%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM638^1 : 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 : n018.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 09:24:02 AM UTC 2026
% Result : Theorem 1.60s 1.31s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 4 unt; 0 typ; 4 def)
% Number of atoms : 241 ( 154 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 301 ( 72 ~; 82 |; 10 &; 113 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 70 ( 24 ^; 40 !; 6 ?; 70 :)
% 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,
n_1: nat ).
thf(func_def_3,type,
suc: nat > nat ).
thf(func_def_4,type,
some: ( nat > $o ) > $o ).
thf(func_def_11,type,
sK0: nat ).
thf(func_def_12,type,
sK1: nat ).
thf(func_def_14,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK4: nat > nat ).
thf(f110,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f32,f37,f42,f100,f109]) ).
thf(f109,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
| ~ spl2_1
| ~ spl2_3
| spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f107,f41]) ).
thf(f41,plain,
( ( sK1 != sK0 )
| spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl2_4
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f107,plain,
( ( sK1 = sK0 )
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( x != x )
| ( sK1 = sK0 )
| ~ spl2_1
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f102,f36]) ).
thf(f36,plain,
( ( x
= ( suc @ sK1 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl2_3
<=> ( x
= ( suc @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f102,plain,
( ! [X0: nat] :
( ( x
!= ( suc @ X0 ) )
| ( sK0 = X0 ) )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f23,f27]) ).
thf(f27,plain,
( ( x
= ( suc @ sK0 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl2_1
<=> ( x
= ( suc @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f23,plain,
! [X0: nat,X1: nat] :
( ( ( suc @ X0 )
!= ( suc @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( ( suc @ X0 )
!= ( suc @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( ( suc @ X0 )
= ( suc @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.j6pKbE1kZ5/DTF2THF_22214.p',ax4) ).
thf(f100,plain,
spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f99]) ).
thf(f99,plain,
( $false
| spl2_2 ),
inference(equality_resolution,[status(thm)],[f79]) ).
thf(f79,plain,
( ! [X0: nat] : ( x != X0 )
| spl2_2 ),
inference(duplicate_literal_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ! [X0: nat] :
( ( x != X0 )
| ( x != X0 ) )
| spl2_2 ),
inference(superposition,[status(thm)],[f18,f67]) ).
thf(f67,plain,
( ! [X0: nat] :
( ( n_1 = X0 )
| ( x != X0 ) )
| spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ! [X0: nat] :
( ( x != X0 )
| ( n_1 = X0 )
| ( x != x ) )
| spl2_2 ),
inference(duplicate_literal_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ! [X0: nat] :
( ( n_1 = X0 )
| ( x != x )
| ( x != X0 )
| ( n_1 = X0 )
| ( x != X0 ) )
| spl2_2 ),
inference(superposition,[status(thm)],[f51,f59]) ).
thf(f59,plain,
( ! [X0: nat] :
( ( x
= ( suc @ ( sK4 @ X0 ) ) )
| ( x != X0 )
| ( n_1 = X0 ) )
| spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ! [X0: nat] :
( ( x
= ( suc @ ( sK4 @ X0 ) ) )
| ( X0 != X0 )
| ( n_1 = X0 )
| ( x != X0 ) )
| spl2_2 ),
inference(duplicate_literal_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ! [X0: nat] :
( ( x != X0 )
| ( X0 != X0 )
| ( n_1 = X0 )
| ( x
= ( suc @ ( sK4 @ X0 ) ) )
| ( n_1 = X0 ) )
| spl2_2 ),
inference(superposition,[status(thm)],[f51,f53]) ).
thf(f53,plain,
( ! [X0: nat] :
( ( ( suc @ ( sK4 @ X0 ) )
= X0 )
| ( n_1 = X0 )
| ( x
= ( suc @ ( sK4 @ X0 ) ) ) )
| spl2_2 ),
inference(equality_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ! [X0: nat] :
( ( ( suc @ ( sK4 @ X0 ) )
= X0 )
| ( n_1 = X0 )
| ( $true
= ( x
= ( suc @ ( sK4 @ X0 ) ) ) ) )
| spl2_2 ),
inference(equality_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ! [X0: nat] :
( ( ( ( suc @ ( sK4 @ X0 ) )
= X0 )
= $true )
| ( n_1 = X0 )
| ( $true
= ( x
= ( suc @ ( sK4 @ X0 ) ) ) ) )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ! [X0: nat] :
( ( n_1 = X0 )
| ( ( ( suc @ ( sK4 @ X0 ) )
= X0 )
!= ( x
= ( suc @ ( sK4 @ X0 ) ) ) ) )
| spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( ! [X0: nat] :
( ( ( ^ [Y0: nat] :
( x
= ( suc @ Y0 ) )
@ ( sK4 @ X0 ) )
!= ( ^ [Y0: nat] :
( ( suc @ Y0 )
= X0 )
@ ( sK4 @ X0 ) ) )
| ( n_1 = X0 ) )
| spl2_2 ),
inference(negative_extensionality,[status(thm)],[f45]) ).
