%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM672^1 : 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 : n004.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 09:24:12 AM UTC 2026
% Result : Theorem 1.64s 1.41s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 198 ( 22 ~; 11 |; 0 &; 156 @)
% ( 0 <=>; 9 =>; 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; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% 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_6,type,
pl: nat > nat > nat ).
thf(func_def_7,type,
more: nat > nat > $o ).
thf(f37,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f36,f25]) ).
thf(f25,plain,
( ( less @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( less @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
less @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
less @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',l) ).
thf(f36,plain,
( ( less @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( less @ x @ y )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f34,f24]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: nat,X0: nat] :
( ( ( more @ X0 @ X1 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X1 @ X0 )
= $true )
=> ( ( more @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: nat,X1: nat] :
( ( less @ X1 @ X0 )
=> ( more @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: nat,X0: nat] :
( ( less @ X0 @ X1 )
=> ( more @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',satz12) ).
thf(f34,plain,
( ( more @ y @ x )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $true != $true )
| ( ( more @ y @ x )
!= $true ) ),
inference(superposition,[status(thm)],[f30,f27]) ).
thf(f27,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) ) )
| ( ( more @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X0 ) ) )
| ( ( more @ X1 @ X2 )
!= $true ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) )
= $true )
| ( ( more @ X2 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( ( more @ X2 @ X0 )
= $true )
=> ( ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( more @ X2 @ X0 )
=> ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X2: nat,X0: nat] :
( ( more @ X0 @ X1 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',satz19a) ).
thf(f30,plain,
( $true
!= ( more @ ( pl @ y @ z ) @ ( pl @ x @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true != $true )
| ( $true
!= ( more @ ( pl @ y @ z ) @ ( pl @ x @ z ) ) ) ),
inference(superposition,[status(thm)],[f26,f28]) ).
thf(f28,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X0 @ X1 )
= $true )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
!= $true )
| ( ( less @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: nat,X0: nat] :
( ( ( more @ X1 @ X0 )
= $true )
=> ( ( less @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( more @ X1 @ X0 )
=> ( less @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',satz11) ).
thf(f26,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
!= $true ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',satz19c) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM672^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.37 % Computer : n004.cluster.edu
% 0.20/0.37 % Model : x86_64 x86_64
% 0.20/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.37 % Memory : 8042.1875MB
% 0.20/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.37 % CPULimit : 300
% 0.20/0.37 % WCLimit : 300
% 0.20/0.37 % DateTime : Tue Feb 24 11:10:26 EST 2026
% 0.20/0.37 % CPUTime :
% 0.20/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : NUM672^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.47 % Domain : Number Theory
% 0.30/0.47 % Problem : Landau theorem 19c
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English : less (pl x z) (pl y z)
% 0.30/0.47
% 0.30/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Bro09]
% 0.30/0.47 % Names : satz19c [Lan30]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % : Without extensionality : Theorem
% 0.30/0.47 % Rating : 0.00 v3.7.0
% 0.30/0.47 % Syntax : Number of formulae : 12 ( 2 unt; 7 typ; 0 def)
% 0.30/0.47 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 2 ( 1 avg)
% 0.30/0.47 % Number of connectives : 27 ( 0 ~; 0 |; 0 &; 24 @)
% 0.30/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 9 ( 6 avg)
% 0.30/0.47 % Number of types : 2 ( 1 usr)
% 0.30/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.30/0.47 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.30/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.47
% 0.30/0.47 % Comments :
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(nat_type,type,
% 0.30/0.47 nat: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(x,type,
% 0.30/0.47 x: nat ).
% 0.30/0.47
% 0.30/0.47 thf(y,type,
% 0.30/0.47 y: nat ).
% 0.30/0.47
% 0.30/0.47 thf(z,type,
% 0.30/0.47 z: nat ).
% 0.30/0.47
% 0.30/0.47 thf(less,type,
% 0.30/0.47 less: nat > nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(l,axiom,
% 0.30/0.47 less @ x @ y ).
