%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM702^1 : 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 : n015.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 09:24:21 AM UTC 2026
% Result : Theorem 1.62s 1.32s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 27 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 142 ( 13 ~; 7 |; 0 &; 116 @)
% ( 0 <=>; 6 =>; 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 : 13 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 31 ( 9 ^; 22 !; 0 ?; 31 :)
% 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,
some: ( nat > $o ) > $o ).
thf(func_def_4,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_5,type,
pl: nat > nat > nat ).
thf(func_def_6,type,
n_1: nat ).
thf(func_def_8,type,
moreis: nat > nat > $o ).
thf(func_def_9,type,
lessis: nat > nat > $o ).
thf(func_def_10,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
$true != $true,
inference(superposition,[status(thm)],[f21,f27]) ).
thf(f27,plain,
( ( moreis @ y @ x )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true != $true )
| ( ( moreis @ y @ x )
= $true ) ),
inference(superposition,[status(thm)],[f19,f25]) ).
thf(f25,plain,
( $true
= ( lessis @ x @ y ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true != $true )
| ( $true
= ( lessis @ x @ y ) ) ),
inference(superposition,[status(thm)],[f22,f23]) ).
thf(f23,plain,
( $true
= ( some @ ( diffprop @ ( pl @ y @ n_1 ) @ x ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ y @ n_1 ) @ x @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ y @ n_1 ) @ x @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ y @ n_1 ) @ x @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ y @ n_1 ) @ x @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.9bvUQYicXS/DTF2THF_1727.p',m) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( some @ ( diffprop @ ( pl @ X0 @ n_1 ) @ X1 ) ) )
| ( $true
= ( lessis @ X1 @ X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X0 @ n_1 ) @ X1 @ Y0 ) ) )
| ( $true
= ( lessis @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X0 @ n_1 ) @ X1 @ Y0 ) ) )
| ( $true
= ( lessis @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X0 @ n_1 ) @ X1 @ Y0 ) ) )
=> ( $true
= ( lessis @ X1 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat,X1: nat] :
( ( some
@ ^ [X2: nat] : ( diffprop @ ( pl @ X0 @ n_1 ) @ X1 @ X2 ) )
=> ( lessis @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X2: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ ( pl @ X1 @ n_1 ) @ X2 @ X3 ) )
=> ( lessis @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.9bvUQYicXS/DTF2THF_1727.p',satz26) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( lessis @ X1 @ X0 ) )
| ( $true
= ( moreis @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( moreis @ X0 @ X1 ) )
| ( $true
!= ( lessis @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X1 @ X0 ) )
=> ( $true
= ( moreis @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( lessis @ X1 @ X0 )
=> ( moreis @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: nat,X1: nat] :
( ( lessis @ X1 @ X2 )
=> ( moreis @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.9bvUQYicXS/DTF2THF_1727.p',satz14) ).
thf(f21,plain,
( ( moreis @ y @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( moreis @ y @ x )
!= $true ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( moreis @ y @ x )
!= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( moreis @ y @ x ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( moreis @ y @ x ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
moreis @ y @ x,
file('/export/starexec/sandbox2/tmp/tmp.9bvUQYicXS/DTF2THF_1727.p',satz26b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM702^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n015.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 11:11:46 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : NUM702^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.46 % Domain : Number Theory
% 0.27/0.46 % Problem : Landau theorem 26b
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English : moreis y x
% 0.27/0.46
% 0.27/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.27/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.27/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Bro09]
% 0.27/0.46 % Names : satz26b [Lan30]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % : Without extensionality : Theorem
% 0.27/0.46 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.27/0.46 % Syntax : Number of formulae : 13 ( 1 unt; 9 typ; 0 def)
% 0.27/0.46 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 3 ( 2 avg)
% 0.27/0.46 % Number of connectives : 22 ( 0 ~; 0 |; 0 &; 20 @)
% 0.27/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 11 ( 7 avg)
% 0.27/0.46 % Number of types : 2 ( 1 usr)
% 0.27/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 8 ( 8 usr; 3 con; 0-3 aty)
% 0.27/0.46 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.27/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.46
% 0.27/0.46 % Comments :
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(nat_type,type,
% 0.27/0.46 nat: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(x,type,
% 0.27/0.46 x: nat ).
