%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM696^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 09:24:19 AM UTC 2026
% Result : Theorem 1.64s 1.30s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 60 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 257 ( 39 ~; 11 |; 1 &; 195 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 68 ( 0 ^; 61 !; 7 ?; 68 :)
% 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_5,type,
n_1: nat ).
thf(func_def_8,type,
sK0: nat ).
thf(func_def_9,type,
sK1: nat > nat > nat > nat ).
thf(func_def_10,type,
sK2: nat > nat ).
thf(f83,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( pl @ x @ n_1 )
!= ( pl @ x @ n_1 ) ),
inference(superposition,[status(thm)],[f36,f79]) ).
thf(f79,plain,
n_1 = sK0,
inference(equality_resolution,[status(thm)],[f76]) ).
thf(f76,plain,
! [X0: nat] :
( ( ( pl @ x @ X0 )
!= ( pl @ x @ sK0 ) )
| ( n_1 = X0 ) ),
inference(superposition,[status(thm)],[f72,f34]) ).
thf(f34,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: nat,X3: nat] :
( ( pl @ X2 @ X3 )
= ( pl @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',satz6) ).
thf(f72,plain,
! [X0: nat] :
( ( ( pl @ X0 @ x )
!= ( pl @ x @ sK0 ) )
| ( n_1 = X0 ) ),
inference(superposition,[status(thm)],[f37,f65]) ).
thf(f65,plain,
! [X0: nat,X1: nat] :
( ( ( pl @ ( pl @ X0 @ n_1 ) @ ( sK1 @ n_1 @ X1 @ X0 ) )
= ( pl @ X1 @ X0 ) )
| ( n_1 = X1 ) ),
inference(superposition,[status(thm)],[f44,f34]) ).
thf(f44,plain,
! [X0: nat,X1: nat] :
( ( ( pl @ ( pl @ n_1 @ X1 ) @ ( sK1 @ n_1 @ X0 @ X1 ) )
= ( pl @ X0 @ X1 ) )
| ( n_1 = X0 ) ),
inference(superposition,[status(thm)],[f39,f35]) ).
thf(f35,plain,
! [X0: nat] :
( ( ( pl @ n_1 @ ( sK2 @ X0 ) )
= X0 )
| ( n_1 = X0 ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: nat] :
( ( ( pl @ n_1 @ ( sK2 @ X0 ) )
= X0 )
| ( n_1 = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f27]) ).
thf(f27,plain,
! [X0: nat] :
( ? [X1: nat] :
( ( pl @ n_1 @ X1 )
= X0 )
=> ( ( pl @ n_1 @ ( sK2 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X0: nat] :
( ? [X1: nat] :
( ( pl @ n_1 @ X1 )
= X0 )
| ( n_1 = X0 ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat] :
( ! [X1: nat] :
( ( pl @ n_1 @ X1 )
!= X0 )
=> ( n_1 = X0 ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat] :
( ~ ~ ! [X1: nat] :
( ( pl @ n_1 @ X1 )
!= X0 )
=> ( n_1 = X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: nat] :
( ~ ~ ! [X0: nat] :
( ( pl @ n_1 @ X0 )
!= X2 )
=> ( n_1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',satz24) ).
thf(f39,plain,
! [X2: nat,X0: nat,X4: nat] :
( ( pl @ ( pl @ X2 @ X4 ) @ X0 )
= ( pl @ ( pl @ X2 @ X0 ) @ ( sK1 @ X2 @ ( pl @ X2 @ X4 ) @ X0 ) ) ),
inference(equality_resolution,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: nat,X0: nat,X1: nat,X4: nat] :
( ( ( pl @ ( pl @ X2 @ X0 ) @ ( sK1 @ X2 @ X1 @ X0 ) )
= ( pl @ X1 @ X0 ) )
| ( ( pl @ X2 @ X4 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( pl @ ( pl @ X2 @ X0 ) @ ( sK1 @ X2 @ X1 @ X0 ) )
= ( pl @ X1 @ X0 ) )
| ! [X4: nat] :
( ( pl @ X2 @ X4 )
!= X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f24,f25]) ).
