%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM666^1 : 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 : n007.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 09:24:10 AM UTC 2026
% Result : Theorem 1.28s 1.15s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 174 ( 42 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 208 ( 22 ~; 15 |; 0 &; 162 @)
% ( 0 <=>; 9 =>; 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 : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 55 ( 22 ^; 33 !; 0 ?; 55 :)
% 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,
some: ( nat > $o ) > $o ).
thf(func_def_5,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_7,type,
moreis: nat > nat > $o ).
thf(func_def_8,type,
lessis: nat > nat > $o ).
thf(func_def_9,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f39,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
$true != $true,
inference(superposition,[status(thm)],[f29,f35]) ).
thf(f35,plain,
( $true
= ( some @ ( diffprop @ x @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( $true
= ( some @ ( diffprop @ x @ z ) ) ) ),
inference(superposition,[status(thm)],[f33,f31]) ).
thf(f31,plain,
( ( lessis @ z @ y )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( lessis @ z @ y )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f23,f22]) ).
thf(f22,plain,
( ( moreis @ y @ z )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( moreis @ y @ z )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
moreis @ y @ z,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
moreis @ y @ z,
file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',n) ).
thf(f23,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( moreis @ X1 @ X0 ) )
| ( $true
= ( lessis @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X0 @ X1 ) )
| ( $true
!= ( moreis @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( moreis @ X1 @ X0 ) )
=> ( $true
= ( lessis @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: nat,X1: nat] :
( ( moreis @ X1 @ X0 )
=> ( lessis @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: nat,X1: nat] :
( ( moreis @ X1 @ X2 )
=> ( lessis @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',satz13) ).
thf(f33,plain,
! [X0: nat] :
( ( ( lessis @ X0 @ y )
!= $true )
| ( $true
= ( some @ ( diffprop @ x @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: nat] :
( ( ( lessis @ X0 @ y )
!= $true )
| ( $true
= ( some @ ( diffprop @ x @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f27,f28]) ).
thf(f28,plain,
( ( some @ ( diffprop @ x @ y ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( some
@ ^ [X0: nat] : ( diffprop @ x @ y @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ x @ y @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',m) ).
thf(f27,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
!= ( some @ ( diffprop @ X2 @ X1 ) ) )
| ( ( some @ ( diffprop @ X2 @ X0 ) )
= $true )
| ( $true
!= ( lessis @ X0 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) ) )
| ( $true
!= ( lessis @ X0 @ X1 ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
!= $true )
| ( $true
!= ( lessis @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
!= $true )
| ( $true
!= ( lessis @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( lessis @ X0 @ X1 ) )
=> ( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
= $true )
=> ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( lessis @ X0 @ X1 )
=> ( ( some
@ ^ [X3: nat] : ( diffprop @ X2 @ X1 @ X3 ) )
=> ( some
@ ^ [X4: nat] : ( diffprop @ X2 @ X0 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( lessis @ X1 @ X2 )
=> ( ( some
@ ^ [X4: nat] : ( diffprop @ X3 @ X2 @ X4 ) )
=> ( some
@ ^ [X4: nat] : ( diffprop @ X3 @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',satz16a) ).
thf(f29,plain,
( $true
!= ( some @ ( diffprop @ x @ z ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ z @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ z @ Y0 ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ z @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ x @ z @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( some
@ ^ [X0: nat] : ( diffprop @ x @ z @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( some
@ ^ [X0: nat] : ( diffprop @ x @ z @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',satz16d) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM666^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 11:09:23 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : NUM666^1 : TPTP v9.2.1. Released v3.7.0.