% 0.30/0.47
% 0.30/0.47 thf(pl,type,
% 0.30/0.47 pl: nat > nat > nat ).
% 0.30/0.47
% 0.30/0.47 thf(more,type,
% 0.30/0.47 more: nat > nat > $o ).
% 0.30/0.47
% 0.30/0.47 thf(satz11,axiom,
% 0.30/0.47 ! [Xx: nat,Xy: nat] :
% 0.30/0.47 ( ( more @ Xx @ Xy )
% 0.30/0.47 => ( less @ Xy @ Xx ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(satz19a,axiom,
% 0.30/0.47 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.30/0.47 ( ( more @ Xx @ Xy )
% 0.30/0.47 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(satz12,axiom,
% 0.30/0.47 ! [Xx: nat,Xy: nat] :
% 0.30/0.47 ( ( less @ Xx @ Xy )
% 0.30/0.47 => ( more @ Xy @ Xx ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(satz19c,conjecture,
% 0.30/0.47 less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.46/1.38 ---- Embedded in THF ---
% 1.46/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.38 %%% Generated on Tue Feb 24 11:10:27 EST 2026
% 1.46/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.38 %%% Logic specification used:
% 1.46/1.38 %%% thf(spec, logic, $$dhol).
% 1.46/1.38
% 1.46/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2DTF29023.p
% See solution above
% 1.46/1.38 ------------------------
% 1.46/1.38 ---- Cleaned THF ---
% 1.46/1.39 thf(nat_type,type,
% 1.46/1.39 nat: $tType ).
% 1.46/1.39
% 1.46/1.39 thf(x,type,
% 1.46/1.39 x: nat ).
% 1.46/1.39
% 1.46/1.39 thf(y,type,
% 1.46/1.39 y: nat ).
% 1.46/1.39
% 1.46/1.39 thf(z,type,
% 1.46/1.39 z: nat ).
% 1.46/1.39
% 1.46/1.39 thf(less,type,
% 1.46/1.39 less: nat > nat > $o ).
% 1.46/1.39
% 1.46/1.39 thf(l,axiom,
% 1.46/1.39 less @ x @ y ).
% 1.46/1.39
% 1.46/1.39 thf(pl,type,
% 1.46/1.39 pl: nat > nat > nat ).
% 1.46/1.39
% 1.46/1.39 thf(more,type,
% 1.46/1.39 more: nat > nat > $o ).
% 1.46/1.39
% 1.46/1.39 thf(satz11,axiom,
% 1.46/1.39 ! [Xx: nat,Xy: nat] :
% 1.46/1.39 ( ( more @ Xx @ Xy )
% 1.46/1.39 => ( less @ Xy @ Xx ) ) ).
% 1.46/1.39
% 1.46/1.39 thf(satz19a,axiom,
% 1.46/1.39 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.46/1.39 ( ( more @ Xx @ Xy )
% 1.46/1.39 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 1.46/1.39
% 1.46/1.39 thf(satz12,axiom,
% 1.46/1.39 ! [Xx: nat,Xy: nat] :
% 1.46/1.39 ( ( less @ Xx @ Xy )
% 1.46/1.39 => ( more @ Xy @ Xx ) ) ).
% 1.46/1.39
% 1.46/1.39 thf(satz19c,conjecture,
% 1.46/1.39 less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ).
% 1.46/1.39 ------------------------
% 1.64/1.40 % (29120)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29023 for (3000ds/183Mi)
% 1.64/1.40 % (29121)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_29023 for (3000ds/4Mi)
% 1.64/1.40 % (29123)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29023 for (3000ds/2Mi)
% 1.64/1.40 % (29122)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_29023 for (3000ds/27Mi)
% 1.64/1.40 % (29124)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_29023 for (3000ds/2Mi)
% 1.64/1.40 % (29126)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29023 for (3000ds/18Mi)
% 1.64/1.41 % (29125)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_29023 for (3000ds/275Mi)
% 1.64/1.41 % (29123)Instruction limit reached!