thf(f45,plain,
( ! [X0: nat] :
( ( ( ^ [Y0: nat] :
( ( suc @ Y0 )
= X0 ) )
!= ( ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) )
| ( n_1 = X0 ) )
| spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ! [X0: nat] :
( ( n_1 = X0 )
| ( $true != $true )
| ( ( ^ [Y0: nat] :
( ( suc @ Y0 )
= X0 ) )
!= ( ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) ) )
| spl2_2 ),
inference(constrained_superposition,[status(thm)],[f31,f22]) ).
thf(f22,plain,
! [X0: nat] :
( ( ( some
@ ^ [Y0: nat] :
( ( suc @ Y0 )
= X0 ) )
= $true )
| ( n_1 = X0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat] :
( ( ( some
@ ^ [Y0: nat] :
( ( suc @ Y0 )
= X0 ) )
= $true )
| ( n_1 = X0 ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat] :
( ( n_1 != X0 )
=> ( ( some
@ ^ [Y0: nat] :
( ( suc @ Y0 )
= X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: nat] :
( ( n_1 != X0 )
=> ( some
@ ^ [X1: nat] :
( ( suc @ X1 )
= X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: nat] :
( ( n_1 != X0 )
=> ( some
@ ^ [X2: nat] :
( ( suc @ X2 )
= X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.j6pKbE1kZ5/DTF2THF_22214.p',satz3) ).
thf(f31,plain,
( ( $true
!= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl2_2
<=> ( $true
= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f51,plain,
( ! [X0: nat] :
( ( ( suc @ ( sK4 @ X0 ) )
!= X0 )
| ( n_1 = X0 )
| ( x
!= ( suc @ ( sK4 @ X0 ) ) ) )
| spl2_2 ),
inference(equality_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ! [X0: nat] :
( ( $false
= ( x
= ( suc @ ( sK4 @ X0 ) ) ) )
| ( ( suc @ ( sK4 @ X0 ) )
!= X0 )
| ( n_1 = X0 ) )
| spl2_2 ),
inference(equality_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ! [X0: nat] :
( ( ( ( suc @ ( sK4 @ X0 ) )
= X0 )
= $false )
| ( $false
= ( x
= ( suc @ ( sK4 @ X0 ) ) ) )
| ( n_1 = X0 ) )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f18,plain,
x != n_1,
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
x != n_1,
file('/export/starexec/sandbox/tmp/tmp.j6pKbE1kZ5/DTF2THF_22214.p',n) ).
thf(f42,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f21,f39,f29]) ).
thf(f21,plain,
( ( $true
!= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) )
| ( sK1 != sK0 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( sK1 != sK0 )
& ( x
= ( suc @ sK1 ) )
& ( x
= ( suc @ sK0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: nat,X1: nat] :
( ( X0 != X1 )
& ( x
= ( suc @ X1 ) )
& ( x
= ( suc @ X0 ) ) )
=> ( ( sK1 != sK0 )
& ( x
= ( suc @ sK1 ) )
& ( x
= ( suc @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X0: nat,X1: nat] :
( ( X0 != X1 )
& ( x
= ( suc @ X1 ) )
& ( x
= ( suc @ X0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $true
!= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) )
| ? [X0: nat,X1: nat] :
( ( X0 != X1 )
& ( x
= ( suc @ X1 ) )
& ( x
= ( suc @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: nat,X1: nat] :
( ( x
= ( suc @ X0 ) )
=> ( ( x
= ( suc @ X1 ) )
=> ( X0 = X1 ) ) )
=> ( $true
!= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ~ ( ! [X0: nat,X1: nat] :
( ( x
= ( suc @ X0 ) )
=> ( ( x
= ( suc @ X1 ) )
=> ( X0 = X1 ) ) )
=> ( $true
!= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ~ ( ! [X0: nat,X1: nat] :
( ( x
= ( suc @ X0 ) )
=> ( ( x
= ( suc @ X1 ) )
=> ( X0 = X1 ) ) )
=> ~ ( some
@ ^ [X2: nat] :
( x
= ( suc @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ~ ( ! [X3: nat,X1: nat] :
( ( x
= ( suc @ X3 ) )
=> ( ( x
= ( suc @ X1 ) )
=> ( X1 = X3 ) ) )
=> ~ ( some
@ ^ [X2: nat] :
( x
= ( suc @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
~ ( ! [X3: nat,X1: nat] :
( ( x
= ( suc @ X3 ) )
=> ( ( x
= ( suc @ X1 ) )
=> ( X1 = X3 ) ) )
=> ~ ( some
@ ^ [X2: nat] :
( x
= ( suc @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.j6pKbE1kZ5/DTF2THF_22214.p',satz3a) ).
