%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM698^1 : 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 : n010.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 09:24:20 AM UTC 2026
% Result : Theorem 1.49s 1.24s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 201 ( 52 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 297 ( 28 ~; 33 |; 0 &; 228 @)
% ( 2 <=>; 6 =>; 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 : 15 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 41 ( 9 ^; 32 !; 0 ?; 41 :)
% 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_6,type,
lessis: nat > nat > $o ).
thf(func_def_7,type,
pl: nat > nat > nat ).
thf(func_def_8,type,
n_1: nat ).
thf(func_def_9,type,
moreis: nat > nat > $o ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK2: nat > nat > nat ).
thf(f63,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f39,f43,f62]) ).
thf(f62,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f61]) ).
thf(f61,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f52,f37]) ).
thf(f37,plain,
( ( $true
!= ( moreis @ x @ ( pl @ y @ n_1 ) ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl0_2
<=> ( $true
= ( moreis @ x @ ( pl @ y @ n_1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f52,plain,
( ( $true
= ( moreis @ x @ ( pl @ y @ n_1 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true = $false )
| ( $true
= ( moreis @ x @ ( pl @ y @ n_1 ) ) )
| ~ spl0_1 ),
inference(duplicate_literal_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true = $false )
| ( $true = $false )
| ( $true
= ( moreis @ x @ ( pl @ y @ n_1 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f28,f34]) ).
thf(f34,plain,
( ( $true
= ( diffprop @ x @ y @ ( sK2 @ y @ x ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl0_1
<=> ( $true
= ( diffprop @ x @ y @ ( sK2 @ y @ x ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f28,plain,
! [X0: nat,X1: nat] :
( ( ( diffprop @ x @ y @ ( sK2 @ X1 @ X0 ) )
= $false )
| ( $true
= ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) )
| ( ( diffprop @ X0 @ X1 @ ( sK2 @ X1 @ X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: nat,X1: nat] :
( ( ( diffprop @ x @ y @ ( sK2 @ X1 @ X0 ) )
!= ( diffprop @ X0 @ X1 @ ( sK2 @ X1 @ X0 ) ) )
| ( $true
= ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) ) ),
inference(negative_extensionality,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( ( diffprop @ x @ y )
!= ( diffprop @ X0 @ X1 ) )
| ( $true
= ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) )
| ( ( diffprop @ x @ y )
!= ( diffprop @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f23,f22]) ).
thf(f22,plain,
( ( some @ ( diffprop @ x @ y ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,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/sandbox/tmp/tmp.4j749jRKDo/DTF2THF_19930.p',l) ).
thf(f23,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( some @ ( diffprop @ X0 @ X1 ) ) )
| ( $true
= ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) ) )
| ( $true
= ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) ) )
=> ( $true
= ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: nat,X1: nat] :
( ( some
@ ^ [X2: nat] : ( diffprop @ X0 @ X1 @ X2 ) )
=> ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: nat,X1: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X2 @ X1 @ X3 ) )
=> ( moreis @ X2 @ ( pl @ X1 @ n_1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4j749jRKDo/DTF2THF_19930.p',satz25) ).
thf(f43,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f41,f18]) ).
thf(f18,plain,
( ( lessis @ ( pl @ y @ n_1 ) @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( lessis @ ( pl @ y @ n_1 ) @ x )
!= $true ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( lessis @ ( pl @ y @ n_1 ) @ x )
!= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( lessis @ ( pl @ y @ n_1 ) @ x ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( lessis @ ( pl @ y @ n_1 ) @ x ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
lessis @ ( pl @ y @ n_1 ) @ x,
file('/export/starexec/sandbox/tmp/tmp.4j749jRKDo/DTF2THF_19930.p',satz25b) ).
thf(f41,plain,
( ( ( lessis @ ( pl @ y @ n_1 ) @ x )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( lessis @ ( pl @ y @ n_1 ) @ x )
= $true )
| ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f21,f38]) ).