% 1.64/1.41 % (29123)------------------------------
% 1.64/1.41 % (29123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.41 % (29123)Termination reason: Unknown
% 1.64/1.41 % (29124)Instruction limit reached!
% 1.64/1.41 % (29124)------------------------------
% 1.64/1.41 % (29124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.41 % (29123)Termination phase: Saturation
% 1.64/1.41
% 1.64/1.41 % (29123)Memory used [KB]: 5500
% 1.64/1.41 % (29123)Time elapsed: 0.003 s
% 1.64/1.41 % (29123)Instructions burned: 2 (million)
% 1.64/1.41 % (29123)------------------------------
% 1.64/1.41 % (29123)------------------------------
% 1.64/1.41 % (29124)Termination reason: Unknown
% 1.64/1.41 % (29124)Termination phase: Saturation
% 1.64/1.41
% 1.64/1.41 % (29124)Memory used [KB]: 5500
% 1.64/1.41 % (29124)Time elapsed: 0.003 s
% 1.64/1.41 % (29124)Instructions burned: 3 (million)
% 1.64/1.41 % (29124)------------------------------
% 1.64/1.41 % (29124)------------------------------
% 1.64/1.41 % (29125)First to succeed.
% 1.64/1.41 % (29121)Instruction limit reached!
% 1.64/1.41 % (29121)------------------------------
% 1.64/1.41 % (29121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.41 % (29121)Termination reason: Unknown
% 1.64/1.41 % (29121)Termination phase: Saturation
% 1.64/1.41
% 1.64/1.41 % (29121)Memory used [KB]: 5500
% 1.64/1.41 % (29121)Time elapsed: 0.004 s
% 1.64/1.41 % (29121)Instructions burned: 4 (million)
% 1.64/1.41 % (29121)------------------------------
% 1.64/1.41 % (29121)------------------------------
% 1.64/1.41 % (29120)Also succeeded, but the first one will report.
% 1.64/1.41 % (29126)Also succeeded, but the first one will report.
% 1.64/1.41 % (29125)Refutation found. Thanks to Tanya!
% 1.64/1.41 % SZS status Theorem for DTF2THF_29023
% 1.64/1.41 % SZS output start Proof for DTF2THF_29023
% 1.64/1.41 thf(type_def_5, type, nat: $tType).
% 1.64/1.41 thf(func_def_0, type, nat: $tType).
% 1.64/1.41 thf(func_def_1, type, x: nat).
% 1.64/1.41 thf(func_def_2, type, y: nat).
% 1.64/1.41 thf(func_def_3, type, z: nat).
% 1.64/1.41 thf(func_def_4, type, less: nat > nat > $o).
% 1.64/1.41 thf(func_def_6, type, pl: nat > nat > nat).
% 1.64/1.41 thf(func_def_7, type, more: nat > nat > $o).
% 1.64/1.41 thf(f37,plain,(
% 1.64/1.41 $false),
% 1.64/1.41 inference(subsumption_resolution,[status(thm)],[f36,f25])).
% 1.64/1.41 thf(f25,plain,(
% 1.64/1.41 ((less @ x @ y) = $true)),
% 1.64/1.41 inference(cnf_transformation,[status(thm)],[f17])).
% 1.64/1.41 thf(f17,plain,(
% 1.64/1.41 ((less @ x @ y) = $true)),
% 1.64/1.41 inference(fool_elimination,[status(thm)],[f16])).
% 1.64/1.41 thf(f16,plain,(
% 1.64/1.41 (less @ x @ y)),
% 1.64/1.41 inference(rectify,[status(thm)],[f1])).
% 1.64/1.41 thf(f1,axiom,(
% 1.64/1.41 (less @ x @ y)),
% 1.64/1.41 file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',l)).
% 1.64/1.41 thf(f36,plain,(
% 1.64/1.41 ((less @ x @ y) != $true)),
% 1.64/1.41 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.64/1.41 thf(f35,plain,(
% 1.64/1.41 ((less @ x @ y) != $true) | ($true != $true)),
% 1.64/1.41 inference(superposition,[status(thm)],[f34,f24])).