thf(f37,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f20,f34,f29]) ).
thf(f20,plain,
( ( x
= ( suc @ sK1 ) )
| ( $true
!= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f32,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f29,f25]) ).
thf(f19,plain,
( ( x
= ( suc @ sK0 ) )
| ( $true
!= ( some
@ ^ [Y0: nat] :
( x
= ( suc @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM638^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.32 % Computer : n018.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue Feb 24 11:08:31 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : NUM638^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.44 % Domain : Number Theory
% 0.18/0.44 % Problem : Landau theorem 3a
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English : ~((forall x_0:nat.forall y:nat.x = suc x_0 -> x = suc y ->
% 0.18/0.44 % x_0 = y) -> ~(some (lambda u.x = suc u)))
% 0.18/0.44
% 0.18/0.44 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.18/0.44 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.18/0.44 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [Bro09]
% 0.18/0.44 % Names : satz3a [Lan30]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % : Without extensionality : Theorem
% 0.18/0.44 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.18/0.44 % Syntax : Number of formulae : 9 ( 1 unt; 5 typ; 0 def)
% 0.18/0.44 % Number of atoms : 11 ( 9 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 5 ( 2 avg)
% 0.18/0.44 % Number of connectives : 17 ( 4 ~; 0 |; 0 &; 8 @)
% 0.18/0.44 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 7 ( 5 avg)
% 0.18/0.44 % Number of types : 2 ( 1 usr)
% 0.18/0.44 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.18/0.44 % Number of variables : 7 ( 2 ^; 5 !; 0 ?; 7 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments :
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(nat_type,type,
% 0.18/0.44 nat: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(x,type,
% 0.18/0.44 x: nat ).
% 0.18/0.44
% 0.18/0.44 thf(n_1,type,
% 0.18/0.44 n_1: nat ).
% 0.18/0.44
% 0.18/0.44 thf(n,axiom,
% 0.18/0.44 x != n_1 ).
% 0.18/0.44
% 0.18/0.44 thf(suc,type,
% 0.18/0.44 suc: nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(some,type,
% 0.18/0.44 some: ( nat > $o ) > $o ).
% 0.18/0.44
% 0.18/0.44 thf(ax4,axiom,
% 0.18/0.44 ! [Xx: nat,Xy: nat] :
% 0.18/0.44 ( ( ( suc @ Xx )
% 0.18/0.44 = ( suc @ Xy ) )
% 0.18/0.44 => ( Xx = Xy ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(satz3,axiom,
% 0.18/0.44 ! [Xx: nat] :
% 0.18/0.44 ( ( Xx != n_1 )
% 0.18/0.44 => ( some
% 0.18/0.44 @ ^ [Xu: nat] :
% 0.18/0.44 ( Xx
% 0.18/0.44 = ( suc @ Xu ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(satz3a,conjecture,
% 0.18/0.44 ~ ( ! [Xx_0: nat,Xy: nat] :
% 0.18/0.44 ( ( x
% 0.18/0.44 = ( suc @ Xx_0 ) )
% 0.18/0.44 => ( ( x
% 0.18/0.44 = ( suc @ Xy ) )
% 0.18/0.44 => ( Xx_0 = Xy ) ) )
% 0.18/0.44 => ~ ( some
% 0.18/0.44 @ ^ [Xu: nat] :
% 0.18/0.44 ( x
% 0.18/0.44 = ( suc @ Xu ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 11:08:32 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.j6pKbE1kZ5/DTF2DTF22214.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.29 thf(nat_type,type,
% 1.46/1.29 nat: $tType ).
