%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM692^1 : 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 : n001.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 09:24:18 AM UTC 2026
% Result : Theorem 1.61s 1.37s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 53 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 271 ( 25 ~; 20 |; 0 &; 214 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% 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,
u: nat ).
thf(func_def_5,type,
lessis: nat > nat > $o ).
thf(func_def_7,type,
ts: nat > nat > nat ).
thf(func_def_8,type,
moreis: nat > nat > $o ).
thf(f56,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f53,f29]) ).
thf(f29,plain,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
!= $true ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ),
file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',satz23a) ).
thf(f53,plain,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $true != $true )
| ( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
= $true ) ),
inference(superposition,[status(thm)],[f28,f48]) ).
thf(f48,plain,
( $true
= ( moreis @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true != $true )
| ( $true
= ( moreis @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) ) ),
inference(superposition,[status(thm)],[f44,f36]) ).
thf(f36,plain,
( ( moreis @ y @ x )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( ( moreis @ y @ x )
= $true ) ),
inference(superposition,[status(thm)],[f33,f30]) ).
thf(f30,plain,
( ( lessis @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( lessis @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
lessis @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
lessis @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',l) ).
thf(f33,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X1 @ X0 )
!= $true )
| ( ( moreis @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X0 @ X1 )
= $true )
| ( ( lessis @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: nat,X0: nat] :
( ( ( moreis @ X1 @ X0 )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
=> ( ( moreis @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: nat,X1: nat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',satz14) ).
thf(f44,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X0 @ X1 )
!= $true )
| ( ( moreis @ ( ts @ X0 @ u ) @ ( ts @ X1 @ z ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( ( moreis @ ( ts @ X0 @ u ) @ ( ts @ X1 @ z ) )
= $true )
| ( ( moreis @ X0 @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f32,f37]) ).
thf(f37,plain,
( ( moreis @ u @ z )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( moreis @ u @ z )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f33,f31]) ).
thf(f31,plain,
( ( lessis @ z @ u )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( lessis @ z @ u )
= $true ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
lessis @ z @ u,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
lessis @ z @ u,
file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',k) ).
thf(f32,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
!= ( moreis @ X2 @ X0 ) )
| ( ( moreis @ X3 @ X1 )
!= $true )
| ( $true
= ( moreis @ ( ts @ X3 @ X2 ) @ ( ts @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
!= ( moreis @ X2 @ X0 ) )
| ( ( moreis @ X3 @ X1 )
!= $true )
| ( $true
= ( moreis @ ( ts @ X3 @ X2 ) @ ( ts @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: nat,X0: nat,X3: nat,X1: nat] :
( ( $true
!= ( moreis @ X3 @ X2 ) )
| ( ( moreis @ X1 @ X0 )
!= $true )
| ( ( moreis @ ( ts @ X1 @ X3 ) @ ( ts @ X0 @ X2 ) )
= $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: nat,X0: nat,X2: nat,X3: nat] :
( ( ( moreis @ ( ts @ X1 @ X3 ) @ ( ts @ X0 @ X2 ) )
= $true )
| ( $true
!= ( moreis @ X3 @ X2 ) )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: nat,X0: nat,X2: nat,X3: nat] :
( ( ( moreis @ X1 @ X0 )
= $true )
=> ( ( $true
= ( moreis @ X3 @ X2 ) )
=> ( ( moreis @ ( ts @ X1 @ X3 ) @ ( ts @ X0 @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( moreis @ X1 @ X0 )
=> ( ( moreis @ X3 @ X2 )
=> ( moreis @ ( ts @ X1 @ X3 ) @ ( ts @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: nat,X0: nat,X3: nat,X2: nat] :
( ( moreis @ X0 @ X1 )
=> ( ( moreis @ X2 @ X3 )
=> ( moreis @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',satz23) ).
