%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM651^1 : 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 : n029.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 09:24:06 AM UTC 2026
% Result : Theorem 1.80s 1.50s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 14 unt; 0 typ; 5 def)
% Number of atoms : 141 ( 98 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 352 ( 94 ~; 43 |; 12 &; 174 @)
% ( 5 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 50 !; 16 ?; 66 :)
% 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,
pl: nat > nat > nat ).
thf(func_def_7,type,
sK0: nat ).
thf(func_def_8,type,
sK1: nat ).
thf(func_def_9,type,
sK2: nat ).
thf(func_def_10,type,
sK3: nat ).
thf(f157,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f54,f67,f68,f77,f138,f146,f156]) ).
thf(f156,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f155]) ).
thf(f155,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(subsumption_resolution,[status(thm)],[f147,f71]) ).
thf(f71,plain,
! [X0: nat,X1: nat] :
( ( pl @ X1 @ X0 )
!= X1 ),
inference(superposition,[status(thm)],[f35,f36]) ).
thf(f36,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.oK7Tg7E792/DTF2THF_27999.p',satz6) ).
thf(f35,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
!= X1 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
!= X1 ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: nat,X0: nat] :
( ( pl @ X1 @ X0 )
!= X0 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
!= X1 ),
file('/export/starexec/sandbox/tmp/tmp.oK7Tg7E792/DTF2THF_27999.p',satz7) ).
thf(f147,plain,
( ( x
= ( pl @ x @ sK0 ) )
| ~ spl4_1
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f58,f44]) ).
thf(f44,plain,
( ( x = y )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl4_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f58,plain,
( ( x
= ( pl @ y @ sK0 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl4_4
<=> ( x
= ( pl @ y @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f146,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f145]) ).
thf(f145,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(subsumption_resolution,[status(thm)],[f142,f44]) ).
thf(f142,plain,
( ( x != y )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f71,f52]) ).
thf(f52,plain,
( ( y
= ( pl @ x @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl4_3
<=> ( y
= ( pl @ x @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f138,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f137]) ).
thf(f137,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
( ( x != x )
| ~ spl4_2
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f118,f48]) ).
thf(f48,plain,
( ( x
= ( pl @ y @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl4_2
<=> ( x
= ( pl @ y @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f118,plain,
( ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) )
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f112,f36]) ).
thf(f112,plain,
( ! [X0: nat] :
( x
!= ( pl @ X0 @ y ) )
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f90,f64]) ).
thf(f64,plain,
( ( y
= ( pl @ x @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f62,definition,
( spl4_5
<=> ( y
= ( pl @ x @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f90,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ X2 @ ( pl @ X1 @ X0 ) )
!= X1 ),
inference(superposition,[status(thm)],[f89,f36]) ).
thf(f89,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ X0 @ ( pl @ X1 @ X2 ) )
!= X2 ),
inference(superposition,[status(thm)],[f35,f37]) ).
thf(f37,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ ( pl @ X1 @ X2 ) @ X0 )
= ( pl @ X1 @ ( pl @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( pl @ ( pl @ X1 @ X2 ) @ X0 )
= ( pl @ X1 @ ( pl @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( pl @ ( pl @ X0 @ X2 ) @ X1 )
= ( pl @ X0 @ ( pl @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: nat,X3: nat,X1: nat] :
( ( pl @ ( pl @ X0 @ X1 ) @ X3 )
= ( pl @ X0 @ ( pl @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oK7Tg7E792/DTF2THF_27999.p',satz5) ).
thf(f77,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f74,f62,f42]) ).
thf(f74,plain,
( ( x != y )
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f71,f64]) ).
thf(f68,plain,
( spl4_5
| spl4_4
| spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f30,f50,f56,f62]) ).
thf(f30,plain,
( ( y
= ( pl @ x @ sK2 ) )
| ( y
= ( pl @ x @ sK1 ) )
| ( x
= ( pl @ y @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( x = y )
& ( x
= ( pl @ y @ sK0 ) ) )
| ( ( y
= ( pl @ x @ sK1 ) )
& ( x = y ) )
| ( ( y
= ( pl @ x @ sK2 ) )
& ( x
= ( pl @ y @ sK3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f22,f21,f20,f19]) ).