% 1.46/1.29
% 1.46/1.29 thf(x,type,
% 1.46/1.29 x: nat ).
% 1.46/1.29
% 1.46/1.29 thf(n_1,type,
% 1.46/1.29 n_1: nat ).
% 1.46/1.29
% 1.46/1.29 thf(n,axiom,
% 1.46/1.29 x != n_1 ).
% 1.46/1.29
% 1.46/1.29 thf(suc,type,
% 1.46/1.29 suc: nat > nat ).
% 1.46/1.29
% 1.46/1.29 thf(some,type,
% 1.46/1.29 some: ( nat > $o ) > $o ).
% 1.46/1.29
% 1.46/1.29 thf(ax4,axiom,
% 1.46/1.29 ! [Xx: nat,Xy: nat] :
% 1.46/1.29 ( ( ( suc @ Xx )
% 1.46/1.29 = ( suc @ Xy ) )
% 1.46/1.29 => ( Xx = Xy ) ) ).
% 1.46/1.29
% 1.46/1.29 thf(satz3,axiom,
% 1.46/1.29 ! [Xx: nat] :
% 1.46/1.29 ( ( Xx != n_1 )
% 1.46/1.29 => ( some
% 1.46/1.29 @ ^ [Xu: nat] :
% 1.46/1.29 ( Xx
% 1.46/1.29 = ( suc @ Xu ) ) ) ) ).
% 1.46/1.29
% 1.46/1.29 thf(satz3a,conjecture,
% 1.46/1.29 ~ ( ! [Xx_0: nat,Xy: nat] :
% 1.46/1.29 ( ( x
% 1.46/1.29 = ( suc @ Xx_0 ) )
% 1.46/1.29 => ( ( x
% 1.46/1.29 = ( suc @ Xy ) )
% 1.46/1.29 => ( Xx_0 = Xy ) ) )
% 1.46/1.29 => ~ ( some
% 1.46/1.29 @ ^ [Xu: nat] :
% 1.46/1.29 ( x
% 1.46/1.29 = ( suc @ Xu ) ) ) ) ).
% 1.46/1.29 ------------------------
% 1.60/1.30 % (22322)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22214 for (3000ds/183Mi)
% 1.60/1.31 % (22323)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_22214 for (3000ds/4Mi)
% 1.60/1.31 % (22324)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_22214 for (3000ds/27Mi)
% 1.60/1.31 % (22325)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22214 for (3000ds/2Mi)
% 1.60/1.31 % (22326)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_22214 for (3000ds/2Mi)
% 1.60/1.31 % (22328)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22214 for (3000ds/18Mi)
% 1.60/1.31 % (22327)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_22214 for (3000ds/275Mi)
% 1.60/1.31 % (22325)Instruction limit reached!
% 1.60/1.31 % (22325)------------------------------
% 1.60/1.31 % (22325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (22325)Termination reason: Unknown
% 1.60/1.31 % (22325)Termination phase: Saturation
% 1.60/1.31
% 1.60/1.31 % (22325)Memory used [KB]: 895
% 1.60/1.31 % (22325)Time elapsed: 0.003 s
% 1.60/1.31 % (22325)Instructions burned: 2 (million)
% 1.60/1.31 % (22325)------------------------------
% 1.60/1.31 % (22325)------------------------------
% 1.60/1.31 % (22326)Instruction limit reached!
% 1.60/1.31 % (22326)------------------------------
% 1.60/1.31 % (22326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (22326)Termination reason: Unknown
% 1.60/1.31 % (22326)Termination phase: Property scanning
% 1.60/1.31
% 1.60/1.31 % (22326)Memory used [KB]: 895
% 1.60/1.31 % (22326)Time elapsed: 0.003 s
% 1.60/1.31 % (22326)Instructions burned: 2 (million)
% 1.60/1.31 % (22326)------------------------------
% 1.60/1.31 % (22326)------------------------------
% 1.60/1.31 % (22327)Refutation not found, incomplete strategy
% 1.60/1.31 % (22327)------------------------------
% 1.60/1.31 % (22327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (22327)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (22327)Memory used [KB]: 5500
% 1.60/1.31 % (22327)Time elapsed: 0.003 s
% 1.60/1.31 % (22327)Instructions burned: 2 (million)
% 1.60/1.31 % (22327)------------------------------
% 1.60/1.31 % (22327)------------------------------
% 1.60/1.31 % (22324)Refutation not found, incomplete strategy
% 1.60/1.31 % (22324)------------------------------
% 1.60/1.31 % (22324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (22324)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (22324)Memory used [KB]: 5500
% 1.60/1.31 % (22324)Time elapsed: 0.004 s
% 1.60/1.31 % (22324)Instructions burned: 2 (million)
% 1.60/1.31 % (22324)------------------------------
% 1.60/1.31 % (22324)------------------------------
% 1.60/1.31 % (22323)Instruction limit reached!