% 0.15/0.42 % Domain : Number Theory
% 0.15/0.42 % Problem : Landau theorem 16d
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English : some (lambda u.diffprop x z u)
% 0.15/0.42
% 0.15/0.42 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.15/0.42 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.15/0.42 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bro09]
% 0.15/0.42 % Names : satz16d [Lan30]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % : Without extensionality : Theorem
% 0.15/0.42 % 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 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.00 v4.0.0, 0.33 v3.7.0
% 0.15/0.42 % Syntax : Number of formulae : 13 ( 1 unt; 8 typ; 0 def)
% 0.15/0.42 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 5 ( 2 avg)
% 0.15/0.42 % Number of connectives : 27 ( 0 ~; 0 |; 0 &; 24 @)
% 0.15/0.42 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 11 ( 6 avg)
% 0.15/0.42 % Number of types : 2 ( 1 usr)
% 0.15/0.42 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 7 ( 7 usr; 3 con; 0-3 aty)
% 0.15/0.42 % Number of variables : 9 ( 4 ^; 5 !; 0 ?; 9 :)
% 0.15/0.42 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.42
% 0.15/0.42 % Comments :
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(nat_type,type,
% 0.15/0.42 nat: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(x,type,
% 0.15/0.42 x: nat ).
% 0.15/0.42
% 0.15/0.42 thf(y,type,
% 0.15/0.42 y: nat ).
% 0.15/0.42
% 0.15/0.42 thf(z,type,
% 0.15/0.42 z: nat ).
% 0.15/0.42
% 0.15/0.42 thf(some,type,
% 0.15/0.42 some: ( nat > $o ) > $o ).
% 0.15/0.42
% 0.15/0.42 thf(diffprop,type,
% 0.15/0.42 diffprop: nat > nat > nat > $o ).
% 0.15/0.42
% 0.15/0.42 thf(m,axiom,
% 0.15/0.42 ( some
% 0.15/0.42 @ ^ [Xu: nat] : ( diffprop @ x @ y @ Xu ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(moreis,type,
% 0.15/0.42 moreis: nat > nat > $o ).
% 0.15/0.42
% 0.15/0.42 thf(n,axiom,
% 0.15/0.42 moreis @ y @ z ).
% 0.15/0.42
% 0.15/0.42 thf(lessis,type,
% 0.15/0.42 lessis: nat > nat > $o ).
% 0.15/0.42
% 0.15/0.42 thf(satz16a,axiom,
% 0.15/0.42 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.15/0.42 ( ( lessis @ Xx @ Xy )
% 0.15/0.42 => ( ( some
% 0.15/0.42 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xy @ Xv ) )
% 0.15/0.42 => ( some
% 0.15/0.42 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(satz13,axiom,
% 0.15/0.42 ! [Xx: nat,Xy: nat] :
% 0.15/0.42 ( ( moreis @ Xx @ Xy )
% 0.15/0.42 => ( lessis @ Xy @ Xx ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(satz16d,conjecture,
% 0.15/0.42 ( some
% 0.15/0.42 @ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.28/1.13 ---- Embedded in THF ---
% 1.28/1.13 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.28/1.13 %%% Generated on Tue Feb 24 11:09:24 EST 2026
% 1.28/1.13 %%% using '$$dhol' embedding, version 1.3.0.
% 1.28/1.13 %%% Logic specification used:
% 1.28/1.13 %%% thf(spec, logic, $$dhol).
% 1.28/1.13
% 1.28/1.13 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2DTF29304.p
% See solution above
% 1.28/1.13 ------------------------
% 1.28/1.13 ---- Cleaned THF ---
% 1.28/1.13 thf(nat_type,type,
% 1.28/1.13 nat: $tType ).
% 1.28/1.13
% 1.28/1.13 thf(x,type,
% 1.28/1.13 x: nat ).
% 1.28/1.13
% 1.28/1.13 thf(y,type,
% 1.28/1.13 y: nat ).
% 1.28/1.13
% 1.28/1.13 thf(z,type,
% 1.28/1.13 z: nat ).
% 1.28/1.13
% 1.28/1.13 thf(some,type,
% 1.28/1.13 some: ( nat > $o ) > $o ).
% 1.28/1.13
% 1.28/1.13 thf(diffprop,type,
% 1.28/1.13 diffprop: nat > nat > nat > $o ).
