%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM690^1 : 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 : n027.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 09:24:17 AM UTC 2026
% Result : Theorem 1.66s 1.32s
% Output : Refutation 1.66s
% 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 : 280 ( 22 ~; 15 |; 0 &; 234 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 64 ( 22 ^; 42 !; 0 ?; 64 :)
% 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,
some: ( nat > $o ) > $o ).
thf(func_def_6,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_8,type,
lessis: nat > nat > $o ).
thf(func_def_9,type,
pl: nat > nat > nat ).
thf(func_def_10,type,
moreis: nat > nat > $o ).
thf(func_def_11,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,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)],[f27,f35]) ).
thf(f35,plain,
( $true
= ( some @ ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( $true
= ( some @ ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) ) ) ) ),
inference(superposition,[status(thm)],[f33,f31]) ).
thf(f31,plain,
( ( moreis @ u @ z )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( moreis @ u @ z )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f24,f23]) ).
thf(f23,plain,
( ( lessis @ z @ u )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( lessis @ z @ u )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
lessis @ z @ u,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
lessis @ z @ u,
file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',k) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( lessis @ X0 @ X1 ) )
| ( ( moreis @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( lessis @ X0 @ X1 ) )
| ( ( moreis @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X0 @ X1 ) )
=> ( ( moreis @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: nat,X2: nat] :
( ( lessis @ X1 @ X2 )
=> ( moreis @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',satz14) ).
thf(f33,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( moreis @ X0 @ X1 ) )
| ( $true
= ( some @ ( diffprop @ ( pl @ y @ X0 ) @ ( pl @ x @ X1 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( moreis @ X0 @ X1 ) )
| ( $true != $true )
| ( $true
= ( some @ ( diffprop @ ( pl @ y @ X0 ) @ ( pl @ x @ X1 ) ) ) ) ),
inference(superposition,[status(thm)],[f28,f29]) ).
thf(f29,plain,
( $true
= ( some @ ( diffprop @ y @ x ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ y @ x @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ y @ x @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( some
@ ^ [X0: nat] : ( diffprop @ y @ x @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ y @ x @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',l) ).
thf(f28,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ X3 @ X2 ) )
!= $true )
| ( $true
= ( some @ ( diffprop @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X0 ) ) ) )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X3 @ X2 @ Y0 ) )
!= $true )
| ( ( moreis @ X1 @ X0 )
!= $true )
| ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X0 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X0 ) @ Y0 ) ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X3 @ X2 @ Y0 ) )
!= $true )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X0 ) @ Y0 ) ) )
| ( ( moreis @ X1 @ X0 )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X3 @ X2 @ Y0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X3 @ X2 @ Y0 ) )
= $true )
=> ( ( ( moreis @ X1 @ X0 )
= $true )
=> ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X0 ) @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( some
@ ^ [X4: nat] : ( diffprop @ X3 @ X2 @ X4 ) )
=> ( ( moreis @ X1 @ X0 )
=> ( some
@ ^ [X5: nat] : ( diffprop @ ( pl @ X3 @ X1 ) @ ( pl @ X2 @ X0 ) @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X4: nat,X3: nat,X2: nat,X1: nat] :
( ( some
@ ^ [X4: nat] : ( diffprop @ X1 @ X2 @ X4 ) )
=> ( ( moreis @ X3 @ X4 )
=> ( some
@ ^ [X5: nat] : ( diffprop @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',satz22b) ).
thf(f27,plain,
( $true
!= ( some @ ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Y0 ) )
!= $true ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Y0 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',satz22d) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM690^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 11:11:22 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
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : NUM690^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Number Theory
% 0.30/0.46 % Problem : Landau theorem 22d
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : some (lambda v.diffprop (pl y u) (pl x z) v)
% 0.30/0.46
% 0.30/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : satz22d [Lan30]
% 0.30/0.46 % : satz35d [Lan30]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % : Without extensionality : Theorem
% 0.30/0.46 % Rating : 0.00 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 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
% 0.30/0.46 % Syntax : Number of formulae : 15 ( 1 unt; 10 typ; 0 def)
% 0.30/0.46 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 5 ( 2 avg)
% 0.30/0.46 % Number of connectives : 35 ( 0 ~; 0 |; 0 &; 32 @)
% 0.30/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 14 ( 7 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 9 ( 9 usr; 4 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(nat_type,type,
% 0.30/0.46 nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(x,type,
% 0.30/0.46 x: nat ).
