%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM663^1 : 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 : n002.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 09:24:09 AM UTC 2026
% Result : Theorem 0.32s 1.33s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 142 ( 43 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 156 ( 30 ~; 22 |; 0 &; 92 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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(f54,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f40,f48,f52]) ).
thf(f52,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f50,f29]) ).
thf(f29,plain,
( ( less @ x @ z )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( less @ x @ z )
!= $true ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( less @ x @ z )
!= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( less @ x @ z ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( less @ x @ z ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
less @ x @ z,
file('/export/starexec/sandbox2/tmp/tmp.2qrp69QGE1/DTF2THF_3275.p',satz16a) ).
thf(f50,plain,
( ( ( less @ x @ z )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f26,f35]) ).
thf(f35,plain,
( ( x = y )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl0_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f26,plain,
( ( less @ y @ z )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( less @ y @ z )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
less @ y @ z,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
less @ y @ z,
file('/export/starexec/sandbox2/tmp/tmp.2qrp69QGE1/DTF2THF_3275.p',k) ).
thf(f48,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f46,f29]) ).
thf(f46,plain,
( ( ( less @ x @ z )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( less @ x @ z )
= $true )
| ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f43,f39]) ).
thf(f39,plain,
( ( ( less @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_2
<=> ( ( less @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f43,plain,
! [X0: nat] :
( ( $true
!= ( less @ X0 @ y ) )
| ( ( less @ X0 @ z )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: nat] :
( ( ( less @ X0 @ z )
= $true )
| ( $true != $true )
| ( $true
!= ( less @ X0 @ y ) ) ),
inference(superposition,[status(thm)],[f27,f26]) ).
thf(f27,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
!= ( less @ X0 @ X1 ) )
| ( ( less @ X2 @ X1 )
= $true )
| ( ( less @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( less @ X2 @ X0 )
!= $true )
| ( ( less @ X2 @ X1 )
= $true )
| ( $true
!= ( less @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( ( less @ X2 @ X1 )
!= $true )
| ( ( less @ X2 @ X0 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( ( less @ X2 @ X0 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true )
| ( ( less @ X2 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( ( less @ X2 @ X1 )
= $true )
=> ( ( ( less @ X1 @ X0 )
= $true )
=> ( ( less @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( less @ X2 @ X1 )
=> ( ( less @ X1 @ X0 )
=> ( less @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: nat,X2: nat,X1: nat] :
( ( less @ X1 @ X2 )
=> ( ( less @ X2 @ X3 )
=> ( less @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2qrp69QGE1/DTF2THF_3275.p',satz15) ).
thf(f40,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f37,f33]) ).
thf(f28,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,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.2qrp69QGE1/DTF2THF_3275.p',l) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : NUM663^1 : TPTP v9.2.1. Released v3.7.0.
% 0.09/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n002.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 11:10:18 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : NUM663^1 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.47 % Domain : Number Theory
% 0.26/0.47 % Problem : Landau theorem 16a
% 0.26/0.47 % Version : Especial.
% 0.26/0.47 % English : less x z
% 0.26/0.47
% 0.26/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.26/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.26/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.47 % Source : [Bro09]
% 0.26/0.47 % Names : satz16a [Lan30]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % : Without extensionality : Theorem
% 0.26/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.26/0.47 % Syntax : Number of formulae : 10 ( 2 unt; 5 typ; 0 def)
% 0.26/0.47 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 3 ( 1 avg)
% 0.26/0.47 % Number of connectives : 19 ( 3 ~; 0 |; 0 &; 12 @)
% 0.26/0.47 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 8 ( 5 avg)
% 0.26/0.47 % Number of types : 2 ( 1 usr)
% 0.26/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.26/0.47 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.26/0.47 % SPC : TH0_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments :
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf(nat_type,type,
% 0.26/0.47 nat: $tType ).
% 0.26/0.47
% 0.26/0.47 thf(x,type,
% 0.26/0.47 x: nat ).
% 0.26/0.47
% 0.26/0.47 thf(y,type,
% 0.26/0.47 y: nat ).
% 0.26/0.47
% 0.26/0.47 thf(z,type,
% 0.26/0.47 z: nat ).
% 0.26/0.47
% 0.26/0.47 thf(less,type,
% 0.26/0.47 less: nat > nat > $o ).