% 1.28/1.13
% 1.28/1.13 thf(m,axiom,
% 1.28/1.13 ( some
% 1.28/1.13 @ ^ [Xu: nat] : ( diffprop @ x @ y @ Xu ) ) ).
% 1.28/1.13
% 1.28/1.13 thf(moreis,type,
% 1.28/1.13 moreis: nat > nat > $o ).
% 1.28/1.13
% 1.28/1.13 thf(n,axiom,
% 1.28/1.13 moreis @ y @ z ).
% 1.28/1.13
% 1.28/1.13 thf(lessis,type,
% 1.28/1.13 lessis: nat > nat > $o ).
% 1.28/1.13
% 1.28/1.13 thf(satz16a,axiom,
% 1.28/1.13 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.28/1.13 ( ( lessis @ Xx @ Xy )
% 1.28/1.13 => ( ( some
% 1.28/1.13 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xy @ Xv ) )
% 1.28/1.13 => ( some
% 1.28/1.13 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) ).
% 1.28/1.13
% 1.28/1.13 thf(satz13,axiom,
% 1.28/1.13 ! [Xx: nat,Xy: nat] :
% 1.28/1.13 ( ( moreis @ Xx @ Xy )
% 1.28/1.13 => ( lessis @ Xy @ Xx ) ) ).
% 1.28/1.13
% 1.28/1.13 thf(satz16d,conjecture,
% 1.28/1.13 ( some
% 1.28/1.13 @ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ) ).
% 1.28/1.14 ------------------------
% 1.28/1.15 % (29456)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_29304 for (3000ds/275Mi)
% 1.28/1.15 % (29455)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_29304 for (3000ds/2Mi)
% 1.28/1.15 % (29451)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29304 for (3000ds/183Mi)
% 1.28/1.15 % (29454)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29304 for (3000ds/2Mi)
% 1.28/1.15 % (29457)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29304 for (3000ds/18Mi)
% 1.28/1.15 % (29453)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_29304 for (3000ds/27Mi)
% 1.28/1.15 % (29452)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_29304 for (3000ds/4Mi)
% 1.28/1.15 % (29454)Instruction limit reached!
% 1.28/1.15 % (29454)------------------------------
% 1.28/1.15 % (29454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.15 % (29454)Termination reason: Unknown
% 1.28/1.15 % (29454)Termination phase: Saturation
% 1.28/1.15
% 1.28/1.15 % (29454)Memory used [KB]: 5500
% 1.28/1.15 % (29454)Time elapsed: 0.003 s
% 1.28/1.15 % (29454)Instructions burned: 2 (million)
% 1.28/1.15 % (29454)------------------------------
% 1.28/1.15 % (29454)------------------------------
% 1.28/1.15 % (29456)Refutation not found, incomplete strategy
% 1.28/1.15 % (29456)------------------------------
% 1.28/1.15 % (29456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.15 % (29456)Termination reason: Refutation not found, incomplete strategy
% 1.28/1.15
% 1.28/1.15
% 1.28/1.15 % (29456)Memory used [KB]: 5500
% 1.28/1.15 % (29456)Time elapsed: 0.002 s
% 1.28/1.15 % (29456)Instructions burned: 1 (million)
% 1.28/1.15 % (29456)------------------------------
% 1.28/1.15 % (29456)------------------------------
% 1.28/1.15 % (29455)Instruction limit reached!
% 1.28/1.15 % (29455)------------------------------
% 1.28/1.15 % (29455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.15 % (29455)Termination reason: Unknown
% 1.28/1.15 % (29455)Termination phase: Saturation
% 1.28/1.15
% 1.28/1.15 % (29455)Memory used [KB]: 5500
% 1.28/1.15 % (29455)Time elapsed: 0.003 s
% 1.28/1.15 % (29455)Instructions burned: 3 (million)
% 1.28/1.15 % (29455)------------------------------
% 1.28/1.15 % (29455)------------------------------
% 1.28/1.15 % (29453)First to succeed.
