%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM657^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 09:24:08 AM UTC 2026
% Result : Theorem 1.61s 1.30s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 169 ( 62 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 230 ( 77 ~; 24 |; 6 &; 96 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 19 ( 0 ^; 19 !; 0 ?; 19 :)
% 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,
less: nat > nat > $o ).
thf(func_def_5,type,
more: nat > nat > $o ).
thf(func_def_6,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f50,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f40,f44,f49]) ).
thf(f49,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f48]) ).
thf(f48,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f46,f24]) ).
thf(f24,plain,
( ( less @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( less @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
less @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
less @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.q32Pul7N9f/DTF2THF_29029.p',l) ).
thf(f46,plain,
( ( ( less @ x @ y )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( less @ x @ y )
!= $true )
| ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f28,f35]) ).
thf(f35,plain,
( ( ( more @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl0_1
<=> ( ( more @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f28,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( more @ X1 @ X0 ) )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( ( ( less @ X1 @ X0 )
!= $true )
| ( $true
!= ( more @ X1 @ X0 ) ) )
& ( ( ( less @ X1 @ X0 )
!= $true )
| ( X0 != X1 ) )
& ( ( $true
!= ( more @ X1 @ X0 ) )
| ( X0 != X1 ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: nat,X0: nat] :
( ( ( ( less @ X0 @ X1 )
!= $true )
| ( $true
!= ( more @ X0 @ X1 ) ) )
& ( ( ( less @ X0 @ X1 )
!= $true )
| ( X0 != X1 ) )
& ( ( $true
!= ( more @ X0 @ X1 ) )
| ( X0 != X1 ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
( ( ( ( less @ X0 @ X1 )
!= $true )
| ( X0 != X1 ) )
& ( ( ( less @ X0 @ X1 )
!= $true )
| ( $true
!= ( more @ X0 @ X1 ) ) )
& ( ( $true
!= ( more @ X0 @ X1 ) )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( $true
!= ( more @ X0 @ X1 ) ) )
=> ( ( ( $true
= ( more @ X0 @ X1 ) )
=> ( ( less @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( less @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( $true
!= ( more @ X0 @ X1 ) ) )
=> ~ ~ ( ( ( $true
= ( more @ X0 @ X1 ) )
=> ( ( less @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( less @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ~ ( more @ X0 @ X1 ) )
=> ~ ~ ( ( ( more @ X0 @ X1 )
=> ~ ( less @ X0 @ X1 ) )
=> ~ ( ( less @ X0 @ X1 )
=> ( X0 != X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X2: nat] :
~ ( ( ( X1 = X2 )
=> ~ ( more @ X1 @ X2 ) )
=> ~ ~ ( ( ( more @ X1 @ X2 )
=> ~ ( less @ X1 @ X2 ) )
=> ~ ( ( less @ X1 @ X2 )
=> ( X1 != X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.q32Pul7N9f/DTF2THF_29029.p',satz10b) ).
thf(f44,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f43]) ).
thf(f43,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f30,f41]) ).
thf(f41,plain,
( ( $true
= ( less @ x @ x ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f24,f39]) ).
thf(f39,plain,
( ( x = y )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f30,plain,
! [X1: nat] :
( ( less @ X1 @ X1 )
!= $true ),
inference(equality_resolution,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X1 @ X0 )
!= $true )
| ( X0 != X1 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f40,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f23,f37,f33]) ).
thf(f23,plain,
( ( x = y )
| ( ( more @ x @ y )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
~ ~ ( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/tmp/tmp.q32Pul7N9f/DTF2THF_29029.p',satz10h) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM657^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n021.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:09:39 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : NUM657^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Number Theory
% 0.19/0.46 % Problem : Landau theorem 10h
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : ~(~(more x y) -> x = y)
% 0.19/0.46
% 0.19/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : satz10h [Lan30]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % : Without extensionality : Theorem
% 0.19/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 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 v3.7.0
% 0.19/0.46 % Syntax : Number of formulae : 9 ( 1 unt; 5 typ; 0 def)
% 0.19/0.46 % Number of atoms : 9 ( 3 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 6 ( 2 avg)
% 0.19/0.46 % Number of connectives : 30 ( 11 ~; 0 |; 0 &; 12 @)
% 0.19/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 12 ( 7 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(nat_type,type,
% 0.19/0.46 nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(x,type,
% 0.19/0.46 x: nat ).
