%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM682^1 : 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 : n017.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 09:24:15 AM UTC 2026
% Result : Theorem 1.43s 1.22s
% Output : Refutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 87 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 350 ( 74 ~; 29 |; 6 &; 210 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 ^; 59 !; 0 ?; 59 :)
% 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(func_def_5,type,
pl: nat > nat > nat ).
thf(func_def_7,type,
more: nat > nat > $o ).
thf(f65,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f63,f49]) ).
thf(f49,plain,
! [X1: nat] :
( $true
!= ( less @ X1 @ X1 ) ),
inference(equality_resolution,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true
!= ( less @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: nat,X1: nat] :
( ( ( $true
!= ( more @ X1 @ X0 ) )
| ( $true
!= ( less @ X1 @ X0 ) ) )
& ( ( X0 != X1 )
| ( $true
!= ( less @ X1 @ X0 ) ) )
& ( ( X0 != X1 )
| ( $true
!= ( more @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: nat,X0: nat] :
( ( ( $true
!= ( more @ X0 @ X1 ) )
| ( $true
!= ( less @ X0 @ X1 ) ) )
& ( ( X0 != X1 )
| ( $true
!= ( less @ X0 @ X1 ) ) )
& ( ( X0 != X1 )
| ( $true
!= ( more @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: nat,X0: nat] :
( ( ( X0 != X1 )
| ( $true
!= ( less @ X0 @ X1 ) ) )
& ( ( $true
!= ( more @ X0 @ X1 ) )
| ( $true
!= ( less @ X0 @ X1 ) ) )
& ( ( X0 != X1 )
| ( $true
!= ( more @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: nat,X0: nat] :
~ ( ( ( X0 = X1 )
=> ( $true
!= ( more @ X0 @ X1 ) ) )
=> ( ( ( $true
= ( more @ X0 @ X1 ) )
=> ( $true
!= ( less @ X0 @ X1 ) ) )
=> ~ ( ( $true
= ( less @ X0 @ X1 ) )
=> ( X0 != X1 ) ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( $true
!= ( more @ X0 @ X1 ) ) )
=> ~ ~ ( ( ( $true
= ( more @ X0 @ X1 ) )
=> ( $true
!= ( less @ X0 @ X1 ) ) )
=> ~ ( ( $true
= ( less @ X0 @ X1 ) )
=> ( X0 != X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,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.ohrUq9R4f8/DTF2THF_4403.p',satz10b) ).
thf(f63,plain,
( $true
= ( less @ ( pl @ x @ z ) @ ( pl @ x @ z ) ) ),
inference(superposition,[status(thm)],[f42,f61]) ).
thf(f61,plain,
x = y,
inference(subsumption_resolution,[status(thm)],[f60,f40]) ).
thf(f40,plain,
( ( less @ x @ y )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( less @ x @ y )
!= $true ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ( less @ x @ y )
!= $true ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( less @ x @ y ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( less @ x @ y ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
less @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2THF_4403.p',satz20c) ).
thf(f60,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f58,f41]) ).
thf(f41,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( more @ X1 @ X0 ) )
| ( $true
= ( less @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true
= ( more @ X1 @ X0 ) )
| ( $true
= ( less @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: nat,X0: nat] :
( ( X0 = X1 )
| ( $true
= ( more @ X0 @ X1 ) )
| ( $true
= ( less @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( less @ X0 @ X1 ) )
| ( $true
= ( more @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true
!= ( more @ X0 @ X1 ) )
=> ( $true
= ( less @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true
!= ( more @ X0 @ X1 ) )
=> ( $true
= ( less @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: nat,X2: nat] :
( ( X1 != X2 )
=> ( ~ ( more @ X1 @ X2 )
=> ( less @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2THF_4403.p',satz10a) ).
thf(f58,plain,
( $true
!= ( more @ x @ y ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true != $true )
| ( $true
!= ( more @ x @ y ) ) ),
inference(superposition,[status(thm)],[f56,f42]) ).
thf(f56,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
!= ( less @ ( pl @ X0 @ X1 ) @ ( pl @ X2 @ X1 ) ) )
| ( $true
!= ( more @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
!= ( more @ X0 @ X2 ) )
| ( $true
!= ( less @ ( pl @ X0 @ X1 ) @ ( pl @ X2 @ X1 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f46,f38]) ).