% 1.28/1.15 % (29452)Instruction limit reached!
% 1.28/1.15 % (29452)------------------------------
% 1.28/1.15 % (29452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.15 % (29452)Termination reason: Unknown
% 1.28/1.15 % (29452)Termination phase: Saturation
% 1.28/1.15
% 1.28/1.15 % (29452)Memory used [KB]: 5500
% 1.28/1.15 % (29452)Time elapsed: 0.003 s
% 1.28/1.15 % (29452)Instructions burned: 5 (million)
% 1.28/1.15 % (29452)------------------------------
% 1.28/1.15 % (29452)------------------------------
% 1.28/1.15 % (29453)Refutation found. Thanks to Tanya!
% 1.28/1.15 % SZS status Theorem for DTF2THF_29304
% 1.28/1.15 % SZS output start Proof for DTF2THF_29304
% 1.28/1.15 thf(type_def_5, type, nat: $tType).
% 1.28/1.15 thf(func_def_0, type, nat: $tType).
% 1.28/1.15 thf(func_def_1, type, x: nat).
% 1.28/1.15 thf(func_def_2, type, y: nat).
% 1.28/1.15 thf(func_def_3, type, z: nat).
% 1.28/1.15 thf(func_def_4, type, some: (nat > $o) > $o).
% 1.28/1.15 thf(func_def_5, type, diffprop: nat > nat > nat > $o).
% 1.28/1.15 thf(func_def_7, type, moreis: nat > nat > $o).
% 1.28/1.15 thf(func_def_8, type, lessis: nat > nat > $o).
% 1.28/1.15 thf(func_def_9, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.28/1.15 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.28/1.15 thf(f39,plain,(
% 1.28/1.15 $false),
% 1.28/1.15 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.28/1.15 thf(f37,plain,(
% 1.28/1.15 ($true != $true)),
% 1.28/1.15 inference(superposition,[status(thm)],[f29,f35])).
% 1.28/1.15 thf(f35,plain,(
% 1.28/1.15 ($true = (some @ (diffprop @ x @ z)))),
% 1.28/1.15 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.28/1.15 thf(f34,plain,(
% 1.28/1.15 ($true != $true) | ($true = (some @ (diffprop @ x @ z)))),
% 1.28/1.15 inference(superposition,[status(thm)],[f33,f31])).
% 1.28/1.15 thf(f31,plain,(
% 1.28/1.15 ((lessis @ z @ y) = $true)),
% 1.28/1.15 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.28/1.15 thf(f30,plain,(
% 1.28/1.15 ((lessis @ z @ y) = $true) | ($true != $true)),
% 1.28/1.15 inference(superposition,[status(thm)],[f23,f22])).
% 1.28/1.15 thf(f22,plain,(
% 1.28/1.15 ((moreis @ y @ z) = $true)),
% 1.28/1.15 inference(cnf_transformation,[status(thm)],[f15])).
% 1.28/1.15 thf(f15,plain,(
% 1.28/1.15 ((moreis @ y @ z) = $true)),
% 1.28/1.15 inference(fool_elimination,[status(thm)],[f14])).
% 1.28/1.15 thf(f14,plain,(
% 1.28/1.15 (moreis @ y @ z)),
% 1.28/1.15 inference(rectify,[status(thm)],[f2])).
% 1.28/1.15 thf(f2,axiom,(
% 1.28/1.15 (moreis @ y @ z)),
% 1.28/1.15 file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',n)).
% 1.28/1.15 thf(f23,plain,(
% 1.28/1.15 ( ! [X0 : nat,X1 : nat] : (($true != (moreis @ X1 @ X0)) | ($true = (lessis @ X0 @ X1))) )),
% 1.28/1.15 inference(cnf_transformation,[status(thm)],[f21])).