% 0.19/0.46
% 0.19/0.46 thf(y,type,
% 0.19/0.46 y: nat ).
% 0.19/0.46
% 0.19/0.46 thf(less,type,
% 0.19/0.46 less: nat > nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(l,axiom,
% 0.19/0.46 less @ x @ y ).
% 0.19/0.46
% 0.19/0.46 thf(more,type,
% 0.19/0.46 more: nat > nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(et,axiom,
% 0.19/0.46 ! [Xa: $o] :
% 0.19/0.46 ( ~ ~ Xa
% 0.19/0.46 => Xa ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz10b,axiom,
% 0.19/0.46 ! [Xx: nat,Xy: nat] :
% 0.19/0.46 ~ ( ( ( Xx = Xy )
% 0.19/0.46 => ~ ( more @ Xx @ Xy ) )
% 0.19/0.46 => ~ ~ ( ( ( more @ Xx @ Xy )
% 0.19/0.46 => ~ ( less @ Xx @ Xy ) )
% 0.19/0.46 => ~ ( ( less @ Xx @ Xy )
% 0.19/0.46 => ( Xx != Xy ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz10h,conjecture,
% 0.19/0.46 ~ ( ~ ( more @ x @ y )
% 0.19/0.46 => ( x = y ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.44/1.27 ---- Embedded in THF ---
% 1.44/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.27 %%% Generated on Tue Feb 24 11:09:39 EST 2026
% 1.44/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.27 %%% Logic specification used:
% 1.44/1.27 %%% thf(spec, logic, $$dhol).
% 1.44/1.27
% 1.44/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.q32Pul7N9f/DTF2DTF29029.p
% See solution above
% 1.44/1.28 ------------------------
% 1.44/1.29 ---- Cleaned THF ---
% 1.44/1.29 thf(nat_type,type,
% 1.44/1.29 nat: $tType ).
% 1.44/1.29
% 1.44/1.29 thf(x,type,
% 1.44/1.29 x: nat ).
% 1.44/1.29
% 1.44/1.29 thf(y,type,
% 1.44/1.29 y: nat ).
% 1.44/1.29
% 1.44/1.29 thf(less,type,
% 1.44/1.29 less: nat > nat > $o ).
% 1.44/1.29
% 1.44/1.29 thf(l,axiom,
% 1.44/1.29 less @ x @ y ).
% 1.44/1.29
% 1.44/1.29 thf(more,type,
% 1.44/1.29 more: nat > nat > $o ).
% 1.44/1.29
% 1.44/1.29 thf(et,axiom,
% 1.44/1.29 ! [Xa: $o] :
% 1.44/1.29 ( ~ ~ Xa
% 1.44/1.29 => Xa ) ).
% 1.44/1.29
% 1.44/1.29 thf(satz10b,axiom,
% 1.44/1.29 ! [Xx: nat,Xy: nat] :
% 1.44/1.29 ~ ( ( ( Xx = Xy )
% 1.44/1.29 => ~ ( more @ Xx @ Xy ) )
% 1.44/1.29 => ~ ~ ( ( ( more @ Xx @ Xy )
% 1.44/1.29 => ~ ( less @ Xx @ Xy ) )
% 1.44/1.29 => ~ ( ( less @ Xx @ Xy )
% 1.44/1.29 => ( Xx != Xy ) ) ) ) ).
% 1.44/1.29
% 1.44/1.29 thf(satz10h,conjecture,
% 1.44/1.29 ~ ( ~ ( more @ x @ y )
% 1.44/1.29 => ( x = y ) ) ).
% 1.44/1.29 ------------------------
% 1.61/1.30 % (29225)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_29029 for (3000ds/27Mi)
% 1.61/1.30 % (29229)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29029 for (3000ds/18Mi)
% 1.61/1.30 % (29223)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29029 for (3000ds/183Mi)
% 1.61/1.30 % (29226)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29029 for (3000ds/2Mi)
% 1.61/1.30 % (29225)First to succeed.
% 1.61/1.30 % (29229)Also succeeded, but the first one will report.
% 1.61/1.30 % (29226)Instruction limit reached!
% 1.61/1.30 % (29226)------------------------------
% 1.61/1.30 % (29226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (29226)Termination reason: Unknown
% 1.61/1.30 % (29226)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (29226)Memory used [KB]: 5500
% 1.61/1.30 % (29226)Time elapsed: 0.003 s
% 1.61/1.30 % (29226)Instructions burned: 2 (million)
% 1.61/1.30 % (29226)------------------------------
% 1.61/1.30 % (29226)------------------------------
% 1.61/1.30 % (29225)Refutation found. Thanks to Tanya!