thf(f38,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X2 ) ) )
| ( $true
!= ( more @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X2 ) ) )
| ( $true
!= ( more @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) ) )
| ( ( more @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( more @ X1 @ X2 )
= $true )
=> ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( more @ X1 @ X2 )
=> ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: nat,X1: nat,X2: nat] :
( ( more @ X1 @ X2 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2THF_4403.p',satz19a) ).
thf(f46,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( more @ X1 @ X0 ) )
| ( $true
!= ( less @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f42,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
file('/export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2THF_4403.p',l) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM682^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:09:11 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.23/0.48 ---- Original DTF file ---
% 0.23/0.48 thf(spec,logic,$$dhol).
% 0.23/0.48 %------------------------------------------------------------------------------
% 0.23/0.48 % File : NUM682^1 : TPTP v9.2.1. Released v3.7.0.
% 0.23/0.48 % Domain : Number Theory
% 0.23/0.48 % Problem : Landau theorem 20c
% 0.23/0.48 % Version : Especial.
% 0.23/0.48 % English : less x y
% 0.23/0.48
% 0.23/0.48 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.23/0.48 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.23/0.48 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.23/0.48 % Source : [Bro09]
% 0.23/0.48 % Names : satz20c [Lan30]
% 0.23/0.48 % : satz33c [Lan30]
% 0.23/0.48
% 0.23/0.48 % Status : Theorem
% 0.23/0.48 % : Without extensionality : Theorem
% 0.23/0.48 % 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 v6.0.0, 0.29 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 v4.0.1, 0.33 v3.7.0
% 0.23/0.48 % Syntax : Number of formulae : 14 ( 2 unt; 7 typ; 0 def)
% 0.23/0.48 % Number of atoms : 15 ( 5 equ; 0 cnn)
% 0.23/0.48 % Maximal formula atoms : 6 ( 2 avg)
% 0.23/0.48 % Number of connectives : 53 ( 11 ~; 0 |; 0 &; 32 @)
% 0.23/0.48 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.23/0.48 % Maximal formula depth : 12 ( 7 avg)
% 0.23/0.48 % Number of types : 2 ( 1 usr)
% 0.23/0.48 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.23/0.48 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.23/0.48 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.23/0.48 % SPC : TH0_THM_EQU_NAR
% 0.23/0.48
% 0.23/0.48 % Comments :
% 0.23/0.48 %------------------------------------------------------------------------------
% 0.23/0.48 thf(nat_type,type,
% 0.23/0.48 nat: $tType ).
% 0.23/0.48
% 0.23/0.48 thf(x,type,
% 0.23/0.48 x: nat ).
% 0.23/0.48
% 0.23/0.48 thf(y,type,
% 0.23/0.48 y: nat ).
% 0.23/0.48
% 0.23/0.48 thf(z,type,
% 0.23/0.48 z: nat ).
% 0.23/0.48
% 0.23/0.48 thf(less,type,
% 0.23/0.48 less: nat > nat > $o ).
% 0.23/0.48
% 0.23/0.48 thf(pl,type,
% 0.23/0.48 pl: nat > nat > nat ).
% 0.23/0.48
% 0.23/0.48 thf(l,axiom,
% 0.23/0.48 less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ).
% 0.23/0.48
% 0.23/0.48 thf(et,axiom,
% 0.23/0.48 ! [Xa: $o] :
% 0.23/0.48 ( ~ ~ Xa
% 0.23/0.48 => Xa ) ).
% 0.23/0.48
% 0.23/0.48 thf(more,type,
% 0.23/0.48 more: nat > nat > $o ).
% 0.23/0.48
% 0.23/0.48 thf(satz10b,axiom,
% 0.23/0.48 ! [Xx: nat,Xy: nat] :
% 0.23/0.48 ~ ( ( ( Xx = Xy )
% 0.23/0.48 => ~ ( more @ Xx @ Xy ) )
% 0.23/0.48 => ~ ~ ( ( ( more @ Xx @ Xy )
% 0.23/0.48 => ~ ( less @ Xx @ Xy ) )
% 0.23/0.48 => ~ ( ( less @ Xx @ Xy )
% 0.23/0.48 => ( Xx != Xy ) ) ) ) ).