thf(f38,plain,
( ( $true
= ( moreis @ x @ ( pl @ y @ n_1 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X1 @ X0 )
!= $true )
| ( ( lessis @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X1 @ X0 )
!= $true )
| ( ( lessis @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X1 @ X0 )
= $true )
=> ( ( lessis @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( moreis @ X1 @ X0 )
=> ( lessis @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: nat,X1: nat] :
( ( moreis @ X1 @ X2 )
=> ( lessis @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.4j749jRKDo/DTF2THF_19930.p',satz13) ).
thf(f39,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f30,f36,f32]) ).
thf(f30,plain,
( ( $true
= ( moreis @ x @ ( pl @ y @ n_1 ) ) )
| ( $true
= ( diffprop @ x @ y @ ( sK2 @ y @ x ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true
= ( moreis @ x @ ( pl @ y @ n_1 ) ) )
| ( $true != $true )
| ( $true
= ( diffprop @ x @ y @ ( sK2 @ y @ x ) ) ) ),
inference(equality_factoring,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( diffprop @ x @ y @ ( sK2 @ X1 @ X0 ) ) )
| ( $true
= ( diffprop @ X0 @ X1 @ ( sK2 @ X1 @ X0 ) ) )
| ( $true
= ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM698^1 : 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
% 0.16/0.34 % Computer : n010.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 11:11:03 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : NUM698^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Number Theory
% 0.29/0.46 % Problem : Landau theorem 25b
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : lessis (pl y n_1) x
% 0.29/0.46
% 0.29/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.29/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : satz25b [Lan30]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % : Without extensionality : Theorem
% 0.29/0.46 % 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
% 0.29/0.46 % Syntax : Number of formulae : 13 ( 1 unt; 9 typ; 0 def)
% 0.29/0.46 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 3 ( 2 avg)
% 0.29/0.46 % Number of connectives : 22 ( 0 ~; 0 |; 0 &; 20 @)
% 0.29/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 9 ( 7 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 8 ( 8 usr; 3 con; 0-3 aty)
% 0.29/0.46 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(nat_type,type,
% 0.29/0.46 nat: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(x,type,
% 0.29/0.46 x: nat ).
% 0.29/0.46
% 0.29/0.46 thf(y,type,
% 0.29/0.46 y: nat ).
% 0.29/0.46
% 0.29/0.46 thf(some,type,
% 0.29/0.46 some: ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(diffprop,type,
% 0.29/0.46 diffprop: nat > nat > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(l,axiom,
% 0.29/0.46 ( some
% 0.29/0.46 @ ^ [Xv: nat] : ( diffprop @ x @ y @ Xv ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lessis,type,
% 0.29/0.46 lessis: nat > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(pl,type,
% 0.29/0.46 pl: nat > nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(n_1,type,
% 0.29/0.46 n_1: nat ).
% 0.29/0.46
% 0.29/0.46 thf(moreis,type,
% 0.29/0.46 moreis: nat > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(satz13,axiom,
% 0.29/0.46 ! [Xx: nat,Xy: nat] :
% 0.29/0.46 ( ( moreis @ Xx @ Xy )
% 0.29/0.46 => ( lessis @ Xy @ Xx ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz25,axiom,
% 0.29/0.46 ! [Xx: nat,Xy: nat] :
% 0.29/0.46 ( ( some
% 0.29/0.46 @ ^ [Xu: nat] : ( diffprop @ Xy @ Xx @ Xu ) )
% 0.29/0.46 => ( moreis @ Xy @ ( pl @ Xx @ n_1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz25b,conjecture,
% 0.29/0.46 lessis @ ( pl @ y @ n_1 ) @ x ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.49/1.21 ---- Embedded in THF ---
% 1.49/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.22 %%% Generated on Tue Feb 24 11:11:04 EST 2026
% 1.49/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.22 %%% Logic specification used:
% 1.49/1.22 %%% thf(spec, logic, $$dhol).
% 1.49/1.22
% 1.49/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4j749jRKDo/DTF2DTF19930.p
% See solution above
% 1.49/1.22 ------------------------
% 1.49/1.22 ---- Cleaned THF ---
% 1.49/1.23 thf(nat_type,type,
% 1.49/1.23 nat: $tType ).
% 1.49/1.23
% 1.49/1.23 thf(x,type,
% 1.49/1.23 x: nat ).