thf(f25,plain,
! [X0: nat,X1: nat,X2: nat] :
( ? [X3: nat] :
( ( pl @ ( pl @ X2 @ X0 ) @ X3 )
= ( pl @ X1 @ X0 ) )
=> ( ( pl @ ( pl @ X2 @ X0 ) @ ( sK1 @ X2 @ X1 @ X0 ) )
= ( pl @ X1 @ X0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
! [X0: nat,X1: nat,X2: nat] :
( ? [X3: nat] :
( ( pl @ ( pl @ X2 @ X0 ) @ X3 )
= ( pl @ X1 @ X0 ) )
| ! [X4: nat] :
( ( pl @ X2 @ X4 )
!= X1 ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X2: nat,X1: nat] :
( ? [X4: nat] :
( ( pl @ ( pl @ X1 @ X0 ) @ X4 )
= ( pl @ X2 @ X0 ) )
| ! [X3: nat] :
( ( pl @ X1 @ X3 )
!= X2 ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat,X2: nat] :
( ~ ! [X3: nat] :
( ( pl @ X1 @ X3 )
!= X2 )
=> ~ ! [X4: nat] :
( ( pl @ ( pl @ X1 @ X0 ) @ X4 )
!= ( pl @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X4: nat,X3: nat,X2: nat] :
( ~ ! [X0: nat] :
( ( pl @ X3 @ X0 )
!= X2 )
=> ~ ! [X0: nat] :
( ( pl @ X2 @ X4 )
!= ( pl @ ( pl @ X3 @ X4 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',satz19a) ).
thf(f37,plain,
! [X0: nat] :
( ( pl @ ( pl @ x @ n_1 ) @ X0 )
!= ( pl @ x @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f30,f29]) ).
thf(f29,plain,
( y
= ( pl @ x @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( y
= ( pl @ x @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f22]) ).
thf(f22,plain,
( ? [X0: nat] :
( y
= ( pl @ x @ X0 ) )
=> ( y
= ( pl @ x @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
? [X0: nat] :
( y
= ( pl @ x @ X0 ) ),
inference(ennf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ! [X0: nat] :
( y
!= ( pl @ x @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',m) ).
thf(f30,plain,
! [X0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( y
!= ( pl @ x @ n_1 ) )
& ! [X0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ! [X0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X0 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( ~ ~ ! [X0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X0 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( ~ ~ ! [X0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X0 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',satz25) ).
thf(f36,plain,
( ( pl @ x @ n_1 )
!= ( pl @ x @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f31,f29]) ).
thf(f31,plain,
( y
!= ( pl @ x @ n_1 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM696^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n002.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 11:11:48 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : NUM696^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.45 % Domain : Number Theory
% 0.30/0.45 % Problem : Landau theorem 25
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English : ~(~(forall x_0:nat.~(y = pl (pl x n_1) x_0))) -> y = pl x n_1
% 0.30/0.45
% 0.30/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : satz25 [Lan30]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % : Without extensionality : Theorem
% 0.30/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 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
% 0.30/0.45 % Syntax : Number of formulae : 11 ( 2 unt; 5 typ; 0 def)
% 0.30/0.45 % Number of atoms : 8 ( 8 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 2 ( 1 avg)
% 0.30/0.45 % Number of connectives : 40 ( 14 ~; 0 |; 0 &; 22 @)
% 0.30/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 8 ( 6 avg)
% 0.30/0.45 % Number of types : 2 ( 1 usr)
% 0.30/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.30/0.45 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments :
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(nat_type,type,
% 0.30/0.45 nat: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(x,type,
% 0.30/0.45 x: nat ).
% 0.30/0.45
% 0.30/0.45 thf(y,type,
% 0.30/0.45 y: nat ).
% 0.30/0.45
% 0.30/0.45 thf(pl,type,
% 0.30/0.45 pl: nat > nat > nat ).
% 0.30/0.45
% 0.30/0.45 thf(m,axiom,
% 0.30/0.45 ~ ! [Xx_0: nat] :
% 0.30/0.45 ( y
% 0.30/0.45 != ( pl @ x @ Xx_0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(n_1,type,
% 0.30/0.45 n_1: nat ).
