 spl0_1 <=> ((less @ y @ z) = $true)),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.62/1.31 thf(f97,plain,(
% 1.62/1.31 spl0_1 | spl0_2),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f96])).
% 1.62/1.31 thf(f96,plain,(
% 1.62/1.31 $false | (spl0_1 | spl0_2)),
% 1.62/1.31 inference(subsumption_resolution,[status(thm)],[f93,f64])).
% 1.62/1.31 thf(f64,plain,(
% 1.62/1.31 (x != y) | spl0_2),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.62/1.31 thf(f93,plain,(
% 1.62/1.31 (x = y) | spl0_1),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.62/1.31 thf(f90,plain,(
% 1.62/1.31 ($true != $true) | (x = y) | spl0_1),
% 1.62/1.31 inference(superposition,[status(thm)],[f74,f40])).
% 1.62/1.31 thf(f40,plain,(
% 1.62/1.31 ((less @ x @ y) = $true) | (x = y)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f28])).
% 1.62/1.31 thf(f28,plain,(
% 1.62/1.31 (x = y) | ((less @ x @ y) = $true)),
% 1.62/1.31 inference(ennf_transformation,[status(thm)],[f23])).
% 1.62/1.31 thf(f23,plain,(
% 1.62/1.31 ((less @ x @ y) != $true) => (x = y)),
% 1.62/1.31 inference(flattening,[status(thm)],[f18])).
% 1.62/1.31 thf(f18,plain,(
% 1.62/1.31 ~((less @ x @ y) = $true) => (x = y)),
% 1.62/1.31 inference(fool_elimination,[status(thm)],[f17])).
% 1.62/1.31 thf(f17,plain,(
% 1.62/1.31 ~(less @ x @ y) => (x = y)),
% 1.62/1.31 inference(rectify,[status(thm)],[f1])).
% 1.62/1.31 thf(f1,axiom,(
% 1.62/1.31 ~(less @ x @ y) => (x = y)),
% 1.62/1.31 file('/export/starexec/sandbox2/tmp/tmp.tdc6EbW2gW/DTF2THF_14129.p',l)).
% 1.62/1.31 thf(f74,plain,(
% 1.62/1.31 ((less @ x @ y) != $true) | spl0_1),
% 1.62/1.31 inference(superposition,[status(thm)],[f42,f71])).
% 1.62/1.31 thf(f71,plain,(
% 1.62/1.31 (y = z) | spl0_1),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.62/1.31 thf(f67,plain,(
% 1.62/1.31 (y = z) | ($true != $true) | spl0_1),
% 1.62/1.31 inference(superposition,[status(thm)],[f61,f37])).
% 1.62/1.31 thf(f37,plain,(
% 1.62/1.31 ((less @ y @ z) = $true) | (y = z)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f33])).
% 1.62/1.31 thf(f33,plain,(
% 1.62/1.31 (y = z) | ((less @ y @ z) = $true)),
% 1.62/1.31 inference(ennf_transformation,[status(thm)],[f26])).
% 1.62/1.31 thf(f26,plain,(
% 1.62/1.31 ((less @ y @ z) != $true) => (y = z)),
% 1.62/1.31 inference(flattening,[status(thm)],[f20])).
% 1.62/1.31 thf(f20,plain,(
% 1.62/1.31 ~((less @ y @ z) = $true) => (y = z)),
% 1.62/1.31 inference(fool_elimination,[status(thm)],[f19])).
% 1.62/1.31 thf(f19,plain,(
% 1.62/1.31 ~(less @ y @ z) => (y = z)),
% 1.62/1.31 inference(rectify,[status(thm)],[f2])).
% 1.62/1.31 thf(f2,axiom,(
% 1.62/1.31 ~(less @ y @ z) => (y = z)),
% 1.62/1.31 file('/export/starexec/sandbox2/tmp/tmp.tdc6EbW2gW/DTF2THF_14129.p',k)).
% 1.62/1.31 thf(f61,plain,(
% 1.62/1.31 ((less @ y @ z) != $true) | spl0_1),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.62/1.31 thf(f77,plain,(
% 1.62/1.31 ~spl0_2 | spl0_1),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f75,f59,f63])).
% 1.62/1.31 thf(f75,plain,(
% 1.62/1.31 (x != y) | spl0_1),
% 1.62/1.31 inference(superposition,[status(thm)],[f41,f71])).