% 1.60/1.31 % (22323)------------------------------
% 1.60/1.31 % (22323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (22323)Termination reason: Unknown
% 1.60/1.31 % (22323)Termination phase: Saturation
% 1.60/1.31
% 1.60/1.31 % (22323)Memory used [KB]: 5500
% 1.60/1.31 % (22323)Time elapsed: 0.005 s
% 1.60/1.31 % (22323)Instructions burned: 4 (million)
% 1.60/1.31 % (22323)------------------------------
% 1.60/1.31 % (22323)------------------------------
% 1.60/1.31 % (22322)First to succeed.
% 1.60/1.31 % (22328)Also succeeded, but the first one will report.
% 1.60/1.31 % (22322)Refutation found. Thanks to Tanya!
% 1.60/1.31 % SZS status Theorem for DTF2THF_22214
% 1.60/1.31 % SZS output start Proof for DTF2THF_22214
% 1.60/1.31 thf(type_def_5, type, nat: $tType).
% 1.60/1.31 thf(func_def_0, type, nat: $tType).
% 1.60/1.31 thf(func_def_1, type, x: nat).
% 1.60/1.31 thf(func_def_2, type, n_1: nat).
% 1.60/1.31 thf(func_def_3, type, suc: nat > nat).
% 1.60/1.31 thf(func_def_4, type, some: (nat > $o) > $o).
% 1.60/1.31 thf(func_def_11, type, sK0: nat).
% 1.60/1.31 thf(func_def_12, type, sK1: nat).
% 1.60/1.31 thf(func_def_14, type, ph3: !>[X0: $tType]:(X0)).
% 1.60/1.31 thf(func_def_15, type, sK4: nat > nat).
% 1.60/1.31 thf(f110,plain,(
% 1.60/1.31 $false),
% 1.60/1.31 inference(avatar_sat_refutation,[status(thm)],[f32,f37,f42,f100,f109])).
% 1.60/1.31 thf(f109,plain,(
% 1.60/1.31 ~spl2_1 | ~spl2_3 | spl2_4),
% 1.60/1.31 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 1.60/1.31 thf(f108,plain,(
% 1.60/1.31 $false | (~spl2_1 | ~spl2_3 | spl2_4)),
% 1.60/1.31 inference(subsumption_resolution,[status(thm)],[f107,f41])).
% 1.60/1.31 thf(f41,plain,(
% 1.60/1.31 (sK1 != sK0) | spl2_4),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.60/1.31 thf(f39,definition,(
% 1.60/1.31 spl2_4 <=> (sK1 = sK0)),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.60/1.31 thf(f107,plain,(
% 1.60/1.31 (sK1 = sK0) | (~spl2_1 | ~spl2_3)),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.60/1.31 thf(f106,plain,(
% 1.60/1.31 (x != x) | (sK1 = sK0) | (~spl2_1 | ~spl2_3)),
% 1.60/1.31 inference(superposition,[status(thm)],[f102,f36])).
% 1.60/1.31 thf(f36,plain,(
% 1.60/1.31 (x = (suc @ sK1)) | ~spl2_3),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.60/1.31 thf(f34,definition,(
% 1.60/1.31 spl2_3 <=> (x = (suc @ sK1))),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.60/1.31 thf(f102,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((x != (suc @ X0)) | (sK0 = X0)) ) | ~spl2_1),
% 1.60/1.31 inference(superposition,[status(thm)],[f23,f27])).
% 1.60/1.31 thf(f27,plain,(
% 1.60/1.31 (x = (suc @ sK0)) | ~spl2_1),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.60/1.31 thf(f25,definition,(
% 1.60/1.31 spl2_1 <=> (x = (suc @ sK0))),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.60/1.31 thf(f23,plain,(
% 1.60/1.31 ( ! [X0 : nat,X1 : nat] : (((suc @ X0) != (suc @ X1)) | (X0 = X1)) )),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.60/1.31 thf(f12,plain,(
% 1.60/1.31 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ((suc @ X0) != (suc @ X1)))),
% 1.60/1.31 inference(ennf_transformation,[status(thm)],[f2])).