% 1.28/1.15 thf(f21,plain,(
% 1.28/1.15 ! [X0 : nat,X1 : nat] : (($true = (lessis @ X0 @ X1)) | ($true != (moreis @ X1 @ X0)))),
% 1.28/1.15 inference(ennf_transformation,[status(thm)],[f9])).
% 1.28/1.15 thf(f9,plain,(
% 1.28/1.15 ! [X0 : nat,X1 : nat] : (($true = (moreis @ X1 @ X0)) => ($true = (lessis @ X0 @ X1)))),
% 1.28/1.15 inference(fool_elimination,[status(thm)],[f8])).
% 1.28/1.15 thf(f8,plain,(
% 1.28/1.15 ! [X0 : nat,X1 : nat] : ((moreis @ X1 @ X0) => (lessis @ X0 @ X1))),
% 1.28/1.15 inference(rectify,[status(thm)],[f4])).
% 1.28/1.15 thf(f4,axiom,(
% 1.28/1.15 ! [X2 : nat,X1 : nat] : ((moreis @ X1 @ X2) => (lessis @ X2 @ X1))),
% 1.28/1.15 file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',satz13)).
% 1.28/1.15 thf(f33,plain,(
% 1.28/1.15 ( ! [X0 : nat] : (((lessis @ X0 @ y) != $true) | ($true = (some @ (diffprop @ x @ X0)))) )),
% 1.28/1.15 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.28/1.15 thf(f32,plain,(
% 1.28/1.15 ( ! [X0 : nat] : (((lessis @ X0 @ y) != $true) | ($true = (some @ (diffprop @ x @ X0))) | ($true != $true)) )),
% 1.28/1.15 inference(superposition,[status(thm)],[f27,f28])).
% 1.28/1.15 thf(f28,plain,(
% 1.28/1.15 ((some @ (diffprop @ x @ y)) = $true)),
% 1.28/1.15 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.28/1.15 thf(f25,plain,(
% 1.28/1.15 ($true = (some @ (^[Y0 : nat]: (diffprop @ x @ y @ Y0))))),
% 1.28/1.15 inference(cnf_transformation,[status(thm)],[f13])).
% 1.28/1.15 thf(f13,plain,(
% 1.28/1.15 ($true = (some @ (^[Y0 : nat]: (diffprop @ x @ y @ Y0))))),
% 1.28/1.15 inference(fool_elimination,[status(thm)],[f12])).
% 1.28/1.15 thf(f12,plain,(
% 1.28/1.15 (some @ (^[X0 : nat] : (diffprop @ x @ y @ X0)))),
% 1.28/1.15 inference(rectify,[status(thm)],[f1])).
% 1.28/1.15 thf(f1,axiom,(
% 1.28/1.15 (some @ (^[X0 : nat] : (diffprop @ x @ y @ X0)))),
% 1.28/1.15 file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',m)).
% 1.28/1.15 thf(f27,plain,(
% 1.28/1.15 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != (some @ (diffprop @ X2 @ X1))) | ((some @ (diffprop @ X2 @ X0)) = $true) | ($true != (lessis @ X0 @ X1))) )),
% 1.28/1.15 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.28/1.15 thf(f24,plain,(
% 1.28/1.15 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (some @ (^[Y0 : nat]: (diffprop @ X2 @ X0 @ Y0)))) | ($true != (lessis @ X0 @ X1)) | ((some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))) != $true)) )),
% 1.28/1.15 inference(cnf_transformation,[status(thm)],[f20])).
% 1.28/1.15 thf(f20,plain,(
% 1.28/1.15 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (some @ (^[Y0 : nat]: (diffprop @ X2 @ X0 @ Y0)))) | ((some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))) != $true) | ($true != (lessis @ X0 @ X1)))),
% 1.28/1.15 inference(flattening,[status(thm)],[f19])).