% 1.62/1.31 thf(f41,plain,(
% 1.62/1.31 (x != z)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.62/1.31 thf(f66,plain,(
% 1.62/1.31 ~spl0_1 | spl0_2),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f55,f63,f59])).
% 1.62/1.31 thf(f55,plain,(
% 1.62/1.31 ((less @ y @ z) != $true) | (x = y)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.62/1.31 thf(f52,plain,(
% 1.62/1.31 ((less @ y @ z) != $true) | ($true != $true) | (x = y)),
% 1.62/1.31 inference(superposition,[status(thm)],[f51,f40])).
% 1.62/1.31 thf(f51,plain,(
% 1.62/1.31 ( ! [X0 : nat] : (((less @ x @ X0) != $true) | ((less @ X0 @ z) != $true)) )),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.62/1.31 thf(f48,plain,(
% 1.62/1.31 ( ! [X0 : nat] : (($true != $true) | ((less @ X0 @ z) != $true) | ((less @ x @ X0) != $true)) )),
% 1.62/1.31 inference(superposition,[status(thm)],[f42,f43])).
% 1.62/1.31 thf(f43,plain,(
% 1.62/1.31 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((less @ X0 @ X1) = $true) | ($true != (less @ X0 @ X2)) | ($true != (less @ X2 @ X1))) )),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f32])).
% 1.62/1.31 thf(f32,plain,(
% 1.62/1.31 ! [X0 : nat,X1 : nat,X2 : nat] : (($true != (less @ X2 @ X1)) | ((X0 != X2) & ($true != (less @ X0 @ X2))) | ((less @ X0 @ X1) = $true))),
% 1.62/1.31 inference(flattening,[status(thm)],[f31])).
% 1.62/1.31 thf(f31,plain,(
% 1.62/1.31 ! [X0 : nat,X2 : nat,X1 : nat] : ((((less @ X0 @ X1) = $true) | ($true != (less @ X2 @ X1))) | ((X0 != X2) & ($true != (less @ X0 @ X2))))),
% 1.62/1.31 inference(ennf_transformation,[status(thm)],[f25])).
% 1.62/1.31 thf(f25,plain,(
% 1.62/1.31 ! [X0 : nat,X2 : nat,X1 : nat] : ((($true != (less @ X0 @ X2)) => (X0 = X2)) => (($true = (less @ X2 @ X1)) => ((less @ X0 @ X1) = $true)))),
% 1.62/1.31 inference(flattening,[status(thm)],[f12])).
% 1.62/1.31 thf(f12,plain,(
% 1.62/1.31 ! [X0 : nat,X1 : nat,X2 : nat] : ((~($true = (less @ X0 @ X2)) => (X0 = X2)) => (($true = (less @ X2 @ X1)) => ((less @ X0 @ X1) = $true)))),
% 1.62/1.31 inference(fool_elimination,[status(thm)],[f11])).
% 1.62/1.31 thf(f11,plain,(
% 1.62/1.31 ! [X0 : nat,X1 : nat,X2 : nat] : ((~(less @ X0 @ X2) => (X0 = X2)) => ((less @ X2 @ X1) => (less @ X0 @ X1)))),
% 1.62/1.31 inference(rectify,[status(thm)],[f4])).
% 1.62/1.31 thf(f4,axiom,(
% 1.62/1.31 ! [X1 : nat,X3 : nat,X2 : nat] : ((~(less @ X1 @ X2) => (X1 = X2)) => ((less @ X2 @ X3) => (less @ X1 @ X3)))),
% 1.62/1.31 file('/export/starexec/sandbox2/tmp/tmp.tdc6EbW2gW/DTF2THF_14129.p',satz16a)).
% 1.62/1.31 % SZS output end Proof for DTF2THF_14129
% 1.62/1.31 % (14405)------------------------------
% 1.62/1.31 % (14405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (14405)Termination reason: Refutation
% 1.62/1.31
% 1.62/1.31 % (14405)Memory used [KB]: 5500
% 1.62/1.31 % (14405)Time elapsed: 0.004 s
% 1.62/1.31 % (14405)Instructions burned: 8 (million)
% 1.62/1.31 % (14405)------------------------------
% 1.62/1.31 % (14405)------------------------------
% 1.62/1.31 % (14399)Success in time 0.014 s
%------------------------------------------------------------------------------