% 0.27/0.46
% 0.27/0.46 thf(y,type,
% 0.27/0.46 y: nat ).
% 0.27/0.46
% 0.27/0.46 thf(some,type,
% 0.27/0.46 some: ( nat > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(diffprop,type,
% 0.27/0.46 diffprop: nat > nat > nat > $o ).
% 0.27/0.46
% 0.27/0.46 thf(pl,type,
% 0.27/0.46 pl: nat > nat > nat ).
% 0.27/0.46
% 0.27/0.46 thf(n_1,type,
% 0.27/0.46 n_1: nat ).
% 0.27/0.46
% 0.27/0.46 thf(m,axiom,
% 0.27/0.46 ( some
% 0.27/0.46 @ ^ [Xu: nat] : ( diffprop @ ( pl @ y @ n_1 ) @ x @ Xu ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(moreis,type,
% 0.27/0.46 moreis: nat > nat > $o ).
% 0.27/0.46
% 0.27/0.46 thf(lessis,type,
% 0.27/0.46 lessis: nat > nat > $o ).
% 0.27/0.46
% 0.27/0.46 thf(satz14,axiom,
% 0.27/0.46 ! [Xx: nat,Xy: nat] :
% 0.27/0.46 ( ( lessis @ Xx @ Xy )
% 0.27/0.46 => ( moreis @ Xy @ Xx ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(satz26,axiom,
% 0.27/0.46 ! [Xx: nat,Xy: nat] :
% 0.27/0.46 ( ( some
% 0.27/0.46 @ ^ [Xv: nat] : ( diffprop @ ( pl @ Xx @ n_1 ) @ Xy @ Xv ) )
% 0.27/0.46 => ( lessis @ Xy @ Xx ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(satz26b,conjecture,
% 0.27/0.46 moreis @ y @ x ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.44/1.28 ---- Embedded in THF ---
% 1.44/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.28 %%% Generated on Tue Feb 24 11:11:47 EST 2026
% 1.44/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.28 %%% Logic specification used:
% 1.44/1.28 %%% thf(spec, logic, $$dhol).
% 1.44/1.28
% 1.44/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.9bvUQYicXS/DTF2DTF1727.p
% See solution above
% 1.44/1.28 ------------------------
% 1.44/1.29 ---- Cleaned THF ---
% 1.44/1.30 thf(nat_type,type,
% 1.44/1.30 nat: $tType ).
% 1.44/1.30
% 1.44/1.30 thf(x,type,
% 1.44/1.30 x: nat ).
% 1.44/1.30
% 1.44/1.30 thf(y,type,
% 1.44/1.30 y: nat ).
% 1.44/1.30
% 1.44/1.30 thf(some,type,
% 1.44/1.30 some: ( nat > $o ) > $o ).
% 1.44/1.30
% 1.44/1.30 thf(diffprop,type,
% 1.44/1.30 diffprop: nat > nat > nat > $o ).
% 1.44/1.30
% 1.44/1.30 thf(pl,type,
% 1.44/1.30 pl: nat > nat > nat ).
% 1.44/1.30
% 1.44/1.30 thf(n_1,type,
% 1.44/1.30 n_1: nat ).
% 1.44/1.30
% 1.44/1.30 thf(m,axiom,
% 1.44/1.30 ( some
% 1.44/1.30 @ ^ [Xu: nat] : ( diffprop @ ( pl @ y @ n_1 ) @ x @ Xu ) ) ).
% 1.44/1.30
% 1.44/1.30 thf(moreis,type,
% 1.44/1.30 moreis: nat > nat > $o ).
% 1.44/1.30
% 1.44/1.30 thf(lessis,type,
% 1.44/1.30 lessis: nat > nat > $o ).
% 1.44/1.30
% 1.44/1.30 thf(satz14,axiom,
% 1.44/1.30 ! [Xx: nat,Xy: nat] :
% 1.44/1.30 ( ( lessis @ Xx @ Xy )
% 1.44/1.30 => ( moreis @ Xy @ Xx ) ) ).
% 1.44/1.30
% 1.44/1.30 thf(satz26,axiom,
% 1.44/1.30 ! [Xx: nat,Xy: nat] :
% 1.44/1.30 ( ( some
% 1.44/1.30 @ ^ [Xv: nat] : ( diffprop @ ( pl @ Xx @ n_1 ) @ Xy @ Xv ) )
% 1.44/1.30 => ( lessis @ Xy @ Xx ) ) ).