% 0.26/0.47
% 0.26/0.47 thf(l,axiom,
% 0.26/0.47 ( ~ ( less @ x @ y )
% 0.26/0.47 => ( x = y ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(k,axiom,
% 0.26/0.47 less @ y @ z ).
% 0.26/0.47
% 0.26/0.47 thf(et,axiom,
% 0.26/0.47 ! [Xa: $o] :
% 0.26/0.47 ( ~ ~ Xa
% 0.26/0.47 => Xa ) ).
% 0.26/0.47
% 0.26/0.47 thf(satz15,axiom,
% 0.26/0.47 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.26/0.47 ( ( less @ Xx @ Xy )
% 0.26/0.47 => ( ( less @ Xy @ Xz )
% 0.26/0.47 => ( less @ Xx @ Xz ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(satz16a,conjecture,
% 0.26/0.47 less @ x @ z ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 0.32/1.30 ---- Embedded in THF ---
% 0.32/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.30 %%% Generated on Tue Feb 24 11:10:19 EST 2026
% 0.32/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.30 %%% Logic specification used:
% 0.32/1.30 %%% thf(spec, logic, $$dhol).
% 0.32/1.30
% 0.32/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2qrp69QGE1/DTF2DTF3275.p
% See solution above
% 0.32/1.30 ------------------------
% 0.32/1.31 ---- Cleaned THF ---
% 0.32/1.31 thf(nat_type,type,
% 0.32/1.31 nat: $tType ).
% 0.32/1.31
% 0.32/1.31 thf(x,type,
% 0.32/1.31 x: nat ).
% 0.32/1.31
% 0.32/1.31 thf(y,type,
% 0.32/1.31 y: nat ).
% 0.32/1.31
% 0.32/1.31 thf(z,type,
% 0.32/1.31 z: nat ).
% 0.32/1.31
% 0.32/1.31 thf(less,type,
% 0.32/1.31 less: nat > nat > $o ).
% 0.32/1.31
% 0.32/1.31 thf(l,axiom,
% 0.32/1.31 ( ~ ( less @ x @ y )
% 0.32/1.31 => ( x = y ) ) ).
% 0.32/1.31
% 0.32/1.31 thf(k,axiom,
% 0.32/1.31 less @ y @ z ).
% 0.32/1.31
% 0.32/1.31 thf(et,axiom,
% 0.32/1.31 ! [Xa: $o] :
% 0.32/1.31 ( ~ ~ Xa
% 0.32/1.31 => Xa ) ).
% 0.32/1.31
% 0.32/1.31 thf(satz15,axiom,
% 0.32/1.31 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.32/1.31 ( ( less @ Xx @ Xy )
% 0.32/1.31 => ( ( less @ Xy @ Xz )
% 0.32/1.31 => ( less @ Xx @ Xz ) ) ) ).
% 0.32/1.31
% 0.32/1.31 thf(satz16a,conjecture,
% 0.32/1.31 less @ x @ z ).
% 0.32/1.31 ------------------------
% 0.32/1.33 % (3549)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3275 for (2999ds/18Mi)
% 0.32/1.33 % (3549)First to succeed.
% 0.32/1.33 % (3547)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_3275 for (2999ds/2Mi)
% 0.32/1.33 % (3549)Refutation found. Thanks to Tanya!
% 0.32/1.33 % SZS status Theorem for DTF2THF_3275
% 0.32/1.33 % SZS output start Proof for DTF2THF_3275
% 0.32/1.33 thf(type_def_5, type, nat: $tType).
% 0.32/1.33 thf(func_def_0, type, nat: $tType).
% 0.32/1.33 thf(func_def_1, type, x: nat).
% 0.32/1.33 thf(func_def_2, type, y: nat).
% 0.32/1.33 thf(func_def_3, type, z: nat).
% 0.32/1.33 thf(func_def_4, type, less: nat > nat > $o).
% 0.32/1.33 thf(f54,plain,(
% 0.32/1.33 $false),
% 0.32/1.33 inference(avatar_sat_refutation,[status(thm)],[f40,f48,f52])).
% 0.32/1.33 thf(f52,plain,(
% 0.32/1.33 ~spl0_1),
% 0.32/1.33 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 0.32/1.33 thf(f51,plain,(
% 0.32/1.33 $false | ~spl0_1),
% 0.32/1.33 inference(subsumption_resolution,[status(thm)],[f50,f29])).