% 0.30/0.45
% 0.30/0.45 thf(et,axiom,
% 0.30/0.45 ! [Xa: $o] :
% 0.30/0.45 ( ~ ~ Xa
% 0.30/0.45 => Xa ) ).
% 0.30/0.45
% 0.30/0.45 thf(satz24,axiom,
% 0.30/0.45 ! [Xx: nat] :
% 0.30/0.45 ( ~ ~ ! [Xx_0: nat] :
% 0.30/0.45 ( Xx
% 0.30/0.45 != ( pl @ n_1 @ Xx_0 ) )
% 0.30/0.45 => ( Xx = n_1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(satz19a,axiom,
% 0.30/0.45 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.30/0.45 ( ~ ! [Xx_0: nat] :
% 0.30/0.45 ( Xx
% 0.30/0.45 != ( pl @ Xy @ Xx_0 ) )
% 0.30/0.45 => ~ ! [Xx_0: nat] :
% 0.30/0.45 ( ( pl @ Xx @ Xz )
% 0.30/0.45 != ( pl @ ( pl @ Xy @ Xz ) @ Xx_0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(satz6,axiom,
% 0.30/0.45 ! [Xx: nat,Xy: nat] :
% 0.30/0.45 ( ( pl @ Xx @ Xy )
% 0.30/0.45 = ( pl @ Xy @ Xx ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(satz25,conjecture,
% 0.30/0.45 ( ~ ~ ! [Xx_0: nat] :
% 0.30/0.45 ( y
% 0.30/0.45 != ( pl @ ( pl @ x @ n_1 ) @ Xx_0 ) )
% 0.30/0.45 => ( y
% 0.30/0.45 = ( pl @ x @ n_1 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.51/1.26 ---- Embedded in THF ---
% 1.51/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.26 %%% Generated on Tue Feb 24 11:11:49 EST 2026
% 1.51/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.26 %%% Logic specification used:
% 1.51/1.26 %%% thf(spec, logic, $$dhol).
% 1.51/1.26
% 1.51/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2DTF9796.p
% See solution above
% 1.51/1.26 ------------------------
% 1.51/1.27 ---- Cleaned THF ---
% 1.51/1.27 thf(nat_type,type,
% 1.51/1.27 nat: $tType ).
% 1.51/1.27
% 1.51/1.27 thf(x,type,
% 1.51/1.27 x: nat ).
% 1.51/1.27
% 1.51/1.27 thf(y,type,
% 1.51/1.27 y: nat ).
% 1.51/1.27
% 1.51/1.27 thf(pl,type,
% 1.51/1.27 pl: nat > nat > nat ).
% 1.51/1.27
% 1.51/1.27 thf(m,axiom,
% 1.51/1.27 ~ ! [Xx_0: nat] :
% 1.51/1.27 ( y
% 1.51/1.27 != ( pl @ x @ Xx_0 ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(n_1,type,
% 1.51/1.27 n_1: nat ).
% 1.51/1.27
% 1.51/1.27 thf(et,axiom,
% 1.51/1.27 ! [Xa: $o] :
% 1.51/1.27 ( ~ ~ Xa
% 1.51/1.27 => Xa ) ).
% 1.51/1.27
% 1.51/1.27 thf(satz24,axiom,
% 1.51/1.27 ! [Xx: nat] :
% 1.51/1.27 ( ~ ~ ! [Xx_0: nat] :
% 1.51/1.27 ( Xx
% 1.51/1.27 != ( pl @ n_1 @ Xx_0 ) )
% 1.51/1.27 => ( Xx = n_1 ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(satz19a,axiom,
% 1.51/1.27 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.51/1.27 ( ~ ! [Xx_0: nat] :
% 1.51/1.27 ( Xx
% 1.51/1.27 != ( pl @ Xy @ Xx_0 ) )
% 1.51/1.27 => ~ ! [Xx_0: nat] :
% 1.51/1.27 ( ( pl @ Xx @ Xz )
% 1.51/1.27 != ( pl @ ( pl @ Xy @ Xz ) @ Xx_0 ) ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(satz6,axiom,
% 1.51/1.27 ! [Xx: nat,Xy: nat] :
% 1.51/1.27 ( ( pl @ Xx @ Xy )
% 1.51/1.27 = ( pl @ Xy @ Xx ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(satz25,conjecture,
% 1.51/1.27 ( ~ ~ ! [Xx_0: nat] :
% 1.51/1.27 ( y
% 1.51/1.27 != ( pl @ ( pl @ x @ n_1 ) @ Xx_0 ) )
% 1.51/1.27 => ( y
% 1.51/1.27 = ( pl @ x @ n_1 ) ) ) ).