thf(f28,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X1 @ X0 )
!= $true )
| ( ( lessis @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X1 @ X0 )
= $true )
=> ( ( lessis @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( moreis @ X1 @ X0 )
=> ( lessis @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X0: nat] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',satz13) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM692^1 : 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 : n001.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 11:11:50 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
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : NUM692^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Number Theory
% 0.28/0.47 % Problem : Landau theorem 23a
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English : lessis (pl x z) (pl y u)
% 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 : satz23a [Lan30]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % : Without extensionality : Theorem
% 0.28/0.47 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 14 ( 3 unt; 8 typ; 0 def)
% 0.28/0.47 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 3 ( 1 avg)
% 0.28/0.47 % Number of connectives : 32 ( 0 ~; 0 |; 0 &; 28 @)
% 0.28/0.47 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 11 ( 6 avg)
% 0.28/0.47 % Number of types : 2 ( 1 usr)
% 0.28/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 7 ( 7 usr; 4 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.28/0.47 % SPC : TH0_THM_NEQ_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(u,type,
% 0.28/0.47 u: nat ).
% 0.28/0.47
% 0.28/0.47 thf(lessis,type,
% 0.28/0.47 lessis: nat > nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(l,axiom,
% 0.28/0.47 lessis @ x @ y ).
% 0.28/0.47
% 0.28/0.47 thf(k,axiom,
% 0.28/0.47 lessis @ z @ u ).
% 0.28/0.47
% 0.28/0.47 thf(ts,type,
% 0.28/0.47 ts: nat > nat > nat ).
% 0.28/0.47
% 0.28/0.47 thf(moreis,type,
% 0.28/0.47 moreis: nat > nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(satz13,axiom,
% 0.28/0.47 ! [Xx: nat,Xy: nat] :
% 0.28/0.47 ( ( moreis @ Xx @ Xy )
% 0.28/0.47 => ( lessis @ Xy @ Xx ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(satz23,axiom,
% 0.28/0.47 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.28/0.47 ( ( moreis @ Xx @ Xy )
% 0.28/0.47 => ( ( moreis @ Xz @ Xu )
% 0.28/0.47 => ( moreis @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(satz14,axiom,
% 0.28/0.47 ! [Xx: nat,Xy: nat] :
% 0.28/0.47 ( ( lessis @ Xx @ Xy )
% 0.28/0.47 => ( moreis @ Xy @ Xx ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(satz23a,conjecture,
% 0.28/0.47 lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.61/1.34 ---- Embedded in THF ---
% 1.61/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.34 %%% Generated on Tue Feb 24 11:11:51 EST 2026
% 1.61/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.34 %%% Logic specification used:
% 1.61/1.34 %%% thf(spec, logic, $$dhol).
% 1.61/1.34
% 1.61/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2DTF6966.p
% See solution above
% 1.61/1.34 ------------------------
% 1.61/1.35 ---- Cleaned THF ---
% 1.61/1.35 thf(nat_type,type,
% 1.61/1.35 nat: $tType ).
% 1.61/1.35
% 1.61/1.35 thf(x,type,
% 1.61/1.35 x: nat ).
% 1.61/1.35
% 1.61/1.35 thf(y,type,
% 1.61/1.35 y: nat ).
% 1.61/1.35
% 1.61/1.35 thf(z,type,
% 1.61/1.35 z: nat ).
% 1.61/1.35
% 1.61/1.35 thf(u,type,
% 1.61/1.35 u: nat ).
% 1.61/1.35
% 1.61/1.35 thf(lessis,type,
% 1.61/1.35 lessis: nat > nat > $o ).
% 1.61/1.35
% 1.61/1.35 thf(l,axiom,
% 1.61/1.35 lessis @ x @ y ).
% 1.61/1.35
% 1.61/1.35 thf(k,axiom,
% 1.61/1.35 lessis @ z @ u ).
% 1.61/1.35
% 1.61/1.35 thf(ts,type,
% 1.61/1.35 ts: nat > nat > nat ).
% 1.61/1.35
% 1.61/1.35 thf(moreis,type,
% 1.61/1.35 moreis: nat > nat > $o ).
% 1.61/1.35
% 1.61/1.35 thf(satz13,axiom,
% 1.61/1.35 ! [Xx: nat,Xy: nat] :
% 1.61/1.35 ( ( moreis @ Xx @ Xy )
% 1.61/1.35 => ( lessis @ Xy @ Xx ) ) ).
% 1.61/1.35
% 1.61/1.35 thf(satz23,axiom,
% 1.61/1.35 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 1.61/1.35 ( ( moreis @ Xx @ Xy )
% 1.61/1.35 => ( ( moreis @ Xz @ Xu )
% 1.61/1.35 => ( moreis @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) ).