thf(f19,plain,
( ? [X0: nat] :
( x
= ( pl @ y @ X0 ) )
=> ( x
= ( pl @ y @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X1: nat] :
( y
= ( pl @ x @ X1 ) )
=> ( y
= ( pl @ x @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X2: nat] :
( y
= ( pl @ x @ X2 ) )
=> ( y
= ( pl @ x @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X3: nat] :
( x
= ( pl @ y @ X3 ) )
=> ( x
= ( pl @ y @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( ( x = y )
& ? [X0: nat] :
( x
= ( pl @ y @ X0 ) ) )
| ( ? [X1: nat] :
( y
= ( pl @ x @ X1 ) )
& ( x = y ) )
| ( ? [X2: nat] :
( y
= ( pl @ x @ X2 ) )
& ? [X3: nat] :
( x
= ( pl @ y @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( x = y )
& ? [X0: nat] :
( x
= ( pl @ y @ X0 ) ) )
| ( ? [X3: nat] :
( y
= ( pl @ x @ X3 ) )
& ( x = y ) )
| ( ? [X2: nat] :
( y
= ( pl @ x @ X2 ) )
& ? [X1: nat] :
( x
= ( pl @ y @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ? [X3: nat] :
( y
= ( pl @ x @ X3 ) )
& ( x = y ) )
| ( ? [X2: nat] :
( y
= ( pl @ x @ X2 ) )
& ? [X1: nat] :
( x
= ( pl @ y @ X1 ) ) )
| ( ( x = y )
& ? [X0: nat] :
( x
= ( pl @ y @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( x = y )
=> ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ) )
=> ( ( ~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) )
=> ! [X2: nat] :
( y
!= ( pl @ x @ X2 ) ) )
=> ~ ( ~ ! [X3: nat] :
( y
!= ( pl @ x @ X3 ) )
=> ( x != y ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ) )
=> ~ ~ ( ( ~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) )
=> ~ ~ ! [X2: nat] :
( y
!= ( pl @ x @ X2 ) ) )
=> ~ ( ~ ! [X3: nat] :
( y
!= ( pl @ x @ X3 ) )
=> ( x != y ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X4: nat] :
( x
!= ( pl @ y @ X4 ) ) )
=> ~ ~ ( ( ~ ! [X4: nat] :
( x
!= ( pl @ y @ X4 ) )
=> ~ ~ ! [X4: nat] :
( y
!= ( pl @ x @ X4 ) ) )
=> ~ ( ~ ! [X4: nat] :
( y
!= ( pl @ x @ X4 ) )
=> ( x != y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
~ ( ( ( x = y )
=> ~ ~ ! [X4: nat] :
( x
!= ( pl @ y @ X4 ) ) )
=> ~ ~ ( ( ~ ! [X4: nat] :
( x
!= ( pl @ y @ X4 ) )
=> ~ ~ ! [X4: nat] :
( y
!= ( pl @ x @ X4 ) ) )
=> ~ ( ~ ! [X4: nat] :
( y
!= ( pl @ x @ X4 ) )
=> ( x != y ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oK7Tg7E792/DTF2THF_27999.p',satz9b) ).
thf(f67,plain,
( spl4_1
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f39,f62,f42]) ).
thf(f39,plain,
( ( y
= ( pl @ x @ sK2 ) )
| ( x = y ) ),
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( x = y )
| ( y
= ( pl @ x @ sK2 ) )
| ( x = y ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f54,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f40,f42,f46]) ).
thf(f40,plain,
( ( x = y )
| ( x
= ( pl @ y @ sK3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( x
= ( pl @ y @ sK3 ) )
| ( x = y )
| ( x = y ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM651^1 : 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 : n029.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 11:09:29 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
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : NUM651^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.47 % Domain : Number Theory
% 0.19/0.47 % Problem : Landau theorem 9b
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English : ~((x = y -> ~(~(forall x_0:nat.~(x = pl y x_0)))) ->
% 0.19/0.47 % ~(~((~(forall x_0:nat.~(x = pl y x_0)) ->
% 0.19/0.47 % ~(~(forall x_0:nat.~(y = pl x x_0)))) ->
% 0.19/0.47 % ~(~(forall x_0:nat.~(y = pl x x_0)) -> ~(x = y)))))
% 0.19/0.47
% 0.19/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : satz9b [Lan30]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % : Without extensionality : Theorem
% 0.19/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.19/0.47 % Syntax : Number of formulae : 9 ( 3 unt; 4 typ; 0 def)
% 0.19/0.47 % Number of atoms : 9 ( 9 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 6 ( 1 avg)
% 0.19/0.47 % Number of connectives : 46 ( 18 ~; 0 |; 0 &; 22 @)
% 0.19/0.47 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 11 ( 5 avg)
% 0.19/0.47 % Number of types : 2 ( 1 usr)
% 0.19/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments :
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(nat_type,type,
% 0.19/0.47 nat: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(x,type,
% 0.19/0.47 x: nat ).