% 1.51/1.27 ------------------------
% 1.51/1.28 % (10083)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9796 for (2999ds/2Mi)
% 1.51/1.28 % (10083)Instruction limit reached!
% 1.51/1.28 % (10083)------------------------------
% 1.51/1.28 % (10083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.28 % (10083)Termination reason: Unknown
% 1.51/1.28 % (10083)Termination phase: Saturation
% 1.51/1.28
% 1.51/1.28 % (10083)Memory used [KB]: 895
% 1.51/1.28 % (10083)Time elapsed: 0.002 s
% 1.51/1.28 % (10083)Instructions burned: 2 (million)
% 1.51/1.28 % (10083)------------------------------
% 1.51/1.28 % (10083)------------------------------
% 1.51/1.28 % (10084)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_9796 for (2999ds/2Mi)
% 1.51/1.29 % (10084)Instruction limit reached!
% 1.51/1.29 % (10084)------------------------------
% 1.51/1.29 % (10084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (10084)Termination reason: Unknown
% 1.51/1.29 % (10084)Termination phase: Saturation
% 1.51/1.29
% 1.51/1.29 % (10084)Memory used [KB]: 1023
% 1.51/1.29 % (10084)Time elapsed: 0.002 s
% 1.51/1.29 % (10084)Instructions burned: 3 (million)
% 1.51/1.29 % (10084)------------------------------
% 1.51/1.29 % (10084)------------------------------
% 1.51/1.29 % (10080)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9796 for (2999ds/183Mi)
% 1.51/1.29 % (10081)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_9796 for (2999ds/4Mi)
% 1.51/1.29 % (10082)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_9796 for (2999ds/27Mi)
% 1.51/1.29 % (10085)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_9796 for (2999ds/275Mi)
% 1.51/1.29 % (10086)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9796 for (2999ds/18Mi)
% 1.51/1.29 % (10087)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9796 for (2999ds/3Mi)
% 1.51/1.29 % (10081)Instruction limit reached!
% 1.51/1.29 % (10081)------------------------------
% 1.51/1.29 % (10081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (10081)Termination reason: Unknown
% 1.51/1.29 % (10081)Termination phase: Saturation
% 1.51/1.29
% 1.51/1.29 % (10081)Memory used [KB]: 5500
% 1.51/1.29 % (10081)Time elapsed: 0.005 s
% 1.51/1.29 % (10081)Instructions burned: 5 (million)
% 1.51/1.29 % (10081)------------------------------
% 1.51/1.29 % (10081)------------------------------
% 1.51/1.30 % (10088)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_9796 for (2999ds/37Mi)
% 1.51/1.30 % (10087)Instruction limit reached!
% 1.51/1.30 % (10087)------------------------------
% 1.51/1.30 % (10087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.30 % (10087)Termination reason: Unknown
% 1.51/1.30 % (10087)Termination phase: Saturation
% 1.51/1.30
% 1.51/1.30 % (10087)Memory used [KB]: 5500
% 1.51/1.30 % (10087)Time elapsed: 0.003 s
% 1.51/1.30 % (10087)Instructions burned: 5 (million)
% 1.51/1.30 % (10087)------------------------------
% 1.51/1.30 % (10087)------------------------------
% 1.51/1.30 % (10085)Refutation not found, incomplete strategy
% 1.51/1.30 % (10085)------------------------------
% 1.51/1.30 % (10085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.30 % (10085)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.30
% 1.51/1.30
% 1.51/1.30 % (10085)Memory used [KB]: 5500
% 1.51/1.30 % (10085)Time elapsed: 0.006 s
% 1.51/1.30 % (10085)Instructions burned: 6 (million)
% 1.51/1.30 % (10085)------------------------------
% 1.51/1.30 % (10085)------------------------------
% 1.64/1.30 % (10080)First to succeed.