% 1.61/1.35
% 1.61/1.35 thf(satz14,axiom,
% 1.61/1.35 ! [Xx: nat,Xy: nat] :
% 1.61/1.35 ( ( lessis @ Xx @ Xy )
% 1.61/1.35 => ( moreis @ Xy @ Xx ) ) ).
% 1.61/1.35
% 1.61/1.35 thf(satz23a,conjecture,
% 1.61/1.35 lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ).
% 1.61/1.35 ------------------------
% 1.61/1.37 % (7252)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6966 for (2999ds/18Mi)
% 1.61/1.37 % (7252)First to succeed.
% 1.61/1.37 % (7252)Refutation found. Thanks to Tanya!
% 1.61/1.37 % SZS status Theorem for DTF2THF_6966
% 1.61/1.37 % SZS output start Proof for DTF2THF_6966
% 1.61/1.37 thf(type_def_5, type, nat: $tType).
% 1.61/1.37 thf(func_def_0, type, nat: $tType).
% 1.61/1.37 thf(func_def_1, type, x: nat).
% 1.61/1.37 thf(func_def_2, type, y: nat).
% 1.61/1.37 thf(func_def_3, type, z: nat).
% 1.61/1.37 thf(func_def_4, type, u: nat).
% 1.61/1.37 thf(func_def_5, type, lessis: nat > nat > $o).
% 1.61/1.37 thf(func_def_7, type, ts: nat > nat > nat).
% 1.61/1.37 thf(func_def_8, type, moreis: nat > nat > $o).
% 1.61/1.37 thf(f56,plain,(
% 1.61/1.37 $false),
% 1.61/1.37 inference(subsumption_resolution,[status(thm)],[f53,f29])).
% 1.61/1.37 thf(f29,plain,(
% 1.61/1.37 ((lessis @ (ts @ x @ z) @ (ts @ y @ u)) != $true)),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f21])).
% 1.61/1.37 thf(f21,plain,(
% 1.61/1.37 ((lessis @ (ts @ x @ z) @ (ts @ y @ u)) != $true)),
% 1.61/1.37 inference(flattening,[status(thm)],[f12])).
% 1.61/1.37 thf(f12,plain,(
% 1.61/1.37 ~((lessis @ (ts @ x @ z) @ (ts @ y @ u)) = $true)),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f11])).
% 1.61/1.37 thf(f11,plain,(
% 1.61/1.37 ~(lessis @ (ts @ x @ z) @ (ts @ y @ u))),
% 1.61/1.37 inference(rectify,[status(thm)],[f7])).
% 1.61/1.37 thf(f7,negated_conjecture,(
% 1.61/1.37 ~(lessis @ (ts @ x @ z) @ (ts @ y @ u))),
% 1.61/1.37 inference(negated_conjecture,[status(cth)],[f6])).
% 1.61/1.37 thf(f6,conjecture,(
% 1.61/1.37 (lessis @ (ts @ x @ z) @ (ts @ y @ u))),
% 1.61/1.37 file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',satz23a)).
% 1.61/1.37 thf(f53,plain,(
% 1.61/1.37 ((lessis @ (ts @ x @ z) @ (ts @ y @ u)) = $true)),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.61/1.37 thf(f52,plain,(
% 1.61/1.37 ($true != $true) | ((lessis @ (ts @ x @ z) @ (ts @ y @ u)) = $true)),
% 1.61/1.37 inference(superposition,[status(thm)],[f28,f48])).
% 1.61/1.37 thf(f48,plain,(
% 1.61/1.37 ($true = (moreis @ (ts @ y @ u) @ (ts @ x @ z)))),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.61/1.37 thf(f46,plain,(
% 1.61/1.37 ($true != $true) | ($true = (moreis @ (ts @ y @ u) @ (ts @ x @ z)))),
% 1.61/1.37 inference(superposition,[status(thm)],[f44,f36])).
% 1.61/1.37 thf(f36,plain,(
% 1.61/1.37 ((moreis @ y @ x) = $true)),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.61/1.37 thf(f34,plain,(
% 1.61/1.37 ($true != $true) | ((moreis @ y @ x) = $true)),
% 1.61/1.37 inference(superposition,[status(thm)],[f33,f30])).