% 0.19/0.47
% 0.19/0.47 thf(y,type,
% 0.19/0.47 y: nat ).
% 0.19/0.47
% 0.19/0.47 thf(pl,type,
% 0.19/0.47 pl: nat > nat > nat ).
% 0.19/0.47
% 0.19/0.47 thf(satz7,axiom,
% 0.19/0.47 ! [Xx: nat,Xy: nat] :
% 0.19/0.47 ( Xy
% 0.19/0.47 != ( pl @ Xx @ Xy ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(satz6,axiom,
% 0.19/0.47 ! [Xx: nat,Xy: nat] :
% 0.19/0.47 ( ( pl @ Xx @ Xy )
% 0.19/0.47 = ( pl @ Xy @ Xx ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(et,axiom,
% 0.19/0.47 ! [Xa: $o] :
% 0.19/0.47 ( ~ ~ Xa
% 0.19/0.47 => Xa ) ).
% 0.19/0.47
% 0.19/0.47 thf(satz5,axiom,
% 0.19/0.47 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.19/0.47 ( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
% 0.19/0.47 = ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(satz9b,conjecture,
% 0.19/0.47 ~ ( ( ( x = y )
% 0.19/0.47 => ~ ~ ! [Xx_0: nat] :
% 0.19/0.47 ( x
% 0.19/0.47 != ( pl @ y @ Xx_0 ) ) )
% 0.19/0.47 => ~ ~ ( ( ~ ! [Xx_0: nat] :
% 0.19/0.47 ( x
% 0.19/0.47 != ( pl @ y @ Xx_0 ) )
% 0.19/0.47 => ~ ~ ! [Xx_0: nat] :
% 0.19/0.47 ( y
% 0.19/0.47 != ( pl @ x @ Xx_0 ) ) )
% 0.19/0.47 => ~ ( ~ ! [Xx_0: nat] :
% 0.19/0.47 ( y
% 0.19/0.47 != ( pl @ x @ Xx_0 ) )
% 0.19/0.47 => ( x != y ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.68/1.46 ---- Embedded in THF ---
% 1.68/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.46 %%% Generated on Tue Feb 24 11:09:30 EST 2026
% 1.68/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.46 %%% Logic specification used:
% 1.68/1.46 %%% thf(spec, logic, $$dhol).
% 1.68/1.46
% 1.68/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oK7Tg7E792/DTF2DTF27999.p
% See solution above
% 1.68/1.46 ------------------------
% 1.68/1.47 ---- Cleaned THF ---
% 1.68/1.47 thf(nat_type,type,
% 1.68/1.47 nat: $tType ).
% 1.68/1.47
% 1.68/1.47 thf(x,type,
% 1.68/1.47 x: nat ).
% 1.68/1.47
% 1.68/1.47 thf(y,type,
% 1.68/1.47 y: nat ).
% 1.68/1.47
% 1.68/1.47 thf(pl,type,
% 1.68/1.47 pl: nat > nat > nat ).
% 1.68/1.47
% 1.68/1.47 thf(satz7,axiom,
% 1.68/1.47 ! [Xx: nat,Xy: nat] :
% 1.68/1.47 ( Xy
% 1.68/1.47 != ( pl @ Xx @ Xy ) ) ).
% 1.68/1.47
% 1.68/1.47 thf(satz6,axiom,
% 1.68/1.47 ! [Xx: nat,Xy: nat] :
% 1.68/1.47 ( ( pl @ Xx @ Xy )
% 1.68/1.47 = ( pl @ Xy @ Xx ) ) ).