% 1.64/1.30 % (10086)Instruction limit reached!
% 1.64/1.30 % (10086)------------------------------
% 1.64/1.30 % (10086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (10086)Termination reason: Unknown
% 1.64/1.30 % (10086)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (10086)Memory used [KB]: 5500
% 1.64/1.30 % (10086)Time elapsed: 0.014 s
% 1.64/1.30 % (10086)Instructions burned: 18 (million)
% 1.64/1.30 % (10086)------------------------------
% 1.64/1.30 % (10086)------------------------------
% 1.64/1.30 % (10080)Refutation found. Thanks to Tanya!
% 1.64/1.30 % SZS status Theorem for DTF2THF_9796
% 1.64/1.30 % SZS output start Proof for DTF2THF_9796
% 1.64/1.30 thf(type_def_5, type, nat: $tType).
% 1.64/1.30 thf(func_def_0, type, nat: $tType).
% 1.64/1.30 thf(func_def_1, type, x: nat).
% 1.64/1.30 thf(func_def_2, type, y: nat).
% 1.64/1.30 thf(func_def_3, type, pl: nat > nat > nat).
% 1.64/1.30 thf(func_def_5, type, n_1: nat).
% 1.64/1.30 thf(func_def_8, type, sK0: nat).
% 1.64/1.30 thf(func_def_9, type, sK1: nat > nat > nat > nat).
% 1.64/1.30 thf(func_def_10, type, sK2: nat > nat).
% 1.64/1.30 thf(f83,plain,(
% 1.64/1.30 $false),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.64/1.30 thf(f82,plain,(
% 1.64/1.30 ((pl @ x @ n_1) != (pl @ x @ n_1))),
% 1.64/1.30 inference(superposition,[status(thm)],[f36,f79])).
% 1.64/1.30 thf(f79,plain,(
% 1.64/1.30 (n_1 = sK0)),
% 1.64/1.30 inference(equality_resolution,[status(thm)],[f76])).
% 1.64/1.30 thf(f76,plain,(
% 1.64/1.30 ( ! [X0 : nat] : (((pl @ x @ X0) != (pl @ x @ sK0)) | (n_1 = X0)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f72,f34])).
% 1.64/1.30 thf(f34,plain,(
% 1.64/1.30 ( ! [X0 : nat,X1 : nat] : (((pl @ X0 @ X1) = (pl @ X1 @ X0))) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.30 thf(f14,plain,(
% 1.64/1.30 ! [X0 : nat,X1 : nat] : ((pl @ X0 @ X1) = (pl @ X1 @ X0))),
% 1.64/1.30 inference(rectify,[status(thm)],[f5])).
% 1.64/1.30 thf(f5,axiom,(
% 1.64/1.30 ! [X2 : nat,X3 : nat] : ((pl @ X2 @ X3) = (pl @ X3 @ X2))),
% 1.64/1.30 file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',satz6)).
% 1.64/1.30 thf(f72,plain,(
% 1.64/1.30 ( ! [X0 : nat] : (((pl @ X0 @ x) != (pl @ x @ sK0)) | (n_1 = X0)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f37,f65])).
% 1.64/1.30 thf(f65,plain,(
% 1.64/1.30 ( ! [X0 : nat,X1 : nat] : (((pl @ (pl @ X0 @ n_1) @ (sK1 @ n_1 @ X1 @ X0)) = (pl @ X1 @ X0)) | (n_1 = X1)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f44,f34])).