% 1.61/1.37 thf(f30,plain,(
% 1.61/1.37 ((lessis @ x @ y) = $true)),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f10])).
% 1.61/1.37 thf(f10,plain,(
% 1.61/1.37 ((lessis @ x @ y) = $true)),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f9])).
% 1.61/1.37 thf(f9,plain,(
% 1.61/1.37 (lessis @ x @ y)),
% 1.61/1.37 inference(rectify,[status(thm)],[f1])).
% 1.61/1.37 thf(f1,axiom,(
% 1.61/1.37 (lessis @ x @ y)),
% 1.61/1.37 file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',l)).
% 1.61/1.37 thf(f33,plain,(
% 1.61/1.37 ( ! [X0 : nat,X1 : nat] : (((lessis @ X1 @ X0) != $true) | ((moreis @ X0 @ X1) = $true)) )),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f27])).
% 1.61/1.37 thf(f27,plain,(
% 1.61/1.37 ! [X0 : nat,X1 : nat] : (((moreis @ X0 @ X1) = $true) | ((lessis @ X1 @ X0) != $true))),
% 1.61/1.37 inference(rectify,[status(thm)],[f23])).
% 1.61/1.37 thf(f23,plain,(
% 1.61/1.37 ! [X1 : nat,X0 : nat] : (((moreis @ X1 @ X0) = $true) | ((lessis @ X0 @ X1) != $true))),
% 1.61/1.37 inference(ennf_transformation,[status(thm)],[f20])).
% 1.61/1.37 thf(f20,plain,(
% 1.61/1.37 ! [X0 : nat,X1 : nat] : (((lessis @ X0 @ X1) = $true) => ((moreis @ X1 @ X0) = $true))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f19])).
% 1.61/1.37 thf(f19,plain,(
% 1.61/1.37 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => (moreis @ X1 @ X0))),
% 1.61/1.37 inference(rectify,[status(thm)],[f5])).
% 1.61/1.37 thf(f5,axiom,(
% 1.61/1.37 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => (moreis @ X1 @ X0))),
% 1.61/1.37 file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',satz14)).
% 1.61/1.37 thf(f44,plain,(
% 1.61/1.37 ( ! [X0 : nat,X1 : nat] : (((moreis @ X0 @ X1) != $true) | ((moreis @ (ts @ X0 @ u) @ (ts @ X1 @ z)) = $true)) )),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.61/1.37 thf(f43,plain,(
% 1.61/1.37 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ((moreis @ (ts @ X0 @ u) @ (ts @ X1 @ z)) = $true) | ((moreis @ X0 @ X1) != $true)) )),
% 1.61/1.37 inference(superposition,[status(thm)],[f32,f37])).
% 1.61/1.37 thf(f37,plain,(
% 1.61/1.37 ((moreis @ u @ z) = $true)),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.61/1.37 thf(f35,plain,(
% 1.61/1.37 ((moreis @ u @ z) = $true) | ($true != $true)),
% 1.61/1.37 inference(superposition,[status(thm)],[f33,f31])).
% 1.61/1.37 thf(f31,plain,(
% 1.61/1.37 ((lessis @ z @ u) = $true)),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f16])).
% 1.61/1.37 thf(f16,plain,(
% 1.61/1.37 ((lessis @ z @ u) = $true)),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f15])).
% 1.61/1.37 thf(f15,plain,(
% 1.61/1.37 (lessis @ z @ u)),
% 1.61/1.37 inference(rectify,[status(thm)],[f2])).
% 1.61/1.37 thf(f2,axiom,(
% 1.61/1.37 (lessis @ z @ u)),
% 1.61/1.37 file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',k)).
% 1.61/1.37 thf(f32,plain,(
% 1.61/1.37 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != (moreis @ X2 @ X0)) | ((moreis @ X3 @ X1) != $true) | ($true = (moreis @ (ts @ X3 @ X2) @ (ts @ X1 @ X0)))) )),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f26])).
% 1.61/1.37 thf(f26,plain,(
% 1.61/1.37 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true != (moreis @ X2 @ X0)) | ((moreis @ X3 @ X1) != $true) | ($true = (moreis @ (ts @ X3 @ X2) @ (ts @ X1 @ X0))))),
% 1.61/1.37 inference(rectify,[status(thm)],[f25])).