% 0.23/0.48
% 0.23/0.48 thf(satz19a,axiom,
% 0.23/0.48 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.23/0.48 ( ( more @ Xx @ Xy )
% 0.23/0.48 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 0.23/0.48
% 0.23/0.48 thf(satz19b,axiom,
% 0.23/0.48 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.23/0.48 ( ( Xx = Xy )
% 0.23/0.48 => ( ( pl @ Xx @ Xz )
% 0.23/0.48 = ( pl @ Xy @ Xz ) ) ) ).
% 0.23/0.48
% 0.23/0.48 thf(satz10a,axiom,
% 0.23/0.48 ! [Xx: nat,Xy: nat] :
% 0.23/0.48 ( ( Xx != Xy )
% 0.23/0.48 => ( ~ ( more @ Xx @ Xy )
% 0.23/0.48 => ( less @ Xx @ Xy ) ) ) ).
% 0.23/0.48
% 0.23/0.48 thf(satz20c,conjecture,
% 0.23/0.48 less @ x @ y ).
% 0.23/0.48
% 0.23/0.48 %------------------------------------------------------------------------------
% 0.23/0.48 ------------------------
% 1.27/1.19 ---- Embedded in THF ---
% 1.27/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.27/1.19 %%% Generated on Tue Feb 24 11:09:11 EST 2026
% 1.27/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.27/1.19 %%% Logic specification used:
% 1.27/1.19 %%% thf(spec, logic, $$dhol).
% 1.27/1.19
% 1.27/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2DTF4403.p
% See solution above
% 1.27/1.19 ------------------------
% 1.43/1.20 ---- Cleaned THF ---
% 1.43/1.20 thf(nat_type,type,
% 1.43/1.20 nat: $tType ).
% 1.43/1.20
% 1.43/1.20 thf(x,type,
% 1.43/1.20 x: nat ).
% 1.43/1.20
% 1.43/1.20 thf(y,type,
% 1.43/1.20 y: nat ).
% 1.43/1.20
% 1.43/1.20 thf(z,type,
% 1.43/1.20 z: nat ).
% 1.43/1.20
% 1.43/1.20 thf(less,type,
% 1.43/1.20 less: nat > nat > $o ).
% 1.43/1.20
% 1.43/1.20 thf(pl,type,
% 1.43/1.20 pl: nat > nat > nat ).
% 1.43/1.20
% 1.43/1.20 thf(l,axiom,
% 1.43/1.20 less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ).
% 1.43/1.20
% 1.43/1.20 thf(et,axiom,
% 1.43/1.20 ! [Xa: $o] :
% 1.43/1.20 ( ~ ~ Xa
% 1.43/1.20 => Xa ) ).
% 1.43/1.20
% 1.43/1.20 thf(more,type,
% 1.43/1.20 more: nat > nat > $o ).
% 1.43/1.20
% 1.43/1.20 thf(satz10b,axiom,
% 1.43/1.20 ! [Xx: nat,Xy: nat] :
% 1.43/1.20 ~ ( ( ( Xx = Xy )
% 1.43/1.20 => ~ ( more @ Xx @ Xy ) )
% 1.43/1.20 => ~ ~ ( ( ( more @ Xx @ Xy )
% 1.43/1.20 => ~ ( less @ Xx @ Xy ) )
% 1.43/1.20 => ~ ( ( less @ Xx @ Xy )
% 1.43/1.20 => ( Xx != Xy ) ) ) ) ).
% 1.43/1.20
% 1.43/1.20 thf(satz19a,axiom,
% 1.43/1.20 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.43/1.20 ( ( more @ Xx @ Xy )
% 1.43/1.20 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 1.43/1.20
% 1.43/1.20 thf(satz19b,axiom,
% 1.43/1.20 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.43/1.20 ( ( Xx = Xy )
% 1.43/1.20 => ( ( pl @ Xx @ Xz )
% 1.43/1.20 = ( pl @ Xy @ Xz ) ) ) ).
% 1.43/1.20
% 1.43/1.20 thf(satz10a,axiom,
% 1.43/1.20 ! [Xx: nat,Xy: nat] :
% 1.43/1.20 ( ( Xx != Xy )
% 1.43/1.20 => ( ~ ( more @ Xx @ Xy )
% 1.43/1.20 => ( less @ Xx @ Xy ) ) ) ).
% 1.43/1.20
% 1.43/1.20 thf(satz20c,conjecture,
% 1.43/1.20 less @ x @ y ).