% 1.61/1.30 % SZS status Theorem for DTF2THF_29029
% 1.61/1.30 % SZS output start Proof for DTF2THF_29029
% 1.61/1.30 thf(type_def_5, type, nat: $tType).
% 1.61/1.30 thf(func_def_0, type, nat: $tType).
% 1.61/1.30 thf(func_def_1, type, x: nat).
% 1.61/1.30 thf(func_def_2, type, y: nat).
% 1.61/1.30 thf(func_def_3, type, less: nat > nat > $o).
% 1.61/1.30 thf(func_def_5, type, more: nat > nat > $o).
% 1.61/1.30 thf(func_def_6, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.61/1.30 thf(f50,plain,(
% 1.61/1.30 $false),
% 1.61/1.30 inference(avatar_sat_refutation,[status(thm)],[f40,f44,f49])).
% 1.61/1.30 thf(f49,plain,(
% 1.61/1.30 ~spl0_1),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f48])).
% 1.61/1.30 thf(f48,plain,(
% 1.61/1.30 $false | ~spl0_1),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.61/1.30 thf(f47,plain,(
% 1.61/1.30 ($true != $true) | ~spl0_1),
% 1.61/1.30 inference(superposition,[status(thm)],[f46,f24])).
% 1.61/1.30 thf(f24,plain,(
% 1.61/1.30 ((less @ x @ y) = $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.30 thf(f12,plain,(
% 1.61/1.30 ((less @ x @ y) = $true)),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f11])).
% 1.61/1.30 thf(f11,plain,(
% 1.61/1.30 (less @ x @ y)),
% 1.61/1.30 inference(rectify,[status(thm)],[f1])).
% 1.61/1.30 thf(f1,axiom,(
% 1.61/1.30 (less @ x @ y)),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.q32Pul7N9f/DTF2THF_29029.p',l)).
% 1.61/1.30 thf(f46,plain,(
% 1.61/1.30 ((less @ x @ y) != $true) | ~spl0_1),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.61/1.30 thf(f45,plain,(
% 1.61/1.30 ((less @ x @ y) != $true) | ($true != $true) | ~spl0_1),
% 1.61/1.30 inference(superposition,[status(thm)],[f28,f35])).
% 1.61/1.30 thf(f35,plain,(
% 1.61/1.30 ((more @ x @ y) = $true) | ~spl0_1),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.61/1.30 thf(f33,definition,(
% 1.61/1.30 spl0_1 <=> ((more @ x @ y) = $true)),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.61/1.30 thf(f28,plain,(
% 1.61/1.30 ( ! [X0 : nat,X1 : nat] : (($true != (more @ X1 @ X0)) | ((less @ X1 @ X0) != $true)) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f22])).
% 1.61/1.30 thf(f22,plain,(
% 1.61/1.30 ! [X0 : nat,X1 : nat] : ((((less @ X1 @ X0) != $true) | ($true != (more @ X1 @ X0))) & (((less @ X1 @ X0) != $true) | (X0 != X1)) & (($true != (more @ X1 @ X0)) | (X0 != X1)))),
% 1.61/1.30 inference(rectify,[status(thm)],[f19])).
% 1.61/1.30 thf(f19,plain,(
% 1.61/1.30 ! [X1 : nat,X0 : nat] : ((((less @ X0 @ X1) != $true) | ($true != (more @ X0 @ X1))) & (((less @ X0 @ X1) != $true) | (X0 != X1)) & (($true != (more @ X0 @ X1)) | (X0 != X1)))),
% 1.61/1.30 inference(flattening,[status(thm)],[f18])).
% 1.61/1.30 thf(f18,plain,(
% 1.61/1.30 ! [X0 : nat,X1 : nat] : (((((less @ X0 @ X1) != $true) | (X0 != X1)) & (((less @ X0 @ X1) != $true) | ($true != (more @ X0 @ X1)))) & (($true != (more @ X0 @ X1)) | (X0 != X1)))),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f17])).
% 1.61/1.30 thf(f17,plain,(
% 1.61/1.30 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ($true != (more @ X0 @ X1))) => ((($true = (more @ X0 @ X1)) => ((less @ X0 @ X1) != $true)) => ~(((less @ X0 @ X1) = $true) => (X0 != X1))))),
% 1.61/1.30 inference(flattening,[status(thm)],[f14])).