% 1.60/1.31 thf(f2,axiom,(
% 1.60/1.31 ! [X0 : nat,X1 : nat] : (((suc @ X0) = (suc @ X1)) => (X0 = X1))),
% 1.60/1.31 file('/export/starexec/sandbox/tmp/tmp.j6pKbE1kZ5/DTF2THF_22214.p',ax4)).
% 1.60/1.31 thf(f100,plain,(
% 1.60/1.31 spl2_2),
% 1.60/1.31 inference(avatar_contradiction_clause,[status(thm)],[f99])).
% 1.60/1.31 thf(f99,plain,(
% 1.60/1.31 $false | spl2_2),
% 1.60/1.31 inference(equality_resolution,[status(thm)],[f79])).
% 1.60/1.31 thf(f79,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((x != X0)) ) | spl2_2),
% 1.60/1.31 inference(duplicate_literal_removal,[status(thm)],[f69])).
% 1.60/1.31 thf(f69,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((x != X0) | (x != X0)) ) | spl2_2),
% 1.60/1.31 inference(superposition,[status(thm)],[f18,f67])).
% 1.60/1.31 thf(f67,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((n_1 = X0) | (x != X0)) ) | spl2_2),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.60/1.31 thf(f66,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((x != X0) | (n_1 = X0) | (x != x)) ) | spl2_2),
% 1.60/1.31 inference(duplicate_literal_removal,[status(thm)],[f62])).
% 1.60/1.31 thf(f62,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((n_1 = X0) | (x != x) | (x != X0) | (n_1 = X0) | (x != X0)) ) | spl2_2),
% 1.60/1.31 inference(superposition,[status(thm)],[f51,f59])).
% 1.60/1.31 thf(f59,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((x = (suc @ (sK4 @ X0))) | (x != X0) | (n_1 = X0)) ) | spl2_2),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.60/1.31 thf(f58,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((x = (suc @ (sK4 @ X0))) | (X0 != X0) | (n_1 = X0) | (x != X0)) ) | spl2_2),
% 1.60/1.31 inference(duplicate_literal_removal,[status(thm)],[f54])).
% 1.60/1.31 thf(f54,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((x != X0) | (X0 != X0) | (n_1 = X0) | (x = (suc @ (sK4 @ X0))) | (n_1 = X0)) ) | spl2_2),
% 1.60/1.31 inference(superposition,[status(thm)],[f51,f53])).
% 1.60/1.31 thf(f53,plain,(
% 1.60/1.31 ( ! [X0 : nat] : (((suc @ (sK4 @ X0)) = X0) | (n_1 = X0) | (x = (suc @ (sK4 @ X0)))) ) | spl2_2),
% 1.60/1.31 inference(equality_proxy_clausification,[status(thm)],[f52])).
% 1.60/1.31 thf(f52,plain,(
% 1.60/1.31 ( ! [X0 : nat] : (((suc @ (sK4 @ X0)) = X0) | (n_1 = X0) | ($true = (x = (suc @ (sK4 @ X0))))) ) | spl2_2),
% 1.60/1.31 inference(equality_proxy_clausification,[status(thm)],[f48])).
% 1.60/1.31 thf(f48,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((((suc @ (sK4 @ X0)) = X0) = $true) | (n_1 = X0) | ($true = (x = (suc @ (sK4 @ X0))))) ) | spl2_2),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.60/1.31 thf(f47,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((n_1 = X0) | (((suc @ (sK4 @ X0)) = X0) != (x = (suc @ (sK4 @ X0))))) ) | spl2_2),
% 1.60/1.31 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.60/1.31 thf(f46,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((((^[Y0 : nat]: (x = (suc @ Y0))) @ (sK4 @ X0)) != ((^[Y0 : nat]: ((suc @ Y0) = X0)) @ (sK4 @ X0))) | (n_1 = X0)) ) | spl2_2),
% 1.60/1.31 inference(negative_extensionality,[status(thm)],[f45])).
% 1.60/1.31 thf(f45,plain,(
% 1.60/1.31 ( ! [X0 : nat] : (((^[Y0 : nat]: ((suc @ Y0) = X0)) != (^[Y0 : nat]: (x = (suc @ Y0)))) | (n_1 = X0)) ) | spl2_2),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.60/1.31 thf(f44,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((n_1 = X0) | ($true != $true) | ((^[Y0 : nat]: ((suc @ Y0) = X0)) != (^[Y0 : nat]: (x = (suc @ Y0))))) ) | spl2_2),
% 1.60/1.31 inference(constrained_superposition,[status(thm)],[f31,f22])).