% 1.64/1.30 thf(f44,plain,(
% 1.64/1.30 ( ! [X0 : nat,X1 : nat] : (((pl @ (pl @ n_1 @ X1) @ (sK1 @ n_1 @ X0 @ X1)) = (pl @ X0 @ X1)) | (n_1 = X0)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f39,f35])).
% 1.64/1.30 thf(f35,plain,(
% 1.64/1.30 ( ! [X0 : nat] : (((pl @ n_1 @ (sK2 @ X0)) = X0) | (n_1 = X0)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.64/1.30 thf(f28,plain,(
% 1.64/1.30 ! [X0 : nat] : (((pl @ n_1 @ (sK2 @ X0)) = X0) | (n_1 = X0))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f27])).
% 1.64/1.30 thf(f27,plain,(
% 1.64/1.30 ! [X0 : nat] : (? [X1 : nat] : ((pl @ n_1 @ X1) = X0) => ((pl @ n_1 @ (sK2 @ X0)) = X0))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f17,plain,(
% 1.64/1.30 ! [X0 : nat] : (? [X1 : nat] : ((pl @ n_1 @ X1) = X0) | (n_1 = X0))),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f12])).
% 1.64/1.30 thf(f12,plain,(
% 1.64/1.30 ! [X0 : nat] : (! [X1 : nat] : ((pl @ n_1 @ X1) != X0) => (n_1 = X0))),
% 1.64/1.30 inference(flattening,[status(thm)],[f11])).
% 1.64/1.30 thf(f11,plain,(
% 1.64/1.30 ! [X0 : nat] : (~~! [X1 : nat] : ((pl @ n_1 @ X1) != X0) => (n_1 = X0))),
% 1.64/1.30 inference(rectify,[status(thm)],[f3])).
% 1.64/1.30 thf(f3,axiom,(
% 1.64/1.30 ! [X2 : nat] : (~~! [X0 : nat] : ((pl @ n_1 @ X0) != X2) => (n_1 = X2))),
% 1.64/1.30 file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',satz24)).
% 1.64/1.30 thf(f39,plain,(
% 1.64/1.30 ( ! [X2 : nat,X0 : nat,X4 : nat] : (((pl @ (pl @ X2 @ X4) @ X0) = (pl @ (pl @ X2 @ X0) @ (sK1 @ X2 @ (pl @ X2 @ X4) @ X0)))) )),
% 1.64/1.30 inference(equality_resolution,[status(thm)],[f33])).
% 1.64/1.30 thf(f33,plain,(
% 1.64/1.30 ( ! [X2 : nat,X0 : nat,X1 : nat,X4 : nat] : (((pl @ (pl @ X2 @ X0) @ (sK1 @ X2 @ X1 @ X0)) = (pl @ X1 @ X0)) | ((pl @ X2 @ X4) != X1)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f26])).
% 1.64/1.30 thf(f26,plain,(
% 1.64/1.30 ! [X0 : nat,X1 : nat,X2 : nat] : (((pl @ (pl @ X2 @ X0) @ (sK1 @ X2 @ X1 @ X0)) = (pl @ X1 @ X0)) | ! [X4 : nat] : ((pl @ X2 @ X4) != X1))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f24,f25])).
% 1.64/1.30 thf(f25,plain,(
% 1.64/1.30 ! [X0 : nat,X1 : nat,X2 : nat] : (? [X3 : nat] : ((pl @ (pl @ X2 @ X0) @ X3) = (pl @ X1 @ X0)) => ((pl @ (pl @ X2 @ X0) @ (sK1 @ X2 @ X1 @ X0)) = (pl @ X1 @ X0)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f24,plain,(
% 1.64/1.30 ! [X0 : nat,X1 : nat,X2 : nat] : (? [X3 : nat] : ((pl @ (pl @ X2 @ X0) @ X3) = (pl @ X1 @ X0)) | ! [X4 : nat] : ((pl @ X2 @ X4) != X1))),
% 1.64/1.30 inference(rectify,[status(thm)],[f21])).
% 1.64/1.30 thf(f21,plain,(
% 1.64/1.30 ! [X0 : nat,X2 : nat,X1 : nat] : (? [X4 : nat] : ((pl @ (pl @ X1 @ X0) @ X4) = (pl @ X2 @ X0)) | ! [X3 : nat] : ((pl @ X1 @ X3) != X2))),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f16])).