% 0.30/0.46
% 0.30/0.46 thf(y,type,
% 0.30/0.46 y: nat ).
% 0.30/0.46
% 0.30/0.46 thf(z,type,
% 0.30/0.46 z: nat ).
% 0.30/0.46
% 0.30/0.46 thf(u,type,
% 0.30/0.46 u: nat ).
% 0.30/0.46
% 0.30/0.46 thf(some,type,
% 0.30/0.46 some: ( nat > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(diffprop,type,
% 0.30/0.46 diffprop: nat > nat > nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(l,axiom,
% 0.30/0.46 ( some
% 0.30/0.46 @ ^ [Xv: nat] : ( diffprop @ y @ x @ Xv ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(lessis,type,
% 0.30/0.46 lessis: nat > nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(k,axiom,
% 0.30/0.46 lessis @ z @ u ).
% 0.30/0.46
% 0.30/0.46 thf(pl,type,
% 0.30/0.46 pl: nat > nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(moreis,type,
% 0.30/0.46 moreis: nat > nat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(satz22b,axiom,
% 0.30/0.46 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.30/0.46 ( ( some
% 0.30/0.46 @ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
% 0.30/0.46 => ( ( moreis @ Xz @ Xu )
% 0.30/0.46 => ( some
% 0.30/0.46 @ ^ [Xu_0: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) @ Xu_0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(satz14,axiom,
% 0.30/0.46 ! [Xx: nat,Xy: nat] :
% 0.30/0.46 ( ( lessis @ Xx @ Xy )
% 0.30/0.46 => ( moreis @ Xy @ Xx ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(satz22d,conjecture,
% 0.30/0.46 ( some
% 0.30/0.46 @ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.47/1.29 ---- Embedded in THF ---
% 1.47/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.29 %%% Generated on Tue Feb 24 11:11:23 EST 2026
% 1.47/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.29 %%% Logic specification used:
% 1.47/1.29 %%% thf(spec, logic, $$dhol).
% 1.47/1.29
% 1.47/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2DTF17386.p
% See solution above
% 1.47/1.29 ------------------------
% 1.66/1.30 ---- Cleaned THF ---
% 1.66/1.30 thf(nat_type,type,
% 1.66/1.30 nat: $tType ).
% 1.66/1.30
% 1.66/1.30 thf(x,type,
% 1.66/1.30 x: nat ).
% 1.66/1.30
% 1.66/1.30 thf(y,type,
% 1.66/1.30 y: nat ).
% 1.66/1.30
% 1.66/1.30 thf(z,type,
% 1.66/1.30 z: nat ).
% 1.66/1.30
% 1.66/1.30 thf(u,type,
% 1.66/1.30 u: nat ).
% 1.66/1.30
% 1.66/1.30 thf(some,type,
% 1.66/1.30 some: ( nat > $o ) > $o ).
% 1.66/1.30
% 1.66/1.30 thf(diffprop,type,
% 1.66/1.30 diffprop: nat > nat > nat > $o ).
% 1.66/1.30
% 1.66/1.30 thf(l,axiom,
% 1.66/1.30 ( some
% 1.66/1.30 @ ^ [Xv: nat] : ( diffprop @ y @ x @ Xv ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(lessis,type,
% 1.66/1.30 lessis: nat > nat > $o ).
% 1.66/1.30
% 1.66/1.30 thf(k,axiom,
% 1.66/1.30 lessis @ z @ u ).
% 1.66/1.30
% 1.66/1.30 thf(pl,type,
% 1.66/1.30 pl: nat > nat > nat ).
% 1.66/1.30
% 1.66/1.30 thf(moreis,type,
% 1.66/1.30 moreis: nat > nat > $o ).