% 1.68/1.47
% 1.68/1.47 thf(et,axiom,
% 1.68/1.47 ! [Xa: $o] :
% 1.68/1.47 ( ~ ~ Xa
% 1.68/1.47 => Xa ) ).
% 1.68/1.47
% 1.68/1.47 thf(satz5,axiom,
% 1.68/1.47 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.68/1.47 ( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
% 1.68/1.47 = ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) ).
% 1.68/1.47
% 1.68/1.47 thf(satz9b,conjecture,
% 1.68/1.47 ~ ( ( ( x = y )
% 1.68/1.47 => ~ ~ ! [Xx_0: nat] :
% 1.68/1.47 ( x
% 1.68/1.47 != ( pl @ y @ Xx_0 ) ) )
% 1.68/1.47 => ~ ~ ( ( ~ ! [Xx_0: nat] :
% 1.68/1.47 ( x
% 1.68/1.47 != ( pl @ y @ Xx_0 ) )
% 1.68/1.47 => ~ ~ ! [Xx_0: nat] :
% 1.68/1.47 ( y
% 1.68/1.47 != ( pl @ x @ Xx_0 ) ) )
% 1.68/1.47 => ~ ( ~ ! [Xx_0: nat] :
% 1.68/1.47 ( y
% 1.68/1.47 != ( pl @ x @ Xx_0 ) )
% 1.68/1.47 => ( x != y ) ) ) ) ).
% 1.68/1.47 ------------------------
% 1.68/1.49 % (28139)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27999 for (2999ds/18Mi)
% 1.68/1.49 % (28133)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27999 for (2999ds/183Mi)
% 1.68/1.49 % (28137)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_27999 for (2999ds/2Mi)
% 1.68/1.49 % (28135)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_27999 for (2999ds/27Mi)
% 1.68/1.49 % (28138)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_27999 for (2999ds/275Mi)
% 1.68/1.49 % (28134)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_27999 for (2999ds/4Mi)
% 1.68/1.49 % (28136)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27999 for (2999ds/2Mi)
% 1.68/1.49 % (28136)Instruction limit reached!
% 1.68/1.49 % (28136)------------------------------
% 1.68/1.49 % (28136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.49 % (28136)Termination reason: Unknown
% 1.68/1.49 % (28136)Termination phase: Property scanning
% 1.68/1.49
% 1.68/1.49 % (28136)Memory used [KB]: 895
% 1.68/1.49 % (28136)Time elapsed: 0.003 s
% 1.68/1.49 % (28136)Instructions burned: 2 (million)
% 1.68/1.49 % (28136)------------------------------
% 1.68/1.49 % (28136)------------------------------
% 1.68/1.49 % (28137)Instruction limit reached!
% 1.68/1.49 % (28137)------------------------------
% 1.68/1.49 % (28137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.49 % (28137)Termination reason: Unknown
% 1.68/1.49 % (28137)Termination phase: Property scanning
% 1.68/1.49
% 1.68/1.49 % (28137)Memory used [KB]: 895
% 1.68/1.49 % (28137)Time elapsed: 0.003 s
% 1.68/1.49 % (28137)Instructions burned: 2 (million)
% 1.68/1.49 % (28137)------------------------------
% 1.68/1.49 % (28137)------------------------------
% 1.68/1.49 % (28134)Instruction limit reached!
% 1.68/1.49 % (28134)------------------------------
% 1.68/1.49 % (28134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.49 % (28134)Termination reason: Unknown
% 1.68/1.49 % (28134)Termination phase: Saturation
% 1.68/1.49
% 1.68/1.49 % (28134)Memory used [KB]: 5500
% 1.68/1.49 % (28134)Time elapsed: 0.005 s
% 1.68/1.49 % (28134)Instructions burned: 5 (million)
% 1.68/1.49 % (28134)------------------------------
% 1.68/1.49 % (28134)------------------------------
% 1.80/1.50 % (28133)First to succeed.
% 1.80/1.50 % (28139)Instruction limit reached!
% 1.80/1.50 % (28139)------------------------------
% 1.80/1.50 % (28139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.50 % (28139)Termination reason: Unknown
% 1.80/1.50 % (28139)Termination phase: Saturation
% 1.80/1.50
% 1.80/1.50 % (28139)Memory used [KB]: 5628
% 1.80/1.50 % (28139)Time elapsed: 0.012 s
% 1.80/1.50 % (28139)Instructions burned: 18 (million)
% 1.80/1.50 % (28139)------------------------------
% 1.80/1.50 % (28139)------------------------------
% 1.80/1.50 % (28133)Refutation found. Thanks to Tanya!