% 1.61/1.30 thf(f14,plain,(
% 1.61/1.30 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~($true = (more @ X0 @ X1))) => ~~((($true = (more @ X0 @ X1)) => ~((less @ X0 @ X1) = $true)) => ~(((less @ X0 @ X1) = $true) => (X0 != X1))))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f13])).
% 1.61/1.30 thf(f13,plain,(
% 1.61/1.30 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~(more @ X0 @ X1)) => ~~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => (X0 != X1))))),
% 1.61/1.30 inference(rectify,[status(thm)],[f3])).
% 1.61/1.30 thf(f3,axiom,(
% 1.61/1.30 ! [X1 : nat,X2 : nat] : ~(((X1 = X2) => ~(more @ X1 @ X2)) => ~~(((more @ X1 @ X2) => ~(less @ X1 @ X2)) => ~((less @ X1 @ X2) => (X1 != X2))))),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.q32Pul7N9f/DTF2THF_29029.p',satz10b)).
% 1.61/1.30 thf(f44,plain,(
% 1.61/1.30 ~spl0_2),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f43])).
% 1.61/1.30 thf(f43,plain,(
% 1.61/1.30 $false | ~spl0_2),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.61/1.30 thf(f42,plain,(
% 1.61/1.30 ($true != $true) | ~spl0_2),
% 1.61/1.30 inference(superposition,[status(thm)],[f30,f41])).
% 1.61/1.30 thf(f41,plain,(
% 1.61/1.30 ($true = (less @ x @ x)) | ~spl0_2),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f24,f39])).
% 1.61/1.30 thf(f39,plain,(
% 1.61/1.30 (x = y) | ~spl0_2),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.61/1.30 thf(f37,definition,(
% 1.61/1.30 spl0_2 <=> (x = y)),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.61/1.30 thf(f30,plain,(
% 1.61/1.30 ( ! [X1 : nat] : (((less @ X1 @ X1) != $true)) )),
% 1.61/1.30 inference(equality_resolution,[status(thm)],[f27])).
% 1.61/1.30 thf(f27,plain,(
% 1.61/1.30 ( ! [X0 : nat,X1 : nat] : (((less @ X1 @ X0) != $true) | (X0 != X1)) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f22])).
% 1.61/1.30 thf(f40,plain,(
% 1.61/1.30 spl0_1 | spl0_2),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f23,f37,f33])).
% 1.61/1.30 thf(f23,plain,(
% 1.61/1.30 (x = y) | ((more @ x @ y) = $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f21])).
% 1.61/1.30 thf(f21,plain,(
% 1.61/1.30 ((more @ x @ y) = $true) | (x = y)),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f16])).
% 1.61/1.30 thf(f16,plain,(
% 1.61/1.30 ((more @ x @ y) != $true) => (x = y)),
% 1.61/1.30 inference(flattening,[status(thm)],[f10])).
% 1.61/1.30 thf(f10,plain,(
% 1.61/1.30 ~~(~((more @ x @ y) = $true) => (x = y))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f9])).
% 1.61/1.30 thf(f9,plain,(
% 1.61/1.30 ~~(~(more @ x @ y) => (x = y))),
% 1.61/1.30 inference(rectify,[status(thm)],[f5])).
% 1.61/1.30 thf(f5,negated_conjecture,(
% 1.61/1.30 ~~(~(more @ x @ y) => (x = y))),
% 1.61/1.30 inference(negated_conjecture,[status(cth)],[f4])).
% 1.61/1.30 thf(f4,conjecture,(
% 1.61/1.30 ~(~(more @ x @ y) => (x = y))),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.q32Pul7N9f/DTF2THF_29029.p',satz10h)).
% 1.61/1.30 % SZS output end Proof for DTF2THF_29029
% 1.61/1.30 % (29225)------------------------------
% 1.61/1.30 % (29225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (29225)Termination reason: Refutation
% 1.61/1.30
% 1.61/1.30 % (29225)Memory used [KB]: 5500
% 1.61/1.30 % (29225)Time elapsed: 0.003 s
% 1.61/1.30 % (29225)Instructions burned: 3 (million)
% 1.61/1.30 % (29225)------------------------------
% 1.61/1.30 % (29225)------------------------------
% 1.61/1.30 % (29221)Success in time 0.003 s
%------------------------------------------------------------------------------