% 1.66/1.30
% 1.66/1.30 thf(satz22b,axiom,
% 1.66/1.30 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 1.66/1.30 ( ( some
% 1.66/1.30 @ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
% 1.66/1.30 => ( ( moreis @ Xz @ Xu )
% 1.66/1.30 => ( some
% 1.66/1.30 @ ^ [Xu_0: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) @ Xu_0 ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(satz14,axiom,
% 1.66/1.30 ! [Xx: nat,Xy: nat] :
% 1.66/1.30 ( ( lessis @ Xx @ Xy )
% 1.66/1.30 => ( moreis @ Xy @ Xx ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(satz22d,conjecture,
% 1.66/1.30 ( some
% 1.66/1.30 @ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) ) ).
% 1.66/1.30 ------------------------
% 1.66/1.32 % (17666)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_17386 for (2999ds/2Mi)
% 1.66/1.32 % (17666)Instruction limit reached!
% 1.66/1.32 % (17666)------------------------------
% 1.66/1.32 % (17666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (17666)Termination reason: Unknown
% 1.66/1.32 % (17666)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (17666)Memory used [KB]: 895
% 1.66/1.32 % (17666)Time elapsed: 0.002 s
% 1.66/1.32 % (17666)Instructions burned: 2 (million)
% 1.66/1.32 % (17666)------------------------------
% 1.66/1.32 % (17666)------------------------------
% 1.66/1.32 % (17664)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_17386 for (2999ds/27Mi)
% 1.66/1.32 % (17664)First to succeed.
% 1.66/1.32 % (17664)Refutation found. Thanks to Tanya!
% 1.66/1.32 % SZS status Theorem for DTF2THF_17386
% 1.66/1.32 % SZS output start Proof for DTF2THF_17386
% 1.66/1.32 thf(type_def_5, type, nat: $tType).
% 1.66/1.32 thf(func_def_0, type, nat: $tType).
% 1.66/1.32 thf(func_def_1, type, x: nat).
% 1.66/1.32 thf(func_def_2, type, y: nat).
% 1.66/1.32 thf(func_def_3, type, z: nat).
% 1.66/1.32 thf(func_def_4, type, u: nat).
% 1.66/1.32 thf(func_def_5, type, some: (nat > $o) > $o).
% 1.66/1.32 thf(func_def_6, type, diffprop: nat > nat > nat > $o).
% 1.66/1.32 thf(func_def_8, type, lessis: nat > nat > $o).
% 1.66/1.32 thf(func_def_9, type, pl: nat > nat > nat).
% 1.66/1.32 thf(func_def_10, type, moreis: nat > nat > $o).
% 1.66/1.32 thf(func_def_11, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.66/1.32 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.66/1.32 thf(f39,plain,(
% 1.66/1.32 $false),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.66/1.32 thf(f37,plain,(
% 1.66/1.32 ($true != $true)),
% 1.66/1.32 inference(superposition,[status(thm)],[f27,f35])).
% 1.66/1.32 thf(f35,plain,(
% 1.66/1.32 ($true = (some @ (diffprop @ (pl @ y @ u) @ (pl @ x @ z))))),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.66/1.32 thf(f34,plain,(
% 1.66/1.32 ($true != $true) | ($true = (some @ (diffprop @ (pl @ y @ u) @ (pl @ x @ z))))),
% 1.66/1.32 inference(superposition,[status(thm)],[f33,f31])).
% 1.66/1.32 thf(f31,plain,(
% 1.66/1.32 ((moreis @ u @ z) = $true)),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.66/1.32 thf(f30,plain,(
% 1.66/1.32 ((moreis @ u @ z) = $true) | ($true != $true)),
% 1.66/1.32 inference(superposition,[status(thm)],[f24,f23])).
% 1.66/1.32 thf(f23,plain,(
% 1.66/1.32 ((lessis @ z @ u) = $true)),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.32 thf(f9,plain,(
% 1.66/1.32 ((lessis @ z @ u) = $true)),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f8])).
% 1.66/1.32 thf(f8,plain,(
% 1.66/1.32 (lessis @ z @ u)),
% 1.66/1.32 inference(rectify,[status(thm)],[f2])).
% 1.66/1.32 thf(f2,axiom,(
% 1.66/1.32 (lessis @ z @ u)),
% 1.66/1.32 file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',k)).