% 0.32/1.33 thf(f29,plain,(
% 0.32/1.33 ((less @ x @ z) != $true)),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 0.32/1.33 thf(f18,plain,(
% 0.32/1.33 ((less @ x @ z) != $true)),
% 0.32/1.33 inference(flattening,[status(thm)],[f9])).
% 0.32/1.33 thf(f9,plain,(
% 0.32/1.33 ~((less @ x @ z) = $true)),
% 0.32/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 0.32/1.33 thf(f8,plain,(
% 0.32/1.33 ~(less @ x @ z)),
% 0.32/1.33 inference(rectify,[status(thm)],[f6])).
% 0.32/1.33 thf(f6,negated_conjecture,(
% 0.32/1.33 ~(less @ x @ z)),
% 0.32/1.33 inference(negated_conjecture,[status(cth)],[f5])).
% 0.32/1.33 thf(f5,conjecture,(
% 0.32/1.33 (less @ x @ z)),
% 0.32/1.33 file('/export/starexec/sandbox2/tmp/tmp.2qrp69QGE1/DTF2THF_3275.p',satz16a)).
% 0.32/1.33 thf(f50,plain,(
% 0.32/1.33 ((less @ x @ z) = $true) | ~spl0_1),
% 0.32/1.33 inference(backward_demodulation,[status(thm)],[f26,f35])).
% 0.32/1.33 thf(f35,plain,(
% 0.32/1.33 (x = y) | ~spl0_1),
% 0.32/1.33 inference(avatar_component_clause,[status(thm)],[f33])).
% 0.32/1.33 thf(f33,definition,(
% 0.32/1.33 spl0_1 <=> (x = y)),
% 0.32/1.33 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 0.32/1.33 thf(f26,plain,(
% 0.32/1.33 ((less @ y @ z) = $true)),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f13])).
% 0.32/1.33 thf(f13,plain,(
% 0.32/1.33 ((less @ y @ z) = $true)),
% 0.32/1.33 inference(fool_elimination,[status(thm)],[f12])).
% 0.32/1.33 thf(f12,plain,(
% 0.32/1.33 (less @ y @ z)),
% 0.32/1.33 inference(rectify,[status(thm)],[f2])).
% 0.32/1.33 thf(f2,axiom,(
% 0.32/1.33 (less @ y @ z)),
% 0.32/1.33 file('/export/starexec/sandbox2/tmp/tmp.2qrp69QGE1/DTF2THF_3275.p',k)).
% 0.32/1.33 thf(f48,plain,(
% 0.32/1.33 ~spl0_2),
% 0.32/1.33 inference(avatar_contradiction_clause,[status(thm)],[f47])).
% 0.32/1.33 thf(f47,plain,(
% 0.32/1.33 $false | ~spl0_2),
% 0.32/1.33 inference(subsumption_resolution,[status(thm)],[f46,f29])).
% 0.32/1.33 thf(f46,plain,(
% 0.32/1.33 ((less @ x @ z) = $true) | ~spl0_2),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 0.32/1.33 thf(f45,plain,(
% 0.32/1.33 ((less @ x @ z) = $true) | ($true != $true) | ~spl0_2),
% 0.32/1.33 inference(superposition,[status(thm)],[f43,f39])).
% 0.32/1.33 thf(f39,plain,(
% 0.32/1.33 ((less @ x @ y) = $true) | ~spl0_2),
% 0.32/1.33 inference(avatar_component_clause,[status(thm)],[f37])).
% 0.32/1.33 thf(f37,definition,(
% 0.32/1.33 spl0_2 <=> ((less @ x @ y) = $true)),
% 0.32/1.33 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 0.32/1.33 thf(f43,plain,(
% 0.32/1.33 ( ! [X0 : nat] : (($true != (less @ X0 @ y)) | ((less @ X0 @ z) = $true)) )),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 0.32/1.33 thf(f41,plain,(
% 0.32/1.33 ( ! [X0 : nat] : (((less @ X0 @ z) = $true) | ($true != $true) | ($true != (less @ X0 @ y))) )),
% 0.32/1.33 inference(superposition,[status(thm)],[f27,f26])).