% 1.44/1.30
% 1.44/1.30 thf(satz26b,conjecture,
% 1.44/1.30 moreis @ y @ x ).
% 1.44/1.30 ------------------------
% 1.62/1.31 % (2020)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_1727 for (2999ds/2Mi)
% 1.62/1.31 % (2020)Instruction limit reached!
% 1.62/1.31 % (2020)------------------------------
% 1.62/1.31 % (2020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (2020)Termination reason: Unknown
% 1.62/1.31 % (2020)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (2020)Memory used [KB]: 5500
% 1.62/1.31 % (2020)Time elapsed: 0.002 s
% 1.62/1.31 % (2020)Instructions burned: 2 (million)
% 1.62/1.31 % (2020)------------------------------
% 1.62/1.31 % (2020)------------------------------
% 1.62/1.32 % (2016)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1727 for (2999ds/183Mi)
% 1.62/1.32 % (2017)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_1727 for (2999ds/4Mi)
% 1.62/1.32 % (2019)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1727 for (2999ds/2Mi)
% 1.62/1.32 % (2018)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_1727 for (2999ds/27Mi)
% 1.62/1.32 % (2021)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_1727 for (2999ds/275Mi)
% 1.62/1.32 % (2022)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1727 for (2999ds/18Mi)
% 1.62/1.32 % (2019)Instruction limit reached!
% 1.62/1.32 % (2019)------------------------------
% 1.62/1.32 % (2019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (2019)Termination reason: Unknown
% 1.62/1.32 % (2019)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (2019)Memory used [KB]: 895
% 1.62/1.32 % (2019)Time elapsed: 0.003 s
% 1.62/1.32 % (2019)Instructions burned: 2 (million)
% 1.62/1.32 % (2019)------------------------------
% 1.62/1.32 % (2019)------------------------------
% 1.62/1.32 % (2021)Refutation not found, incomplete strategy
% 1.62/1.32 % (2021)------------------------------
% 1.62/1.32 % (2021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (2021)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.32
% 1.62/1.32
% 1.62/1.32 % (2021)Memory used [KB]: 5500
% 1.62/1.32 % (2021)Time elapsed: 0.003 s
% 1.62/1.32 % (2021)Instructions burned: 2 (million)
% 1.62/1.32 % (2021)------------------------------
% 1.62/1.32 % (2021)------------------------------
% 1.62/1.32 % (2023)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1727 for (2999ds/3Mi)
% 1.62/1.32 % (2018)First to succeed.
% 1.62/1.32 % (2017)Instruction limit reached!
% 1.62/1.32 % (2017)------------------------------
% 1.62/1.32 % (2017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (2017)Termination reason: Unknown
% 1.62/1.32 % (2017)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (2017)Memory used [KB]: 5500
% 1.62/1.32 % (2017)Time elapsed: 0.005 s
% 1.62/1.32 % (2017)Instructions burned: 4 (million)
% 1.62/1.32 % (2017)------------------------------
% 1.62/1.32 % (2017)------------------------------
% 1.62/1.32 % (2023)Instruction limit reached!
% 1.62/1.32 % (2023)------------------------------
% 1.62/1.32 % (2023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (2023)Termination reason: Unknown
% 1.62/1.32 % (2023)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (2023)Memory used [KB]: 5500
% 1.62/1.32 % (2023)Time elapsed: 0.002 s
% 1.62/1.32 % (2023)Instructions burned: 3 (million)
% 1.62/1.32 % (2023)------------------------------
% 1.62/1.32 % (2023)------------------------------
% 1.62/1.32 % (2016)Also succeeded, but the first one will report.
% 1.62/1.32 % (2018)Refutation found. Thanks to Tanya!
% 1.62/1.32 % SZS status Theorem for DTF2THF_1727
% 1.62/1.32 % SZS output start Proof for DTF2THF_1727
% 1.62/1.32 thf(type_def_5, type, nat: $tType).
% 1.62/1.32 thf(func_def_0, type, nat: $tType).
% 1.62/1.32 thf(func_def_1, type, x: nat).
% 1.62/1.32 thf(func_def_2, type, y: nat).