% 1.64/1.41 thf(f24,plain,(
% 1.64/1.41 ( ! [X0 : nat,X1 : nat] : (((more @ X1 @ X0) = $true) | ((less @ X0 @ X1) != $true)) )),
% 1.64/1.41 inference(cnf_transformation,[status(thm)],[f22])).
% 1.64/1.41 thf(f22,plain,(
% 1.64/1.41 ! [X0 : nat,X1 : nat] : (((more @ X1 @ X0) = $true) | ((less @ X0 @ X1) != $true))),
% 1.64/1.41 inference(rectify,[status(thm)],[f21])).
% 1.64/1.41 thf(f21,plain,(
% 1.64/1.41 ! [X1 : nat,X0 : nat] : (((more @ X0 @ X1) = $true) | ((less @ X1 @ X0) != $true))),
% 1.64/1.41 inference(ennf_transformation,[status(thm)],[f9])).
% 1.64/1.41 thf(f9,plain,(
% 1.64/1.41 ! [X0 : nat,X1 : nat] : (((less @ X1 @ X0) = $true) => ((more @ X0 @ X1) = $true))),
% 1.64/1.41 inference(fool_elimination,[status(thm)],[f8])).
% 1.64/1.41 thf(f8,plain,(
% 1.64/1.41 ! [X0 : nat,X1 : nat] : ((less @ X1 @ X0) => (more @ X0 @ X1))),
% 1.64/1.41 inference(rectify,[status(thm)],[f4])).
% 1.64/1.41 thf(f4,axiom,(
% 1.64/1.41 ! [X1 : nat,X0 : nat] : ((less @ X0 @ X1) => (more @ X1 @ X0))),
% 1.64/1.41 file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',satz12)).
% 1.64/1.41 thf(f34,plain,(
% 1.64/1.41 ((more @ y @ x) != $true)),
% 1.64/1.41 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.64/1.41 thf(f31,plain,(
% 1.64/1.41 ($true != $true) | ((more @ y @ x) != $true)),
% 1.64/1.41 inference(superposition,[status(thm)],[f30,f27])).
% 1.64/1.41 thf(f27,plain,(
% 1.64/1.41 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (more @ (pl @ X1 @ X0) @ (pl @ X2 @ X0))) | ((more @ X1 @ X2) != $true)) )),
% 1.64/1.41 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.41 thf(f23,plain,(
% 1.64/1.41 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (more @ (pl @ X1 @ X0) @ (pl @ X2 @ X0))) | ((more @ X1 @ X2) != $true))),
% 1.64/1.41 inference(rectify,[status(thm)],[f19])).
% 1.64/1.41 thf(f19,plain,(
% 1.64/1.41 ! [X1 : nat,X2 : nat,X0 : nat] : (((more @ (pl @ X2 @ X1) @ (pl @ X0 @ X1)) = $true) | ((more @ X2 @ X0) != $true))),
% 1.64/1.41 inference(ennf_transformation,[status(thm)],[f13])).
% 1.64/1.41 thf(f13,plain,(
% 1.64/1.41 ! [X1 : nat,X2 : nat,X0 : nat] : (((more @ X2 @ X0) = $true) => ((more @ (pl @ X2 @ X1) @ (pl @ X0 @ X1)) = $true))),
% 1.64/1.41 inference(fool_elimination,[status(thm)],[f12])).
% 1.64/1.41 thf(f12,plain,(
% 1.64/1.41 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X2 @ X0) => (more @ (pl @ X2 @ X1) @ (pl @ X0 @ X1)))),
% 1.64/1.41 inference(rectify,[status(thm)],[f3])).
% 1.64/1.41 thf(f3,axiom,(
% 1.64/1.41 ! [X1 : nat,X2 : nat,X0 : nat] : ((more @ X0 @ X1) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 1.64/1.41 file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',satz19a)).