% 1.28/1.15 thf(f19,plain,(
% 1.28/1.15 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = (some @ (^[Y0 : nat]: (diffprop @ X2 @ X0 @ Y0)))) | ((some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))) != $true)) | ($true != (lessis @ X0 @ X1)))),
% 1.28/1.15 inference(ennf_transformation,[status(thm)],[f17])).
% 1.28/1.15 thf(f17,plain,(
% 1.28/1.15 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (lessis @ X0 @ X1)) => (((some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))) = $true) => ($true = (some @ (^[Y0 : nat]: (diffprop @ X2 @ X0 @ Y0))))))),
% 1.28/1.15 inference(fool_elimination,[status(thm)],[f16])).
% 1.28/1.15 thf(f16,plain,(
% 1.28/1.15 ! [X0 : nat,X1 : nat,X2 : nat] : ((lessis @ X0 @ X1) => ((some @ (^[X3 : nat] : (diffprop @ X2 @ X1 @ X3))) => (some @ (^[X4 : nat] : (diffprop @ X2 @ X0 @ X4)))))),
% 1.28/1.15 inference(rectify,[status(thm)],[f3])).
% 1.28/1.15 thf(f3,axiom,(
% 1.28/1.15 ! [X1 : nat,X2 : nat,X3 : nat] : ((lessis @ X1 @ X2) => ((some @ (^[X4 : nat] : (diffprop @ X3 @ X2 @ X4))) => (some @ (^[X4 : nat] : (diffprop @ X3 @ X1 @ X4)))))),
% 1.28/1.15 file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',satz16a)).
% 1.28/1.15 thf(f29,plain,(
% 1.28/1.15 ($true != (some @ (diffprop @ x @ z)))),
% 1.28/1.15 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.28/1.15 thf(f26,plain,(
% 1.28/1.15 ($true != (some @ (^[Y0 : nat]: (diffprop @ x @ z @ Y0))))),
% 1.28/1.15 inference(cnf_transformation,[status(thm)],[f18])).
% 1.28/1.15 thf(f18,plain,(
% 1.28/1.15 ($true != (some @ (^[Y0 : nat]: (diffprop @ x @ z @ Y0))))),
% 1.28/1.15 inference(flattening,[status(thm)],[f11])).
% 1.28/1.15 thf(f11,plain,(
% 1.28/1.15 ~($true = (some @ (^[Y0 : nat]: (diffprop @ x @ z @ Y0))))),
% 1.28/1.15 inference(fool_elimination,[status(thm)],[f10])).
% 1.28/1.15 thf(f10,plain,(
% 1.28/1.15 ~(some @ (^[X0 : nat] : (diffprop @ x @ z @ X0)))),
% 1.28/1.15 inference(rectify,[status(thm)],[f6])).
% 1.28/1.15 thf(f6,negated_conjecture,(
% 1.28/1.15 ~(some @ (^[X0 : nat] : (diffprop @ x @ z @ X0)))),
% 1.28/1.15 inference(negated_conjecture,[status(cth)],[f5])).
% 1.28/1.15 thf(f5,conjecture,(
% 1.28/1.15 (some @ (^[X0 : nat] : (diffprop @ x @ z @ X0)))),
% 1.28/1.15 file('/export/starexec/sandbox2/tmp/tmp.R9WTvIdGuD/DTF2THF_29304.p',satz16d)).
% 1.28/1.15 % SZS output end Proof for DTF2THF_29304
% 1.28/1.15 % (29453)------------------------------
% 1.28/1.15 % (29453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.15 % (29453)Termination reason: Refutation
% 1.28/1.15
% 1.28/1.15 % (29453)Memory used [KB]: 5500
% 1.28/1.15 % (29453)Time elapsed: 0.003 s
% 1.28/1.15 % (29453)Instructions burned: 2 (million)
% 1.28/1.15 % (29453)------------------------------
% 1.28/1.15 % (29453)------------------------------
% 1.28/1.15 % (29449)Success in time 0.012 s
%------------------------------------------------------------------------------