% 1.60/1.31 thf(f22,plain,(
% 1.60/1.31 ( ! [X0 : nat] : (((some @ (^[Y0 : nat]: ((suc @ Y0) = X0))) = $true) | (n_1 = X0)) )),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f13])).
% 1.60/1.31 thf(f13,plain,(
% 1.60/1.31 ! [X0 : nat] : (((some @ (^[Y0 : nat]: ((suc @ Y0) = X0))) = $true) | (n_1 = X0))),
% 1.60/1.31 inference(ennf_transformation,[status(thm)],[f10])).
% 1.60/1.31 thf(f10,plain,(
% 1.60/1.31 ! [X0 : nat] : ((n_1 != X0) => ((some @ (^[Y0 : nat]: ((suc @ Y0) = X0))) = $true))),
% 1.60/1.31 inference(fool_elimination,[status(thm)],[f9])).
% 1.60/1.31 thf(f9,plain,(
% 1.60/1.31 ! [X0 : nat] : ((n_1 != X0) => (some @ (^[X1 : nat] : (((suc @ X1) = X0)))))),
% 1.60/1.31 inference(rectify,[status(thm)],[f3])).
% 1.60/1.31 thf(f3,axiom,(
% 1.60/1.31 ! [X0 : nat] : ((n_1 != X0) => (some @ (^[X2 : nat] : (((suc @ X2) = X0)))))),
% 1.60/1.31 file('/export/starexec/sandbox/tmp/tmp.j6pKbE1kZ5/DTF2THF_22214.p',satz3)).
% 1.60/1.31 thf(f31,plain,(
% 1.60/1.31 ($true != (some @ (^[Y0 : nat]: (x = (suc @ Y0))))) | spl2_2),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.60/1.31 thf(f29,definition,(
% 1.60/1.31 spl2_2 <=> ($true = (some @ (^[Y0 : nat]: (x = (suc @ Y0)))))),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.60/1.31 thf(f51,plain,(
% 1.60/1.31 ( ! [X0 : nat] : (((suc @ (sK4 @ X0)) != X0) | (n_1 = X0) | (x != (suc @ (sK4 @ X0)))) ) | spl2_2),
% 1.60/1.31 inference(equality_proxy_clausification,[status(thm)],[f50])).
% 1.60/1.31 thf(f50,plain,(
% 1.60/1.31 ( ! [X0 : nat] : (($false = (x = (suc @ (sK4 @ X0)))) | ((suc @ (sK4 @ X0)) != X0) | (n_1 = X0)) ) | spl2_2),
% 1.60/1.31 inference(equality_proxy_clausification,[status(thm)],[f49])).
% 1.60/1.31 thf(f49,plain,(
% 1.60/1.31 ( ! [X0 : nat] : ((((suc @ (sK4 @ X0)) = X0) = $false) | ($false = (x = (suc @ (sK4 @ X0)))) | (n_1 = X0)) ) | spl2_2),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.60/1.31 thf(f18,plain,(
% 1.60/1.31 (x != n_1)),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f1])).
% 1.60/1.31 thf(f1,axiom,(
% 1.60/1.31 (x != n_1)),
% 1.60/1.31 file('/export/starexec/sandbox/tmp/tmp.j6pKbE1kZ5/DTF2THF_22214.p',n)).
% 1.60/1.31 thf(f42,plain,(
% 1.60/1.31 ~spl2_2 | ~spl2_4),
% 1.60/1.31 inference(avatar_split_clause,[status(thm)],[f21,f39,f29])).
% 1.60/1.31 thf(f21,plain,(
% 1.60/1.31 ($true != (some @ (^[Y0 : nat]: (x = (suc @ Y0))))) | (sK1 != sK0)),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 1.60/1.31 thf(f17,plain,(
% 1.60/1.31 ((sK1 != sK0) & (x = (suc @ sK1)) & (x = (suc @ sK0))) | ($true != (some @ (^[Y0 : nat]: (x = (suc @ Y0)))))),
% 1.60/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16])).