% 1.64/1.41 thf(f30,plain,(
% 1.64/1.41 ($true != (more @ (pl @ y @ z) @ (pl @ x @ z)))),
% 1.64/1.41 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.64/1.41 thf(f29,plain,(
% 1.64/1.41 ($true != $true) | ($true != (more @ (pl @ y @ z) @ (pl @ x @ z)))),
% 1.64/1.41 inference(superposition,[status(thm)],[f26,f28])).
% 1.64/1.41 thf(f28,plain,(
% 1.64/1.41 ( ! [X0 : nat,X1 : nat] : (((less @ X0 @ X1) = $true) | ((more @ X1 @ X0) != $true)) )),
% 1.64/1.41 inference(cnf_transformation,[status(thm)],[f20])).
% 1.64/1.41 thf(f20,plain,(
% 1.64/1.41 ! [X0 : nat,X1 : nat] : (((more @ X1 @ X0) != $true) | ((less @ X0 @ X1) = $true))),
% 1.64/1.41 inference(ennf_transformation,[status(thm)],[f15])).
% 1.64/1.41 thf(f15,plain,(
% 1.64/1.41 ! [X1 : nat,X0 : nat] : (((more @ X1 @ X0) = $true) => ((less @ X0 @ X1) = $true))),
% 1.64/1.41 inference(fool_elimination,[status(thm)],[f14])).
% 1.64/1.41 thf(f14,plain,(
% 1.64/1.41 ! [X0 : nat,X1 : nat] : ((more @ X1 @ X0) => (less @ X0 @ X1))),
% 1.64/1.41 inference(rectify,[status(thm)],[f2])).
% 1.64/1.41 thf(f2,axiom,(
% 1.64/1.41 ! [X1 : nat,X0 : nat] : ((more @ X0 @ X1) => (less @ X1 @ X0))),
% 1.64/1.41 file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',satz11)).
% 1.64/1.41 thf(f26,plain,(
% 1.64/1.41 ((less @ (pl @ x @ z) @ (pl @ y @ z)) != $true)),
% 1.64/1.41 inference(cnf_transformation,[status(thm)],[f18])).
% 1.64/1.41 thf(f18,plain,(
% 1.64/1.41 ((less @ (pl @ x @ z) @ (pl @ y @ z)) != $true)),
% 1.64/1.41 inference(flattening,[status(thm)],[f11])).
% 1.64/1.41 thf(f11,plain,(
% 1.64/1.41 ~((less @ (pl @ x @ z) @ (pl @ y @ z)) = $true)),
% 1.64/1.41 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.41 thf(f10,plain,(
% 1.64/1.41 ~(less @ (pl @ x @ z) @ (pl @ y @ z))),
% 1.64/1.41 inference(rectify,[status(thm)],[f6])).
% 1.64/1.41 thf(f6,negated_conjecture,(
% 1.64/1.41 ~(less @ (pl @ x @ z) @ (pl @ y @ z))),
% 1.64/1.41 inference(negated_conjecture,[status(cth)],[f5])).
% 1.64/1.41 thf(f5,conjecture,(
% 1.64/1.41 (less @ (pl @ x @ z) @ (pl @ y @ z))),
% 1.64/1.41 file('/export/starexec/sandbox2/tmp/tmp.ggHPs2GGSQ/DTF2THF_29023.p',satz19c)).
% 1.64/1.41 % SZS output end Proof for DTF2THF_29023
% 1.64/1.41 % (29125)------------------------------
% 1.64/1.41 % (29125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.41 % (29125)Termination reason: Refutation
% 1.64/1.41
% 1.64/1.41 % (29125)Memory used [KB]: 5500
% 1.64/1.41 % (29125)Time elapsed: 0.004 s
% 1.64/1.41 % (29125)Instructions burned: 2 (million)
% 1.64/1.41 % (29125)------------------------------
% 1.64/1.41 % (29125)------------------------------
% 1.64/1.41 % (29119)Success in time 0.017 s
%------------------------------------------------------------------------------