% 0.32/1.33 thf(f27,plain,(
% 0.32/1.33 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != (less @ X0 @ X1)) | ((less @ X2 @ X1) = $true) | ((less @ X2 @ X0) != $true)) )),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f25])).
% 0.32/1.33 thf(f25,plain,(
% 0.32/1.33 ! [X0 : nat,X1 : nat,X2 : nat] : (((less @ X2 @ X0) != $true) | ((less @ X2 @ X1) = $true) | ($true != (less @ X0 @ X1)))),
% 0.32/1.33 inference(rectify,[status(thm)],[f24])).
% 0.32/1.33 thf(f24,plain,(
% 0.32/1.33 ! [X1 : nat,X0 : nat,X2 : nat] : (((less @ X2 @ X1) != $true) | ((less @ X2 @ X0) = $true) | ((less @ X1 @ X0) != $true))),
% 0.32/1.33 inference(flattening,[status(thm)],[f23])).
% 0.32/1.33 thf(f23,plain,(
% 0.32/1.33 ! [X1 : nat,X2 : nat,X0 : nat] : ((((less @ X2 @ X0) = $true) | ((less @ X1 @ X0) != $true)) | ((less @ X2 @ X1) != $true))),
% 0.32/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 0.32/1.33 thf(f11,plain,(
% 0.32/1.33 ! [X1 : nat,X2 : nat,X0 : nat] : (((less @ X2 @ X1) = $true) => (((less @ X1 @ X0) = $true) => ((less @ X2 @ X0) = $true)))),
% 0.32/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 0.32/1.33 thf(f10,plain,(
% 0.32/1.33 ! [X0 : nat,X1 : nat,X2 : nat] : ((less @ X2 @ X1) => ((less @ X1 @ X0) => (less @ X2 @ X0)))),
% 0.32/1.33 inference(rectify,[status(thm)],[f4])).
% 0.32/1.33 thf(f4,axiom,(
% 0.32/1.33 ! [X3 : nat,X2 : nat,X1 : nat] : ((less @ X1 @ X2) => ((less @ X2 @ X3) => (less @ X1 @ X3)))),
% 0.32/1.33 file('/export/starexec/sandbox2/tmp/tmp.2qrp69QGE1/DTF2THF_3275.p',satz15)).
% 0.32/1.33 thf(f40,plain,(
% 0.32/1.33 spl0_1 | spl0_2),
% 0.32/1.33 inference(avatar_split_clause,[status(thm)],[f28,f37,f33])).
% 0.32/1.33 thf(f28,plain,(
% 0.32/1.33 (x = y) | ((less @ x @ y) = $true)),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f21])).
% 0.32/1.33 thf(f21,plain,(
% 0.32/1.33 (x = y) | ((less @ x @ y) = $true)),
% 0.32/1.33 inference(ennf_transformation,[status(thm)],[f20])).
% 0.32/1.33 thf(f20,plain,(
% 0.32/1.33 ((less @ x @ y) != $true) => (x = y)),
% 0.32/1.33 inference(flattening,[status(thm)],[f17])).
% 0.32/1.33 thf(f17,plain,(
% 0.32/1.33 ~((less @ x @ y) = $true) => (x = y)),
% 0.32/1.33 inference(fool_elimination,[status(thm)],[f16])).
% 0.32/1.33 thf(f16,plain,(
% 0.32/1.33 ~(less @ x @ y) => (x = y)),
% 0.32/1.33 inference(rectify,[status(thm)],[f1])).
% 0.32/1.33 thf(f1,axiom,(
% 0.32/1.33 ~(less @ x @ y) => (x = y)),
% 0.32/1.33 file('/export/starexec/sandbox2/tmp/tmp.2qrp69QGE1/DTF2THF_3275.p',l)).
% 0.32/1.33 % SZS output end Proof for DTF2THF_3275
% 0.32/1.33 % (3549)------------------------------
% 0.32/1.33 % (3549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (3549)Termination reason: Refutation
% 0.32/1.33
% 0.32/1.33 % (3549)Memory used [KB]: 5500
% 0.32/1.33 % (3549)Time elapsed: 0.003 s
% 0.32/1.33 % (3549)Instructions burned: 3 (million)
% 0.32/1.33 % (3549)------------------------------
% 0.32/1.33 % (3549)------------------------------
% 0.32/1.33 % (3542)Success in time 0.015 s
%------------------------------------------------------------------------------