% 1.80/1.50 % SZS status Theorem for DTF2THF_27999
% 1.80/1.50 % SZS output start Proof for DTF2THF_27999
% 1.80/1.50 thf(type_def_5, type, nat: $tType).
% 1.80/1.50 thf(func_def_0, type, nat: $tType).
% 1.80/1.50 thf(func_def_1, type, x: nat).
% 1.80/1.50 thf(func_def_2, type, y: nat).
% 1.80/1.50 thf(func_def_3, type, pl: nat > nat > nat).
% 1.80/1.50 thf(func_def_7, type, sK0: nat).
% 1.80/1.50 thf(func_def_8, type, sK1: nat).
% 1.80/1.50 thf(func_def_9, type, sK2: nat).
% 1.80/1.50 thf(func_def_10, type, sK3: nat).
% 1.80/1.50 thf(f157,plain,(
% 1.80/1.50 $false),
% 1.80/1.50 inference(avatar_sat_refutation,[status(thm)],[f54,f67,f68,f77,f138,f146,f156])).
% 1.80/1.50 thf(f156,plain,(
% 1.80/1.50 ~spl4_1 | ~spl4_4),
% 1.80/1.50 inference(avatar_contradiction_clause,[status(thm)],[f155])).
% 1.80/1.50 thf(f155,plain,(
% 1.80/1.50 $false | (~spl4_1 | ~spl4_4)),
% 1.80/1.50 inference(subsumption_resolution,[status(thm)],[f147,f71])).
% 1.80/1.50 thf(f71,plain,(
% 1.80/1.50 ( ! [X0 : nat,X1 : nat] : (((pl @ X1 @ X0) != X1)) )),
% 1.80/1.50 inference(superposition,[status(thm)],[f35,f36])).
% 1.80/1.50 thf(f36,plain,(
% 1.80/1.50 ( ! [X0 : nat,X1 : nat] : (((pl @ X0 @ X1) = (pl @ X1 @ X0))) )),
% 1.80/1.50 inference(cnf_transformation,[status(thm)],[f2])).
% 1.80/1.50 thf(f2,axiom,(
% 1.80/1.50 ! [X0 : nat,X1 : nat] : ((pl @ X0 @ X1) = (pl @ X1 @ X0))),
% 1.80/1.50 file('/export/starexec/sandbox/tmp/tmp.oK7Tg7E792/DTF2THF_27999.p',satz6)).
% 1.80/1.50 thf(f35,plain,(
% 1.80/1.50 ( ! [X0 : nat,X1 : nat] : (((pl @ X0 @ X1) != X1)) )),
% 1.80/1.50 inference(cnf_transformation,[status(thm)],[f24])).
% 1.80/1.50 thf(f24,plain,(
% 1.80/1.50 ! [X0 : nat,X1 : nat] : ((pl @ X0 @ X1) != X1)),
% 1.80/1.50 inference(rectify,[status(thm)],[f11])).
% 1.80/1.50 thf(f11,plain,(
% 1.80/1.50 ! [X1 : nat,X0 : nat] : ((pl @ X1 @ X0) != X0)),
% 1.80/1.50 inference(rectify,[status(thm)],[f1])).
% 1.80/1.50 thf(f1,axiom,(
% 1.80/1.50 ! [X1 : nat,X0 : nat] : ((pl @ X0 @ X1) != X1)),
% 1.80/1.50 file('/export/starexec/sandbox/tmp/tmp.oK7Tg7E792/DTF2THF_27999.p',satz7)).
% 1.80/1.50 thf(f147,plain,(
% 1.80/1.50 (x = (pl @ x @ sK0)) | (~spl4_1 | ~spl4_4)),
% 1.80/1.50 inference(superposition,[status(thm)],[f58,f44])).