% 1.43/1.20 ------------------------
% 1.43/1.21 % (4501)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4403 for (3000ds/183Mi)
% 1.43/1.21 % (4501)First to succeed.
% 1.43/1.22 % (4501)Refutation found. Thanks to Tanya!
% 1.43/1.22 % SZS status Theorem for DTF2THF_4403
% 1.43/1.22 % SZS output start Proof for DTF2THF_4403
% 1.43/1.22 thf(type_def_5, type, nat: $tType).
% 1.43/1.22 thf(func_def_0, type, nat: $tType).
% 1.43/1.22 thf(func_def_1, type, x: nat).
% 1.43/1.22 thf(func_def_2, type, y: nat).
% 1.43/1.22 thf(func_def_3, type, z: nat).
% 1.43/1.22 thf(func_def_4, type, less: nat > nat > $o).
% 1.43/1.22 thf(func_def_5, type, pl: nat > nat > nat).
% 1.43/1.22 thf(func_def_7, type, more: nat > nat > $o).
% 1.43/1.22 thf(f65,plain,(
% 1.43/1.22 $false),
% 1.43/1.22 inference(subsumption_resolution,[status(thm)],[f63,f49])).
% 1.43/1.22 thf(f49,plain,(
% 1.43/1.22 ( ! [X1 : nat] : (($true != (less @ X1 @ X1))) )),
% 1.43/1.22 inference(equality_resolution,[status(thm)],[f45])).
% 1.43/1.22 thf(f45,plain,(
% 1.43/1.22 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | ($true != (less @ X1 @ X0))) )),
% 1.43/1.22 inference(cnf_transformation,[status(thm)],[f37])).
% 1.43/1.22 thf(f37,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat] : ((($true != (more @ X1 @ X0)) | ($true != (less @ X1 @ X0))) & ((X0 != X1) | ($true != (less @ X1 @ X0))) & ((X0 != X1) | ($true != (more @ X1 @ X0))))),
% 1.43/1.22 inference(rectify,[status(thm)],[f28])).
% 1.43/1.22 thf(f28,plain,(
% 1.43/1.22 ! [X1 : nat,X0 : nat] : ((($true != (more @ X0 @ X1)) | ($true != (less @ X0 @ X1))) & ((X0 != X1) | ($true != (less @ X0 @ X1))) & ((X0 != X1) | ($true != (more @ X0 @ X1))))),
% 1.43/1.22 inference(flattening,[status(thm)],[f27])).
% 1.43/1.22 thf(f27,plain,(
% 1.43/1.22 ! [X1 : nat,X0 : nat] : ((((X0 != X1) | ($true != (less @ X0 @ X1))) & (($true != (more @ X0 @ X1)) | ($true != (less @ X0 @ X1)))) & ((X0 != X1) | ($true != (more @ X0 @ X1))))),
% 1.43/1.22 inference(ennf_transformation,[status(thm)],[f26])).
% 1.43/1.22 thf(f26,plain,(
% 1.43/1.22 ! [X1 : nat,X0 : nat] : ~(((X0 = X1) => ($true != (more @ X0 @ X1))) => ((($true = (more @ X0 @ X1)) => ($true != (less @ X0 @ X1))) => ~(($true = (less @ X0 @ X1)) => (X0 != X1))))),
% 1.43/1.22 inference(flattening,[status(thm)],[f21])).
% 1.43/1.22 thf(f21,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~($true = (more @ X0 @ X1))) => ~~((($true = (more @ X0 @ X1)) => ~($true = (less @ X0 @ X1))) => ~(($true = (less @ X0 @ X1)) => (X0 != X1))))),
% 1.43/1.22 inference(fool_elimination,[status(thm)],[f20])).
% 1.43/1.22 thf(f20,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~(more @ X0 @ X1)) => ~~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => (X0 != X1))))),
% 1.43/1.22 inference(rectify,[status(thm)],[f3])).
% 1.43/1.22 thf(f3,axiom,(
% 1.43/1.22 ! [X1 : nat,X2 : nat] : ~(((X1 = X2) => ~(more @ X1 @ X2)) => ~~(((more @ X1 @ X2) => ~(less @ X1 @ X2)) => ~((less @ X1 @ X2) => (X1 != X2))))),
% 1.43/1.22 file('/export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2THF_4403.p',satz10b)).