% 1.62/1.32 thf(func_def_3, type, some: (nat > $o) > $o).
% 1.62/1.32 thf(func_def_4, type, diffprop: nat > nat > nat > $o).
% 1.62/1.32 thf(func_def_5, type, pl: nat > nat > nat).
% 1.62/1.32 thf(func_def_6, type, n_1: nat).
% 1.62/1.32 thf(func_def_8, type, moreis: nat > nat > $o).
% 1.62/1.32 thf(func_def_9, type, lessis: nat > nat > $o).
% 1.62/1.32 thf(func_def_10, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.62/1.32 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.62/1.32 thf(f29,plain,(
% 1.62/1.32 $false),
% 1.62/1.32 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.62/1.32 thf(f28,plain,(
% 1.62/1.32 ($true != $true)),
% 1.62/1.32 inference(superposition,[status(thm)],[f21,f27])).
% 1.62/1.32 thf(f27,plain,(
% 1.62/1.32 ((moreis @ y @ x) = $true)),
% 1.62/1.32 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.62/1.32 thf(f26,plain,(
% 1.62/1.32 ($true != $true) | ((moreis @ y @ x) = $true)),
% 1.62/1.32 inference(superposition,[status(thm)],[f19,f25])).
% 1.62/1.32 thf(f25,plain,(
% 1.62/1.32 ($true = (lessis @ x @ y))),
% 1.62/1.32 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.62/1.32 thf(f24,plain,(
% 1.62/1.32 ($true != $true) | ($true = (lessis @ x @ y))),
% 1.62/1.32 inference(superposition,[status(thm)],[f22,f23])).
% 1.62/1.32 thf(f23,plain,(
% 1.62/1.32 ($true = (some @ (diffprop @ (pl @ y @ n_1) @ x)))),
% 1.62/1.32 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.62/1.32 thf(f20,plain,(
% 1.62/1.32 ($true = (some @ (^[Y0 : nat]: (diffprop @ (pl @ y @ n_1) @ x @ Y0))))),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f8])).
% 1.62/1.32 thf(f8,plain,(
% 1.62/1.32 ($true = (some @ (^[Y0 : nat]: (diffprop @ (pl @ y @ n_1) @ x @ Y0))))),
% 1.62/1.32 inference(fool_elimination,[status(thm)],[f7])).
% 1.62/1.32 thf(f7,plain,(
% 1.62/1.32 (some @ (^[X0 : nat] : (diffprop @ (pl @ y @ n_1) @ x @ X0)))),
% 1.62/1.32 inference(rectify,[status(thm)],[f1])).
% 1.62/1.32 thf(f1,axiom,(
% 1.62/1.32 (some @ (^[X0 : nat] : (diffprop @ (pl @ y @ n_1) @ x @ X0)))),
% 1.62/1.32 file('/export/starexec/sandbox2/tmp/tmp.9bvUQYicXS/DTF2THF_1727.p',m)).
% 1.62/1.32 thf(f22,plain,(
% 1.62/1.32 ( ! [X0 : nat,X1 : nat] : (($true != (some @ (diffprop @ (pl @ X0 @ n_1) @ X1))) | ($true = (lessis @ X1 @ X0))) )),
% 1.62/1.32 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.62/1.32 thf(f18,plain,(
% 1.62/1.32 ( ! [X0 : nat,X1 : nat] : (($true != (some @ (^[Y0 : nat]: (diffprop @ (pl @ X0 @ n_1) @ X1 @ Y0)))) | ($true = (lessis @ X1 @ X0))) )),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f16])).
% 1.62/1.32 thf(f16,plain,(
% 1.62/1.32 ! [X0 : nat,X1 : nat] : (($true != (some @ (^[Y0 : nat]: (diffprop @ (pl @ X0 @ n_1) @ X1 @ Y0)))) | ($true = (lessis @ X1 @ X0)))),
% 1.62/1.32 inference(ennf_transformation,[status(thm)],[f14])).
% 1.62/1.32 thf(f14,plain,(
% 1.62/1.32 ! [X0 : nat,X1 : nat] : (($true = (some @ (^[Y0 : nat]: (diffprop @ (pl @ X0 @ n_1) @ X1 @ Y0)))) => ($true = (lessis @ X1 @ X0)))),
% 1.62/1.32 inference(fool_elimination,[status(thm)],[f13])).