% 1.80/1.50 thf(f44,plain,(
% 1.80/1.50 (x = y) | ~spl4_1),
% 1.80/1.50 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.80/1.50 thf(f42,definition,(
% 1.80/1.50 spl4_1 <=> (x = y)),
% 1.80/1.50 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.80/1.50 thf(f58,plain,(
% 1.80/1.50 (x = (pl @ y @ sK0)) | ~spl4_4),
% 1.80/1.50 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.80/1.50 thf(f56,definition,(
% 1.80/1.50 spl4_4 <=> (x = (pl @ y @ sK0))),
% 1.80/1.50 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.80/1.50 thf(f146,plain,(
% 1.80/1.50 ~spl4_1 | ~spl4_3),
% 1.80/1.50 inference(avatar_contradiction_clause,[status(thm)],[f145])).
% 1.80/1.50 thf(f145,plain,(
% 1.80/1.50 $false | (~spl4_1 | ~spl4_3)),
% 1.80/1.50 inference(subsumption_resolution,[status(thm)],[f142,f44])).
% 1.80/1.50 thf(f142,plain,(
% 1.80/1.50 (x != y) | ~spl4_3),
% 1.80/1.50 inference(superposition,[status(thm)],[f71,f52])).
% 1.80/1.50 thf(f52,plain,(
% 1.80/1.50 (y = (pl @ x @ sK1)) | ~spl4_3),
% 1.80/1.50 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.80/1.50 thf(f50,definition,(
% 1.80/1.50 spl4_3 <=> (y = (pl @ x @ sK1))),
% 1.80/1.50 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.80/1.50 thf(f138,plain,(
% 1.80/1.50 ~spl4_2 | ~spl4_5),
% 1.80/1.50 inference(avatar_contradiction_clause,[status(thm)],[f137])).
% 1.80/1.50 thf(f137,plain,(
% 1.80/1.50 $false | (~spl4_2 | ~spl4_5)),
% 1.80/1.50 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 1.80/1.50 thf(f134,plain,(
% 1.80/1.50 (x != x) | (~spl4_2 | ~spl4_5)),
% 1.80/1.50 inference(superposition,[status(thm)],[f118,f48])).
% 1.80/1.50 thf(f48,plain,(
% 1.80/1.50 (x = (pl @ y @ sK3)) | ~spl4_2),
% 1.80/1.50 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.80/1.50 thf(f46,definition,(
% 1.80/1.50 spl4_2 <=> (x = (pl @ y @ sK3))),
% 1.80/1.50 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.80/1.50 thf(f118,plain,(
% 1.80/1.50 ( ! [X0 : nat] : ((x != (pl @ y @ X0))) ) | ~spl4_5),
% 1.80/1.50 inference(superposition,[status(thm)],[f112,f36])).
% 1.80/1.50 thf(f112,plain,(
% 1.80/1.50 ( ! [X0 : nat] : ((x != (pl @ X0 @ y))) ) | ~spl4_5),
% 1.80/1.50 inference(superposition,[status(thm)],[f90,f64])).
% 1.80/1.50 thf(f64,plain,(
% 1.80/1.50 (y = (pl @ x @ sK2)) | ~spl4_5),
% 1.80/1.50 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.80/1.50 thf(f62,definition,(
% 1.80/1.50 spl4_5 <=> (y = (pl @ x @ sK2))),
% 1.80/1.50 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.80/1.50 thf(f90,plain,(
% 1.80/1.50 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((pl @ X2 @ (pl @ X1 @ X0)) != X1)) )),
% 1.80/1.50 inference(superposition,[status(thm)],[f89,f36])).
% 1.80/1.50 thf(f89,plain,(
% 1.80/1.50 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((pl @ X0 @ (pl @ X1 @ X2)) != X2)) )),
% 1.80/1.50 inference(superposition,[status(thm)],[f35,f37])).
% 1.80/1.50 thf(f37,plain,(
% 1.80/1.50 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((pl @ (pl @ X1 @ X2) @ X0) = (pl @ X1 @ (pl @ X2 @ X0)))) )),
% 1.80/1.50 inference(cnf_transformation,[status(thm)],[f25])).
% 1.80/1.50 thf(f25,plain,(
% 1.80/1.50 ! [X0 : nat,X1 : nat,X2 : nat] : ((pl @ (pl @ X1 @ X2) @ X0) = (pl @ X1 @ (pl @ X2 @ X0)))),
% 1.80/1.50 inference(rectify,[status(thm)],[f10])).