% 1.43/1.22 thf(f63,plain,(
% 1.43/1.22 ($true = (less @ (pl @ x @ z) @ (pl @ x @ z)))),
% 1.43/1.22 inference(superposition,[status(thm)],[f42,f61])).
% 1.43/1.22 thf(f61,plain,(
% 1.43/1.22 (x = y)),
% 1.43/1.22 inference(subsumption_resolution,[status(thm)],[f60,f40])).
% 1.43/1.22 thf(f40,plain,(
% 1.43/1.22 ((less @ x @ y) != $true)),
% 1.43/1.22 inference(cnf_transformation,[status(thm)],[f24])).
% 1.43/1.22 thf(f24,plain,(
% 1.43/1.22 ((less @ x @ y) != $true)),
% 1.43/1.22 inference(flattening,[status(thm)],[f19])).
% 1.43/1.22 thf(f19,plain,(
% 1.43/1.22 ~((less @ x @ y) = $true)),
% 1.43/1.22 inference(fool_elimination,[status(thm)],[f18])).
% 1.43/1.22 thf(f18,plain,(
% 1.43/1.22 ~(less @ x @ y)),
% 1.43/1.22 inference(rectify,[status(thm)],[f8])).
% 1.43/1.22 thf(f8,negated_conjecture,(
% 1.43/1.22 ~(less @ x @ y)),
% 1.43/1.22 inference(negated_conjecture,[status(cth)],[f7])).
% 1.43/1.22 thf(f7,conjecture,(
% 1.43/1.22 (less @ x @ y)),
% 1.43/1.22 file('/export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2THF_4403.p',satz20c)).
% 1.43/1.22 thf(f60,plain,(
% 1.43/1.22 (x = y) | ((less @ x @ y) = $true)),
% 1.43/1.22 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.43/1.22 thf(f59,plain,(
% 1.43/1.22 (x = y) | ((less @ x @ y) = $true) | ($true != $true)),
% 1.43/1.22 inference(superposition,[status(thm)],[f58,f41])).
% 1.43/1.22 thf(f41,plain,(
% 1.43/1.22 ( ! [X0 : nat,X1 : nat] : (($true = (more @ X1 @ X0)) | ($true = (less @ X1 @ X0)) | (X0 = X1)) )),
% 1.43/1.22 inference(cnf_transformation,[status(thm)],[f35])).
% 1.43/1.22 thf(f35,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = (more @ X1 @ X0)) | ($true = (less @ X1 @ X0)))),
% 1.43/1.22 inference(rectify,[status(thm)],[f33])).
% 1.43/1.22 thf(f33,plain,(
% 1.43/1.22 ! [X1 : nat,X0 : nat] : ((X0 = X1) | ($true = (more @ X0 @ X1)) | ($true = (less @ X0 @ X1)))),
% 1.43/1.22 inference(flattening,[status(thm)],[f32])).
% 1.43/1.22 thf(f32,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat] : ((($true = (less @ X0 @ X1)) | ($true = (more @ X0 @ X1))) | (X0 = X1))),
% 1.43/1.22 inference(ennf_transformation,[status(thm)],[f23])).
% 1.43/1.22 thf(f23,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (($true != (more @ X0 @ X1)) => ($true = (less @ X0 @ X1))))),
% 1.43/1.22 inference(flattening,[status(thm)],[f17])).
% 1.43/1.22 thf(f17,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~($true = (more @ X0 @ X1)) => ($true = (less @ X0 @ X1))))),
% 1.43/1.22 inference(fool_elimination,[status(thm)],[f16])).
% 1.43/1.22 thf(f16,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 1.43/1.22 inference(rectify,[status(thm)],[f6])).
% 1.43/1.22 thf(f6,axiom,(
% 1.43/1.22 ! [X1 : nat,X2 : nat] : ((X1 != X2) => (~(more @ X1 @ X2) => (less @ X1 @ X2)))),
% 1.43/1.22 file('/export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2THF_4403.p',satz10a)).
% 1.43/1.22 thf(f58,plain,(
% 1.43/1.22 ($true != (more @ x @ y))),
% 1.43/1.22 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.43/1.22 thf(f57,plain,(
% 1.43/1.22 ($true != $true) | ($true != (more @ x @ y))),
% 1.43/1.22 inference(superposition,[status(thm)],[f56,f42])).