% 1.66/1.32 thf(f24,plain,(
% 1.66/1.32 ( ! [X0 : nat,X1 : nat] : (($true != (lessis @ X0 @ X1)) | ((moreis @ X1 @ X0) = $true)) )),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f19])).
% 1.66/1.32 thf(f19,plain,(
% 1.66/1.32 ! [X0 : nat,X1 : nat] : (($true != (lessis @ X0 @ X1)) | ((moreis @ X1 @ X0) = $true))),
% 1.66/1.32 inference(ennf_transformation,[status(thm)],[f15])).
% 1.66/1.32 thf(f15,plain,(
% 1.66/1.32 ! [X0 : nat,X1 : nat] : (($true = (lessis @ X0 @ X1)) => ((moreis @ X1 @ X0) = $true))),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f14])).
% 1.66/1.32 thf(f14,plain,(
% 1.66/1.32 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => (moreis @ X1 @ X0))),
% 1.66/1.32 inference(rectify,[status(thm)],[f4])).
% 1.66/1.32 thf(f4,axiom,(
% 1.66/1.32 ! [X1 : nat,X2 : nat] : ((lessis @ X1 @ X2) => (moreis @ X2 @ X1))),
% 1.66/1.32 file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',satz14)).
% 1.66/1.32 thf(f33,plain,(
% 1.66/1.32 ( ! [X0 : nat,X1 : nat] : (($true != (moreis @ X0 @ X1)) | ($true = (some @ (diffprop @ (pl @ y @ X0) @ (pl @ x @ X1))))) )),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.66/1.32 thf(f32,plain,(
% 1.66/1.32 ( ! [X0 : nat,X1 : nat] : (($true != (moreis @ X0 @ X1)) | ($true != $true) | ($true = (some @ (diffprop @ (pl @ y @ X0) @ (pl @ x @ X1))))) )),
% 1.66/1.32 inference(superposition,[status(thm)],[f28,f29])).
% 1.66/1.32 thf(f29,plain,(
% 1.66/1.32 ($true = (some @ (diffprop @ y @ x)))),
% 1.66/1.32 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.66/1.32 thf(f22,plain,(
% 1.66/1.32 ($true = (some @ (^[Y0 : nat]: (diffprop @ y @ x @ Y0))))),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.32 thf(f13,plain,(
% 1.66/1.32 ($true = (some @ (^[Y0 : nat]: (diffprop @ y @ x @ Y0))))),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f12])).
% 1.66/1.32 thf(f12,plain,(
% 1.66/1.32 (some @ (^[X0 : nat] : (diffprop @ y @ x @ X0)))),
% 1.66/1.32 inference(rectify,[status(thm)],[f1])).
% 1.66/1.32 thf(f1,axiom,(
% 1.66/1.32 (some @ (^[X0 : nat] : (diffprop @ y @ x @ X0)))),
% 1.66/1.32 file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',l)).
% 1.66/1.32 thf(f28,plain,(
% 1.66/1.32 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (((some @ (diffprop @ X3 @ X2)) != $true) | ($true = (some @ (diffprop @ (pl @ X3 @ X1) @ (pl @ X2 @ X0)))) | ((moreis @ X1 @ X0) != $true)) )),
% 1.66/1.32 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.66/1.32 thf(f26,plain,(
% 1.66/1.32 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X3 @ X2 @ Y0))) != $true) | ((moreis @ X1 @ X0) != $true) | ($true = (some @ (^[Y0 : nat]: (diffprop @ (pl @ X3 @ X1) @ (pl @ X2 @ X0) @ Y0))))) )),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.66/1.32 thf(f21,plain,(
% 1.66/1.32 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = (some @ (^[Y0 : nat]: (diffprop @ (pl @ X3 @ X1) @ (pl @ X2 @ X0) @ Y0)))) | ((some @ (^[Y0 : nat]: (diffprop @ X3 @ X2 @ Y0))) != $true) | ((moreis @ X1 @ X0) != $true))),
% 1.66/1.32 inference(flattening,[status(thm)],[f20])).