% 1.49/1.23
% 1.49/1.23 thf(y,type,
% 1.49/1.23 y: nat ).
% 1.49/1.23
% 1.49/1.23 thf(some,type,
% 1.49/1.23 some: ( nat > $o ) > $o ).
% 1.49/1.23
% 1.49/1.23 thf(diffprop,type,
% 1.49/1.23 diffprop: nat > nat > nat > $o ).
% 1.49/1.23
% 1.49/1.23 thf(l,axiom,
% 1.49/1.23 ( some
% 1.49/1.23 @ ^ [Xv: nat] : ( diffprop @ x @ y @ Xv ) ) ).
% 1.49/1.23
% 1.49/1.23 thf(lessis,type,
% 1.49/1.23 lessis: nat > nat > $o ).
% 1.49/1.23
% 1.49/1.23 thf(pl,type,
% 1.49/1.23 pl: nat > nat > nat ).
% 1.49/1.23
% 1.49/1.23 thf(n_1,type,
% 1.49/1.23 n_1: nat ).
% 1.49/1.23
% 1.49/1.23 thf(moreis,type,
% 1.49/1.23 moreis: nat > nat > $o ).
% 1.49/1.23
% 1.49/1.23 thf(satz13,axiom,
% 1.49/1.23 ! [Xx: nat,Xy: nat] :
% 1.49/1.23 ( ( moreis @ Xx @ Xy )
% 1.49/1.23 => ( lessis @ Xy @ Xx ) ) ).
% 1.49/1.23
% 1.49/1.23 thf(satz25,axiom,
% 1.49/1.23 ! [Xx: nat,Xy: nat] :
% 1.49/1.23 ( ( some
% 1.49/1.23 @ ^ [Xu: nat] : ( diffprop @ Xy @ Xx @ Xu ) )
% 1.49/1.23 => ( moreis @ Xy @ ( pl @ Xx @ n_1 ) ) ) ).
% 1.49/1.23
% 1.49/1.23 thf(satz25b,conjecture,
% 1.49/1.23 lessis @ ( pl @ y @ n_1 ) @ x ).
% 1.49/1.23 ------------------------
% 1.49/1.24 % (20043)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19930 for (3000ds/18Mi)
% 1.49/1.24 % (20040)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19930 for (3000ds/2Mi)
% 1.49/1.24 % (20038)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_19930 for (3000ds/4Mi)
% 1.49/1.24 % (20040)Instruction limit reached!
% 1.49/1.24 % (20040)------------------------------
% 1.49/1.24 % (20040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.24 % (20040)Termination reason: Unknown
% 1.49/1.24 % (20040)Termination phase: Saturation
% 1.49/1.24
% 1.49/1.24 % (20040)Memory used [KB]: 5500
% 1.49/1.24 % (20040)Time elapsed: 0.002 s
% 1.49/1.24 % (20040)Instructions burned: 2 (million)
% 1.49/1.24 % (20040)------------------------------
% 1.49/1.24 % (20040)------------------------------
% 1.49/1.24 % (20043)First to succeed.
% 1.49/1.24 % (20038)Also succeeded, but the first one will report.
% 1.49/1.24 % (20043)Refutation found. Thanks to Tanya!
% 1.49/1.24 % SZS status Theorem for DTF2THF_19930
% 1.49/1.24 % SZS output start Proof for DTF2THF_19930
% 1.49/1.24 thf(type_def_5, type, nat: $tType).
% 1.49/1.24 thf(func_def_0, type, nat: $tType).
% 1.49/1.24 thf(func_def_1, type, x: nat).
% 1.49/1.24 thf(func_def_2, type, y: nat).
% 1.49/1.24 thf(func_def_3, type, some: (nat > $o) > $o).
% 1.49/1.24 thf(func_def_4, type, diffprop: nat > nat > nat > $o).
% 1.49/1.24 thf(func_def_6, type, lessis: nat > nat > $o).
% 1.49/1.24 thf(func_def_7, type, pl: nat > nat > nat).
% 1.49/1.24 thf(func_def_8, type, n_1: nat).