% 1.80/1.50 thf(f10,plain,(
% 1.80/1.50 ! [X1 : nat,X0 : nat,X2 : nat] : ((pl @ (pl @ X0 @ X2) @ X1) = (pl @ X0 @ (pl @ X2 @ X1)))),
% 1.80/1.50 inference(rectify,[status(thm)],[f4])).
% 1.80/1.50 thf(f4,axiom,(
% 1.80/1.50 ! [X0 : nat,X3 : nat,X1 : nat] : ((pl @ (pl @ X0 @ X1) @ X3) = (pl @ X0 @ (pl @ X1 @ X3)))),
% 1.80/1.50 file('/export/starexec/sandbox/tmp/tmp.oK7Tg7E792/DTF2THF_27999.p',satz5)).
% 1.80/1.50 thf(f77,plain,(
% 1.80/1.50 ~spl4_1 | ~spl4_5),
% 1.80/1.50 inference(avatar_split_clause,[status(thm)],[f74,f62,f42])).
% 1.80/1.50 thf(f74,plain,(
% 1.80/1.50 (x != y) | ~spl4_5),
% 1.80/1.50 inference(superposition,[status(thm)],[f71,f64])).
% 1.80/1.50 thf(f68,plain,(
% 1.80/1.50 spl4_5 | spl4_4 | spl4_3),
% 1.80/1.50 inference(avatar_split_clause,[status(thm)],[f30,f50,f56,f62])).
% 1.80/1.50 thf(f30,plain,(
% 1.80/1.50 (y = (pl @ x @ sK2)) | (y = (pl @ x @ sK1)) | (x = (pl @ y @ sK0))),
% 1.80/1.50 inference(cnf_transformation,[status(thm)],[f23])).
% 1.80/1.50 thf(f23,plain,(
% 1.80/1.50 ((x = y) & (x = (pl @ y @ sK0))) | ((y = (pl @ x @ sK1)) & (x = y)) | ((y = (pl @ x @ sK2)) & (x = (pl @ y @ sK3)))),
% 1.80/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f22,f21,f20,f19])).
% 1.80/1.50 thf(f19,plain,(
% 1.80/1.50 ? [X0 : nat] : (x = (pl @ y @ X0)) => (x = (pl @ y @ sK0))),
% 1.80/1.50 introduced(definition,[],[choice_axiom])).
% 1.80/1.50 thf(f20,plain,(
% 1.80/1.50 ? [X1 : nat] : (y = (pl @ x @ X1)) => (y = (pl @ x @ sK1))),
% 1.80/1.50 introduced(definition,[],[choice_axiom])).
% 1.80/1.50 thf(f21,plain,(
% 1.80/1.50 ? [X2 : nat] : (y = (pl @ x @ X2)) => (y = (pl @ x @ sK2))),
% 1.80/1.50 introduced(definition,[],[choice_axiom])).
% 1.80/1.50 thf(f22,plain,(
% 1.80/1.50 ? [X3 : nat] : (x = (pl @ y @ X3)) => (x = (pl @ y @ sK3))),
% 1.80/1.50 introduced(definition,[],[choice_axiom])).
% 1.80/1.50 thf(f18,plain,(
% 1.80/1.50 ((x = y) & ? [X0 : nat] : (x = (pl @ y @ X0))) | (? [X1 : nat] : (y = (pl @ x @ X1)) & (x = y)) | (? [X2 : nat] : (y = (pl @ x @ X2)) & ? [X3 : nat] : (x = (pl @ y @ X3)))),
% 1.80/1.50 inference(rectify,[status(thm)],[f17])).
% 1.80/1.50 thf(f17,plain,(
% 1.80/1.50 ((x = y) & ? [X0 : nat] : (x = (pl @ y @ X0))) | (? [X3 : nat] : (y = (pl @ x @ X3)) & (x = y)) | (? [X2 : nat] : (y = (pl @ x @ X2)) & ? [X1 : nat] : (x = (pl @ y @ X1)))),
% 1.80/1.50 inference(flattening,[status(thm)],[f16])).