% 1.66/1.32 thf(f20,plain,(
% 1.66/1.32 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((($true = (some @ (^[Y0 : nat]: (diffprop @ (pl @ X3 @ X1) @ (pl @ X2 @ X0) @ Y0)))) | ((moreis @ X1 @ X0) != $true)) | ((some @ (^[Y0 : nat]: (diffprop @ X3 @ X2 @ Y0))) != $true))),
% 1.66/1.32 inference(ennf_transformation,[status(thm)],[f11])).
% 1.66/1.32 thf(f11,plain,(
% 1.66/1.32 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X3 @ X2 @ Y0))) = $true) => (((moreis @ X1 @ X0) = $true) => ($true = (some @ (^[Y0 : nat]: (diffprop @ (pl @ X3 @ X1) @ (pl @ X2 @ X0) @ Y0))))))),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.32 thf(f10,plain,(
% 1.66/1.32 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((some @ (^[X4 : nat] : (diffprop @ X3 @ X2 @ X4))) => ((moreis @ X1 @ X0) => (some @ (^[X5 : nat] : (diffprop @ (pl @ X3 @ X1) @ (pl @ X2 @ X0) @ X5)))))),
% 1.66/1.32 inference(rectify,[status(thm)],[f3])).
% 1.66/1.32 thf(f3,axiom,(
% 1.66/1.32 ! [X4 : nat,X3 : nat,X2 : nat,X1 : nat] : ((some @ (^[X4 : nat] : (diffprop @ X1 @ X2 @ X4))) => ((moreis @ X3 @ X4) => (some @ (^[X5 : nat] : (diffprop @ (pl @ X1 @ X3) @ (pl @ X2 @ X4) @ X5)))))),
% 1.66/1.32 file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',satz22b)).
% 1.66/1.32 thf(f27,plain,(
% 1.66/1.32 ($true != (some @ (diffprop @ (pl @ y @ u) @ (pl @ x @ z))))),
% 1.66/1.32 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.66/1.32 thf(f25,plain,(
% 1.66/1.32 ((some @ (^[Y0 : nat]: (diffprop @ (pl @ y @ u) @ (pl @ x @ z) @ Y0))) != $true)),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.32 thf(f18,plain,(
% 1.66/1.32 ((some @ (^[Y0 : nat]: (diffprop @ (pl @ y @ u) @ (pl @ x @ z) @ Y0))) != $true)),
% 1.66/1.32 inference(flattening,[status(thm)],[f17])).
% 1.66/1.32 thf(f17,plain,(
% 1.66/1.32 ~((some @ (^[Y0 : nat]: (diffprop @ (pl @ y @ u) @ (pl @ x @ z) @ Y0))) = $true)),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f16])).
% 1.66/1.32 thf(f16,plain,(
% 1.66/1.32 ~(some @ (^[X0 : nat] : (diffprop @ (pl @ y @ u) @ (pl @ x @ z) @ X0)))),
% 1.66/1.32 inference(rectify,[status(thm)],[f6])).
% 1.66/1.32 thf(f6,negated_conjecture,(
% 1.66/1.32 ~(some @ (^[X0 : nat] : (diffprop @ (pl @ y @ u) @ (pl @ x @ z) @ X0)))),
% 1.66/1.32 inference(negated_conjecture,[status(cth)],[f5])).
% 1.66/1.32 thf(f5,conjecture,(
% 1.66/1.32 (some @ (^[X0 : nat] : (diffprop @ (pl @ y @ u) @ (pl @ x @ z) @ X0)))),
% 1.66/1.32 file('/export/starexec/sandbox/tmp/tmp.4DX18WBxto/DTF2THF_17386.p',satz22d)).
% 1.66/1.32 % SZS output end Proof for DTF2THF_17386
% 1.66/1.32 % (17664)------------------------------
% 1.66/1.32 % (17664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (17664)Termination reason: Refutation
% 1.66/1.32
% 1.66/1.32 % (17664)Memory used [KB]: 5500
% 1.66/1.32 % (17664)Time elapsed: 0.004 s
% 1.66/1.32 % (17664)Instructions burned: 4 (million)
% 1.66/1.32 % (17664)------------------------------
% 1.66/1.32 % (17664)------------------------------
% 1.66/1.32 % (17661)Success in time 0.014 s
%------------------------------------------------------------------------------