% 1.49/1.24 thf(func_def_9, type, moreis: nat > nat > $o).
% 1.49/1.24 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.49/1.24 thf(func_def_16, type, sK2: nat > nat > nat).
% 1.49/1.24 thf(f63,plain,(
% 1.49/1.24 $false),
% 1.49/1.24 inference(avatar_sat_refutation,[status(thm)],[f39,f43,f62])).
% 1.49/1.24 thf(f62,plain,(
% 1.49/1.24 ~spl0_1 | spl0_2),
% 1.49/1.24 inference(avatar_contradiction_clause,[status(thm)],[f61])).
% 1.49/1.24 thf(f61,plain,(
% 1.49/1.24 $false | (~spl0_1 | spl0_2)),
% 1.49/1.24 inference(subsumption_resolution,[status(thm)],[f52,f37])).
% 1.49/1.24 thf(f37,plain,(
% 1.49/1.24 ($true != (moreis @ x @ (pl @ y @ n_1))) | spl0_2),
% 1.49/1.24 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.49/1.24 thf(f36,definition,(
% 1.49/1.24 spl0_2 <=> ($true = (moreis @ x @ (pl @ y @ n_1)))),
% 1.49/1.24 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.49/1.24 thf(f52,plain,(
% 1.49/1.24 ($true = (moreis @ x @ (pl @ y @ n_1))) | ~spl0_1),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.49/1.24 thf(f51,plain,(
% 1.49/1.24 ($true = $false) | ($true = (moreis @ x @ (pl @ y @ n_1))) | ~spl0_1),
% 1.49/1.24 inference(duplicate_literal_removal,[status(thm)],[f45])).
% 1.49/1.24 thf(f45,plain,(
% 1.49/1.24 ($true = $false) | ($true = $false) | ($true = (moreis @ x @ (pl @ y @ n_1))) | ~spl0_1),
% 1.49/1.24 inference(superposition,[status(thm)],[f28,f34])).
% 1.49/1.24 thf(f34,plain,(
% 1.49/1.24 ($true = (diffprop @ x @ y @ (sK2 @ y @ x))) | ~spl0_1),
% 1.49/1.24 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.49/1.24 thf(f32,definition,(
% 1.49/1.24 spl0_1 <=> ($true = (diffprop @ x @ y @ (sK2 @ y @ x)))),
% 1.49/1.24 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.49/1.24 thf(f28,plain,(
% 1.49/1.24 ( ! [X0 : nat,X1 : nat] : (((diffprop @ x @ y @ (sK2 @ X1 @ X0)) = $false) | ($true = (moreis @ X0 @ (pl @ X1 @ n_1))) | ((diffprop @ X0 @ X1 @ (sK2 @ X1 @ X0)) = $false)) )),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.49/1.24 thf(f26,plain,(
% 1.49/1.24 ( ! [X0 : nat,X1 : nat] : (((diffprop @ x @ y @ (sK2 @ X1 @ X0)) != (diffprop @ X0 @ X1 @ (sK2 @ X1 @ X0))) | ($true = (moreis @ X0 @ (pl @ X1 @ n_1)))) )),
% 1.49/1.24 inference(negative_extensionality,[status(thm)],[f25])).
% 1.49/1.24 thf(f25,plain,(
% 1.49/1.24 ( ! [X0 : nat,X1 : nat] : (((diffprop @ x @ y) != (diffprop @ X0 @ X1)) | ($true = (moreis @ X0 @ (pl @ X1 @ n_1)))) )),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.49/1.24 thf(f24,plain,(
% 1.49/1.24 ( ! [X0 : nat,X1 : nat] : (($true = (moreis @ X0 @ (pl @ X1 @ n_1))) | ((diffprop @ x @ y) != (diffprop @ X0 @ X1)) | ($true != $true)) )),
% 1.49/1.24 inference(constrained_superposition,[status(thm)],[f23,f22])).