% 1.80/1.50 thf(f16,plain,(
% 1.80/1.50 ((? [X3 : nat] : (y = (pl @ x @ X3)) & (x = y)) | (? [X2 : nat] : (y = (pl @ x @ X2)) & ? [X1 : nat] : (x = (pl @ y @ X1)))) | ((x = y) & ? [X0 : nat] : (x = (pl @ y @ X0)))),
% 1.80/1.50 inference(ennf_transformation,[status(thm)],[f13])).
% 1.80/1.50 thf(f13,plain,(
% 1.80/1.50 ((x = y) => ! [X0 : nat] : (x != (pl @ y @ X0))) => ((~! [X1 : nat] : (x != (pl @ y @ X1)) => ! [X2 : nat] : (y != (pl @ x @ X2))) => ~(~! [X3 : nat] : (y != (pl @ x @ X3)) => (x != y)))),
% 1.80/1.50 inference(flattening,[status(thm)],[f12])).
% 1.80/1.50 thf(f12,plain,(
% 1.80/1.50 ~~(((x = y) => ~~! [X0 : nat] : (x != (pl @ y @ X0))) => ~~((~! [X1 : nat] : (x != (pl @ y @ X1)) => ~~! [X2 : nat] : (y != (pl @ x @ X2))) => ~(~! [X3 : nat] : (y != (pl @ x @ X3)) => (x != y))))),
% 1.80/1.50 inference(rectify,[status(thm)],[f6])).
% 1.80/1.50 thf(f6,negated_conjecture,(
% 1.80/1.50 ~~(((x = y) => ~~! [X4 : nat] : (x != (pl @ y @ X4))) => ~~((~! [X4 : nat] : (x != (pl @ y @ X4)) => ~~! [X4 : nat] : (y != (pl @ x @ X4))) => ~(~! [X4 : nat] : (y != (pl @ x @ X4)) => (x != y))))),
% 1.80/1.50 inference(negated_conjecture,[status(cth)],[f5])).
% 1.80/1.50 thf(f5,conjecture,(
% 1.80/1.50 ~(((x = y) => ~~! [X4 : nat] : (x != (pl @ y @ X4))) => ~~((~! [X4 : nat] : (x != (pl @ y @ X4)) => ~~! [X4 : nat] : (y != (pl @ x @ X4))) => ~(~! [X4 : nat] : (y != (pl @ x @ X4)) => (x != y))))),
% 1.80/1.50 file('/export/starexec/sandbox/tmp/tmp.oK7Tg7E792/DTF2THF_27999.p',satz9b)).
% 1.80/1.50 thf(f67,plain,(
% 1.80/1.50 spl4_1 | spl4_5),
% 1.80/1.50 inference(avatar_split_clause,[status(thm)],[f39,f62,f42])).
% 1.80/1.50 thf(f39,plain,(
% 1.80/1.50 (y = (pl @ x @ sK2)) | (x = y)),
% 1.80/1.50 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.80/1.50 thf(f32,plain,(
% 1.80/1.50 (x = y) | (y = (pl @ x @ sK2)) | (x = y)),
% 1.80/1.50 inference(cnf_transformation,[status(thm)],[f23])).
% 1.80/1.50 thf(f54,plain,(
% 1.80/1.50 spl4_2 | spl4_1),
% 1.80/1.50 inference(avatar_split_clause,[status(thm)],[f40,f42,f46])).
% 1.80/1.50 thf(f40,plain,(
% 1.80/1.50 (x = y) | (x = (pl @ y @ sK3))),
% 1.80/1.50 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 1.80/1.50 thf(f31,plain,(
% 1.80/1.50 (x = (pl @ y @ sK3)) | (x = y) | (x = y)),
% 1.80/1.50 inference(cnf_transformation,[status(thm)],[f23])).
% 1.80/1.50 % SZS output end Proof for DTF2THF_27999
% 1.80/1.50 % (28133)------------------------------
% 1.80/1.50 % (28133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.50 % (28133)Termination reason: Refutation
% 1.80/1.50
% 1.80/1.50 % (28133)Memory used [KB]: 5628
% 1.80/1.50 % (28133)Time elapsed: 0.013 s
% 1.80/1.50 % (28133)Instructions burned: 17 (million)
% 1.80/1.50 % (28133)------------------------------
% 1.80/1.50 % (28133)------------------------------
% 1.80/1.50 % (28132)Success in time 0.028 s
%------------------------------------------------------------------------------