% 1.61/1.37 thf(f25,plain,(
% 1.61/1.37 ! [X2 : nat,X0 : nat,X3 : nat,X1 : nat] : (($true != (moreis @ X3 @ X2)) | ((moreis @ X1 @ X0) != $true) | ((moreis @ (ts @ X1 @ X3) @ (ts @ X0 @ X2)) = $true))),
% 1.61/1.37 inference(flattening,[status(thm)],[f24])).
% 1.61/1.37 thf(f24,plain,(
% 1.61/1.37 ! [X1 : nat,X0 : nat,X2 : nat,X3 : nat] : ((((moreis @ (ts @ X1 @ X3) @ (ts @ X0 @ X2)) = $true) | ($true != (moreis @ X3 @ X2))) | ((moreis @ X1 @ X0) != $true))),
% 1.61/1.37 inference(ennf_transformation,[status(thm)],[f14])).
% 1.61/1.37 thf(f14,plain,(
% 1.61/1.37 ! [X1 : nat,X0 : nat,X2 : nat,X3 : nat] : (((moreis @ X1 @ X0) = $true) => (($true = (moreis @ X3 @ X2)) => ((moreis @ (ts @ X1 @ X3) @ (ts @ X0 @ X2)) = $true)))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f13])).
% 1.61/1.37 thf(f13,plain,(
% 1.61/1.37 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((moreis @ X1 @ X0) => ((moreis @ X3 @ X2) => (moreis @ (ts @ X1 @ X3) @ (ts @ X0 @ X2))))),
% 1.61/1.37 inference(rectify,[status(thm)],[f4])).
% 1.61/1.37 thf(f4,axiom,(
% 1.61/1.37 ! [X1 : nat,X0 : nat,X3 : nat,X2 : nat] : ((moreis @ X0 @ X1) => ((moreis @ X2 @ X3) => (moreis @ (ts @ X0 @ X2) @ (ts @ X1 @ X3))))),
% 1.61/1.37 file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',satz23)).
% 1.61/1.37 thf(f28,plain,(
% 1.61/1.37 ( ! [X0 : nat,X1 : nat] : (((moreis @ X1 @ X0) != $true) | ((lessis @ X0 @ X1) = $true)) )),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f22])).
% 1.61/1.37 thf(f22,plain,(
% 1.61/1.37 ! [X0 : nat,X1 : nat] : (((lessis @ X0 @ X1) = $true) | ((moreis @ X1 @ X0) != $true))),
% 1.61/1.37 inference(ennf_transformation,[status(thm)],[f18])).
% 1.61/1.37 thf(f18,plain,(
% 1.61/1.37 ! [X0 : nat,X1 : nat] : (((moreis @ X1 @ X0) = $true) => ((lessis @ X0 @ X1) = $true))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f17])).
% 1.61/1.37 thf(f17,plain,(
% 1.61/1.37 ! [X0 : nat,X1 : nat] : ((moreis @ X1 @ X0) => (lessis @ X0 @ X1))),
% 1.61/1.37 inference(rectify,[status(thm)],[f3])).
% 1.61/1.37 thf(f3,axiom,(
% 1.61/1.37 ! [X1 : nat,X0 : nat] : ((moreis @ X0 @ X1) => (lessis @ X1 @ X0))),
% 1.61/1.37 file('/export/starexec/sandbox2/tmp/tmp.fzgx963jtN/DTF2THF_6966.p',satz13)).
% 1.61/1.37 % SZS output end Proof for DTF2THF_6966
% 1.61/1.37 % (7252)------------------------------
% 1.61/1.37 % (7252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (7252)Termination reason: Refutation
% 1.61/1.37
% 1.61/1.37 % (7252)Memory used [KB]: 5500
% 1.61/1.37 % (7252)Time elapsed: 0.004 s
% 1.61/1.37 % (7252)Instructions burned: 6 (million)
% 1.61/1.37 % (7252)------------------------------
% 1.61/1.37 % (7252)------------------------------
% 1.61/1.37 % (7245)Success in time 0.016 s
%------------------------------------------------------------------------------