% 1.49/1.24 thf(f22,plain,(
% 1.49/1.24 ((some @ (diffprop @ x @ y)) = $true)),
% 1.49/1.24 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.49/1.24 thf(f20,plain,(
% 1.49/1.24 ((some @ (^[Y0 : nat]: (diffprop @ x @ y @ Y0))) = $true)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.24 thf(f14,plain,(
% 1.49/1.24 ((some @ (^[Y0 : nat]: (diffprop @ x @ y @ Y0))) = $true)),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f13])).
% 1.49/1.24 thf(f13,plain,(
% 1.49/1.24 (some @ (^[X0 : nat] : (diffprop @ x @ y @ X0)))),
% 1.49/1.24 inference(rectify,[status(thm)],[f1])).
% 1.49/1.24 thf(f1,axiom,(
% 1.49/1.24 (some @ (^[X0 : nat] : (diffprop @ x @ y @ X0)))),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.4j749jRKDo/DTF2THF_19930.p',l)).
% 1.49/1.24 thf(f23,plain,(
% 1.49/1.24 ( ! [X0 : nat,X1 : nat] : (($true != (some @ (diffprop @ X0 @ X1))) | ($true = (moreis @ X0 @ (pl @ X1 @ n_1)))) )),
% 1.49/1.24 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.49/1.24 thf(f19,plain,(
% 1.49/1.24 ( ! [X0 : nat,X1 : nat] : (($true = (moreis @ X0 @ (pl @ X1 @ n_1))) | ($true != (some @ (^[Y0 : nat]: (diffprop @ X0 @ X1 @ Y0))))) )),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f17])).
% 1.49/1.24 thf(f17,plain,(
% 1.49/1.24 ! [X0 : nat,X1 : nat] : (($true != (some @ (^[Y0 : nat]: (diffprop @ X0 @ X1 @ Y0)))) | ($true = (moreis @ X0 @ (pl @ X1 @ n_1))))),
% 1.49/1.24 inference(ennf_transformation,[status(thm)],[f8])).
% 1.49/1.24 thf(f8,plain,(
% 1.49/1.24 ! [X0 : nat,X1 : nat] : (($true = (some @ (^[Y0 : nat]: (diffprop @ X0 @ X1 @ Y0)))) => ($true = (moreis @ X0 @ (pl @ X1 @ n_1))))),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f7])).
% 1.49/1.24 thf(f7,plain,(
% 1.49/1.24 ! [X0 : nat,X1 : nat] : ((some @ (^[X2 : nat] : (diffprop @ X0 @ X1 @ X2))) => (moreis @ X0 @ (pl @ X1 @ n_1)))),
% 1.49/1.24 inference(rectify,[status(thm)],[f3])).
% 1.49/1.24 thf(f3,axiom,(
% 1.49/1.24 ! [X2 : nat,X1 : nat] : ((some @ (^[X3 : nat] : (diffprop @ X2 @ X1 @ X3))) => (moreis @ X2 @ (pl @ X1 @ n_1)))),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.4j749jRKDo/DTF2THF_19930.p',satz25)).
% 1.49/1.24 thf(f43,plain,(
% 1.49/1.24 ~spl0_2),
% 1.49/1.24 inference(avatar_contradiction_clause,[status(thm)],[f42])).
% 1.49/1.24 thf(f42,plain,(
% 1.49/1.24 $false | ~spl0_2),
% 1.49/1.24 inference(subsumption_resolution,[status(thm)],[f41,f18])).
% 1.49/1.24 thf(f18,plain,(
% 1.49/1.24 ((lessis @ (pl @ y @ n_1) @ x) != $true)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.24 thf(f15,plain,(
% 1.49/1.24 ((lessis @ (pl @ y @ n_1) @ x) != $true)),
% 1.49/1.24 inference(flattening,[status(thm)],[f12])).
% 1.49/1.24 thf(f12,plain,(
% 1.49/1.24 ~((lessis @ (pl @ y @ n_1) @ x) = $true)),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f11])).
% 1.49/1.24 thf(f11,plain,(
% 1.49/1.24 ~(lessis @ (pl @ y @ n_1) @ x)),
% 1.49/1.24 inference(rectify,[status(thm)],[f5])).
% 1.49/1.24 thf(f5,negated_conjecture,(
% 1.49/1.24 ~(lessis @ (pl @ y @ n_1) @ x)),
% 1.49/1.24 inference(negated_conjecture,[status(cth)],[f4])).