% 1.60/1.31 thf(f16,plain,(
% 1.60/1.31 ? [X0 : nat,X1 : nat] : ((X0 != X1) & (x = (suc @ X1)) & (x = (suc @ X0))) => ((sK1 != sK0) & (x = (suc @ sK1)) & (x = (suc @ sK0)))),
% 1.60/1.31 introduced(definition,[],[choice_axiom])).
% 1.60/1.31 thf(f15,plain,(
% 1.60/1.31 ? [X0 : nat,X1 : nat] : ((X0 != X1) & (x = (suc @ X1)) & (x = (suc @ X0))) | ($true != (some @ (^[Y0 : nat]: (x = (suc @ Y0)))))),
% 1.60/1.31 inference(flattening,[status(thm)],[f14])).
% 1.60/1.31 thf(f14,plain,(
% 1.60/1.31 ($true != (some @ (^[Y0 : nat]: (x = (suc @ Y0))))) | ? [X0 : nat,X1 : nat] : (((X0 != X1) & (x = (suc @ X1))) & (x = (suc @ X0)))),
% 1.60/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.60/1.31 thf(f11,plain,(
% 1.60/1.31 ! [X0 : nat,X1 : nat] : ((x = (suc @ X0)) => ((x = (suc @ X1)) => (X0 = X1))) => ($true != (some @ (^[Y0 : nat]: (x = (suc @ Y0)))))),
% 1.60/1.31 inference(flattening,[status(thm)],[f8])).
% 1.60/1.31 thf(f8,plain,(
% 1.60/1.31 ~~(! [X0 : nat,X1 : nat] : ((x = (suc @ X0)) => ((x = (suc @ X1)) => (X0 = X1))) => ~($true = (some @ (^[Y0 : nat]: (x = (suc @ Y0))))))),
% 1.60/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.60/1.31 thf(f7,plain,(
% 1.60/1.31 ~~(! [X0 : nat,X1 : nat] : ((x = (suc @ X0)) => ((x = (suc @ X1)) => (X0 = X1))) => ~(some @ (^[X2 : nat] : ((x = (suc @ X2))))))),
% 1.60/1.31 inference(rectify,[status(thm)],[f5])).
% 1.60/1.31 thf(f5,negated_conjecture,(
% 1.60/1.31 ~~(! [X3 : nat,X1 : nat] : ((x = (suc @ X3)) => ((x = (suc @ X1)) => (X1 = X3))) => ~(some @ (^[X2 : nat] : ((x = (suc @ X2))))))),
% 1.60/1.31 inference(negated_conjecture,[status(cth)],[f4])).
% 1.60/1.31 thf(f4,conjecture,(
% 1.60/1.31 ~(! [X3 : nat,X1 : nat] : ((x = (suc @ X3)) => ((x = (suc @ X1)) => (X1 = X3))) => ~(some @ (^[X2 : nat] : ((x = (suc @ X2))))))),
% 1.60/1.31 file('/export/starexec/sandbox/tmp/tmp.j6pKbE1kZ5/DTF2THF_22214.p',satz3a)).
% 1.60/1.31 thf(f37,plain,(
% 1.60/1.31 ~spl2_2 | spl2_3),
% 1.60/1.31 inference(avatar_split_clause,[status(thm)],[f20,f34,f29])).
% 1.60/1.31 thf(f20,plain,(
% 1.60/1.31 (x = (suc @ sK1)) | ($true != (some @ (^[Y0 : nat]: (x = (suc @ Y0)))))),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 1.60/1.31 thf(f32,plain,(
% 1.60/1.31 spl2_1 | ~spl2_2),
% 1.60/1.31 inference(avatar_split_clause,[status(thm)],[f19,f29,f25])).
% 1.60/1.31 thf(f19,plain,(
% 1.60/1.31 (x = (suc @ sK0)) | ($true != (some @ (^[Y0 : nat]: (x = (suc @ Y0)))))),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 1.60/1.31 % SZS output end Proof for DTF2THF_22214
% 1.60/1.31 % (22322)------------------------------
% 1.60/1.31 % (22322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (22322)Termination reason: Refutation
% 1.60/1.31
% 1.60/1.31 % (22322)Memory used [KB]: 5500
% 1.60/1.31 % (22322)Time elapsed: 0.009 s
% 1.60/1.31 % (22322)Instructions burned: 8 (million)
% 1.60/1.31 % (22322)------------------------------
% 1.60/1.31 % (22322)------------------------------
% 1.60/1.31 % (22321)Success in time 0.022 s
%------------------------------------------------------------------------------