% 1.62/1.32 thf(f13,plain,(
% 1.62/1.32 ! [X0 : nat,X1 : nat] : ((some @ (^[X2 : nat] : (diffprop @ (pl @ X0 @ n_1) @ X1 @ X2))) => (lessis @ X1 @ X0))),
% 1.62/1.32 inference(rectify,[status(thm)],[f3])).
% 1.62/1.32 thf(f3,axiom,(
% 1.62/1.32 ! [X1 : nat,X2 : nat] : ((some @ (^[X3 : nat] : (diffprop @ (pl @ X1 @ n_1) @ X2 @ X3))) => (lessis @ X2 @ X1))),
% 1.62/1.32 file('/export/starexec/sandbox2/tmp/tmp.9bvUQYicXS/DTF2THF_1727.p',satz26)).
% 1.62/1.32 thf(f19,plain,(
% 1.62/1.32 ( ! [X0 : nat,X1 : nat] : (($true != (lessis @ X1 @ X0)) | ($true = (moreis @ X0 @ X1))) )),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f17])).
% 1.62/1.32 thf(f17,plain,(
% 1.62/1.32 ! [X0 : nat,X1 : nat] : (($true = (moreis @ X0 @ X1)) | ($true != (lessis @ X1 @ X0)))),
% 1.62/1.32 inference(ennf_transformation,[status(thm)],[f12])).
% 1.62/1.32 thf(f12,plain,(
% 1.62/1.32 ! [X0 : nat,X1 : nat] : (($true = (lessis @ X1 @ X0)) => ($true = (moreis @ X0 @ X1)))),
% 1.62/1.32 inference(fool_elimination,[status(thm)],[f11])).
% 1.62/1.32 thf(f11,plain,(
% 1.62/1.32 ! [X0 : nat,X1 : nat] : ((lessis @ X1 @ X0) => (moreis @ X0 @ X1))),
% 1.62/1.32 inference(rectify,[status(thm)],[f2])).
% 1.62/1.32 thf(f2,axiom,(
% 1.62/1.32 ! [X2 : nat,X1 : nat] : ((lessis @ X1 @ X2) => (moreis @ X2 @ X1))),
% 1.62/1.32 file('/export/starexec/sandbox2/tmp/tmp.9bvUQYicXS/DTF2THF_1727.p',satz14)).
% 1.62/1.32 thf(f21,plain,(
% 1.62/1.32 ((moreis @ y @ x) != $true)),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.32 thf(f15,plain,(
% 1.62/1.32 ((moreis @ y @ x) != $true)),
% 1.62/1.32 inference(flattening,[status(thm)],[f10])).
% 1.62/1.32 thf(f10,plain,(
% 1.62/1.32 ~((moreis @ y @ x) = $true)),
% 1.62/1.32 inference(fool_elimination,[status(thm)],[f9])).
% 1.62/1.32 thf(f9,plain,(
% 1.62/1.32 ~(moreis @ y @ x)),
% 1.62/1.32 inference(rectify,[status(thm)],[f5])).
% 1.62/1.32 thf(f5,negated_conjecture,(
% 1.62/1.32 ~(moreis @ y @ x)),
% 1.62/1.32 inference(negated_conjecture,[status(cth)],[f4])).
% 1.62/1.32 thf(f4,conjecture,(
% 1.62/1.32 (moreis @ y @ x)),
% 1.62/1.32 file('/export/starexec/sandbox2/tmp/tmp.9bvUQYicXS/DTF2THF_1727.p',satz26b)).
% 1.62/1.32 % SZS output end Proof for DTF2THF_1727
% 1.62/1.32 % (2018)------------------------------
% 1.62/1.32 % (2018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (2018)Termination reason: Refutation
% 1.62/1.32
% 1.62/1.32 % (2018)Memory used [KB]: 5500
% 1.62/1.32 % (2018)Time elapsed: 0.005 s
% 1.62/1.32 % (2018)Instructions burned: 2 (million)
% 1.62/1.32 % (2018)------------------------------
% 1.62/1.32 % (2018)------------------------------
% 1.62/1.32 % (2015)Success in time 0.019 s
%------------------------------------------------------------------------------