% 1.49/1.24 thf(f4,conjecture,(
% 1.49/1.24 (lessis @ (pl @ y @ n_1) @ x)),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.4j749jRKDo/DTF2THF_19930.p',satz25b)).
% 1.49/1.24 thf(f41,plain,(
% 1.49/1.24 ((lessis @ (pl @ y @ n_1) @ x) = $true) | ~spl0_2),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.49/1.24 thf(f40,plain,(
% 1.49/1.24 ((lessis @ (pl @ y @ n_1) @ x) = $true) | ($true != $true) | ~spl0_2),
% 1.49/1.24 inference(superposition,[status(thm)],[f21,f38])).
% 1.49/1.24 thf(f38,plain,(
% 1.49/1.24 ($true = (moreis @ x @ (pl @ y @ n_1))) | ~spl0_2),
% 1.49/1.24 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.49/1.24 thf(f21,plain,(
% 1.49/1.24 ( ! [X0 : nat,X1 : nat] : (((moreis @ X1 @ X0) != $true) | ((lessis @ X0 @ X1) = $true)) )),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f16])).
% 1.49/1.24 thf(f16,plain,(
% 1.49/1.24 ! [X0 : nat,X1 : nat] : (((moreis @ X1 @ X0) != $true) | ((lessis @ X0 @ X1) = $true))),
% 1.49/1.24 inference(ennf_transformation,[status(thm)],[f10])).
% 1.49/1.24 thf(f10,plain,(
% 1.49/1.24 ! [X0 : nat,X1 : nat] : (((moreis @ X1 @ X0) = $true) => ((lessis @ X0 @ X1) = $true))),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f9])).
% 1.49/1.24 thf(f9,plain,(
% 1.49/1.24 ! [X0 : nat,X1 : nat] : ((moreis @ X1 @ X0) => (lessis @ X0 @ X1))),
% 1.49/1.24 inference(rectify,[status(thm)],[f2])).
% 1.49/1.24 thf(f2,axiom,(
% 1.49/1.24 ! [X2 : nat,X1 : nat] : ((moreis @ X1 @ X2) => (lessis @ X2 @ X1))),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.4j749jRKDo/DTF2THF_19930.p',satz13)).
% 1.49/1.24 thf(f39,plain,(
% 1.49/1.24 spl0_1 | spl0_2),
% 1.49/1.24 inference(avatar_split_clause,[status(thm)],[f30,f36,f32])).
% 1.49/1.24 thf(f30,plain,(
% 1.49/1.24 ($true = (moreis @ x @ (pl @ y @ n_1))) | ($true = (diffprop @ x @ y @ (sK2 @ y @ x)))),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.49/1.24 thf(f29,plain,(
% 1.49/1.24 ($true = (moreis @ x @ (pl @ y @ n_1))) | ($true != $true) | ($true = (diffprop @ x @ y @ (sK2 @ y @ x)))),
% 1.49/1.24 inference(equality_factoring,[status(thm)],[f27])).
% 1.49/1.24 thf(f27,plain,(
% 1.49/1.24 ( ! [X0 : nat,X1 : nat] : (($true = (diffprop @ x @ y @ (sK2 @ X1 @ X0))) | ($true = (diffprop @ X0 @ X1 @ (sK2 @ X1 @ X0))) | ($true = (moreis @ X0 @ (pl @ X1 @ n_1)))) )),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.49/1.24 % SZS output end Proof for DTF2THF_19930
% 1.49/1.24 % (20043)------------------------------
% 1.49/1.24 % (20043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.24 % (20043)Termination reason: Refutation
% 1.49/1.24
% 1.49/1.24 % (20043)Memory used [KB]: 5500
% 1.49/1.24 % (20043)Time elapsed: 0.005 s
% 1.49/1.24 % (20043)Instructions burned: 7 (million)
% 1.49/1.24 % (20043)------------------------------
% 1.49/1.24 % (20043)------------------------------
% 1.49/1.24 % (20036)Success in time 0.011 s
%------------------------------------------------------------------------------