% 1.43/1.22 thf(f56,plain,(
% 1.43/1.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != (less @ (pl @ X0 @ X1) @ (pl @ X2 @ X1))) | ($true != (more @ X0 @ X2))) )),
% 1.43/1.22 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.43/1.22 thf(f54,plain,(
% 1.43/1.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != (more @ X0 @ X2)) | ($true != (less @ (pl @ X0 @ X1) @ (pl @ X2 @ X1))) | ($true != $true)) )),
% 1.43/1.22 inference(superposition,[status(thm)],[f46,f38])).
% 1.43/1.22 thf(f38,plain,(
% 1.43/1.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) | ($true != (more @ X0 @ X1))) )),
% 1.43/1.22 inference(cnf_transformation,[status(thm)],[f34])).
% 1.43/1.22 thf(f34,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) | ($true != (more @ X0 @ X1)))),
% 1.43/1.22 inference(rectify,[status(thm)],[f30])).
% 1.43/1.22 thf(f30,plain,(
% 1.43/1.22 ! [X1 : nat,X2 : nat,X0 : nat] : (($true = (more @ (pl @ X1 @ X0) @ (pl @ X2 @ X0))) | ((more @ X1 @ X2) != $true))),
% 1.43/1.22 inference(ennf_transformation,[status(thm)],[f11])).
% 1.43/1.22 thf(f11,plain,(
% 1.43/1.22 ! [X0 : nat,X2 : nat,X1 : nat] : (((more @ X1 @ X2) = $true) => ($true = (more @ (pl @ X1 @ X0) @ (pl @ X2 @ X0))))),
% 1.43/1.22 inference(fool_elimination,[status(thm)],[f10])).
% 1.43/1.22 thf(f10,plain,(
% 1.43/1.22 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X1 @ X2) => (more @ (pl @ X1 @ X0) @ (pl @ X2 @ X0)))),
% 1.43/1.22 inference(rectify,[status(thm)],[f4])).
% 1.43/1.22 thf(f4,axiom,(
% 1.43/1.22 ! [X3 : nat,X1 : nat,X2 : nat] : ((more @ X1 @ X2) => (more @ (pl @ X1 @ X3) @ (pl @ X2 @ X3)))),
% 1.43/1.22 file('/export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2THF_4403.p',satz19a)).
% 1.43/1.22 thf(f46,plain,(
% 1.43/1.22 ( ! [X0 : nat,X1 : nat] : (($true != (more @ X1 @ X0)) | ($true != (less @ X1 @ X0))) )),
% 1.43/1.22 inference(cnf_transformation,[status(thm)],[f37])).
% 1.43/1.22 thf(f42,plain,(
% 1.43/1.22 ((less @ (pl @ x @ z) @ (pl @ y @ z)) = $true)),
% 1.43/1.22 inference(cnf_transformation,[status(thm)],[f13])).
% 1.43/1.22 thf(f13,plain,(
% 1.43/1.22 ((less @ (pl @ x @ z) @ (pl @ y @ z)) = $true)),
% 1.43/1.22 inference(fool_elimination,[status(thm)],[f12])).
% 1.43/1.22 thf(f12,plain,(
% 1.43/1.22 (less @ (pl @ x @ z) @ (pl @ y @ z))),
% 1.43/1.22 inference(rectify,[status(thm)],[f1])).
% 1.43/1.22 thf(f1,axiom,(
% 1.43/1.22 (less @ (pl @ x @ z) @ (pl @ y @ z))),
% 1.43/1.22 file('/export/starexec/sandbox/tmp/tmp.ohrUq9R4f8/DTF2THF_4403.p',l)).
% 1.43/1.22 % SZS output end Proof for DTF2THF_4403
% 1.43/1.22 % (4501)------------------------------
% 1.43/1.22 % (4501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.22 % (4501)Termination reason: Refutation
% 1.43/1.22
% 1.43/1.22 % (4501)Memory used [KB]: 5500
% 1.43/1.22 % (4501)Time elapsed: 0.004 s
% 1.43/1.22 % (4501)Instructions burned: 4 (million)
% 1.43/1.22 % (4501)------------------------------
% 1.43/1.22 % (4501)------------------------------
% 1.43/1.22 % (4500)Success in time 0.012 s
%------------------------------------------------------------------------------