% 1.64/1.30 thf(f16,plain,(
% 1.64/1.30 ! [X0 : nat,X1 : nat,X2 : nat] : (~! [X3 : nat] : ((pl @ X1 @ X3) != X2) => ~! [X4 : nat] : ((pl @ (pl @ X1 @ X0) @ X4) != (pl @ X2 @ X0)))),
% 1.64/1.30 inference(rectify,[status(thm)],[f4])).
% 1.64/1.30 thf(f4,axiom,(
% 1.64/1.30 ! [X4 : nat,X3 : nat,X2 : nat] : (~! [X0 : nat] : ((pl @ X3 @ X0) != X2) => ~! [X0 : nat] : ((pl @ X2 @ X4) != (pl @ (pl @ X3 @ X4) @ X0)))),
% 1.64/1.30 file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',satz19a)).
% 1.64/1.30 thf(f37,plain,(
% 1.64/1.30 ( ! [X0 : nat] : (((pl @ (pl @ x @ n_1) @ X0) != (pl @ x @ sK0))) )),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f30,f29])).
% 1.64/1.30 thf(f29,plain,(
% 1.64/1.30 (y = (pl @ x @ sK0))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.30 thf(f23,plain,(
% 1.64/1.30 (y = (pl @ x @ sK0))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f22])).
% 1.64/1.30 thf(f22,plain,(
% 1.64/1.30 ? [X0 : nat] : (y = (pl @ x @ X0)) => (y = (pl @ x @ sK0))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f18,plain,(
% 1.64/1.30 ? [X0 : nat] : (y = (pl @ x @ X0))),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f1])).
% 1.64/1.31 thf(f1,axiom,(
% 1.64/1.31 ~! [X0 : nat] : (y != (pl @ x @ X0))),
% 1.64/1.31 file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',m)).
% 1.64/1.31 thf(f30,plain,(
% 1.64/1.31 ( ! [X0 : nat] : ((y != (pl @ (pl @ x @ n_1) @ X0))) )),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f20])).
% 1.64/1.31 thf(f20,plain,(
% 1.64/1.31 (y != (pl @ x @ n_1)) & ! [X0 : nat] : (y != (pl @ (pl @ x @ n_1) @ X0))),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f13])).
% 1.64/1.31 thf(f13,plain,(
% 1.64/1.31 ~(! [X0 : nat] : (y != (pl @ (pl @ x @ n_1) @ X0)) => (y = (pl @ x @ n_1)))),
% 1.64/1.31 inference(flattening,[status(thm)],[f7])).
% 1.64/1.31 thf(f7,negated_conjecture,(
% 1.64/1.31 ~(~~! [X0 : nat] : (y != (pl @ (pl @ x @ n_1) @ X0)) => (y = (pl @ x @ n_1)))),
% 1.64/1.31 inference(negated_conjecture,[status(cth)],[f6])).
% 1.64/1.31 thf(f6,conjecture,(
% 1.64/1.31 ~~! [X0 : nat] : (y != (pl @ (pl @ x @ n_1) @ X0)) => (y = (pl @ x @ n_1))),
% 1.64/1.31 file('/export/starexec/sandbox2/tmp/tmp.K96eELbJRk/DTF2THF_9796.p',satz25)).
% 1.64/1.31 thf(f36,plain,(
% 1.64/1.31 ((pl @ x @ n_1) != (pl @ x @ sK0))),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f31,f29])).
% 1.64/1.31 thf(f31,plain,(
% 1.64/1.31 (y != (pl @ x @ n_1))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f20])).
% 1.64/1.31 % SZS output end Proof for DTF2THF_9796
% 1.64/1.31 % (10080)------------------------------
% 1.64/1.31 % (10080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (10080)Termination reason: Refutation
% 1.64/1.31
% 1.64/1.31 % (10080)Memory used [KB]: 5628
% 1.64/1.31 % (10080)Time elapsed: 0.014 s
% 1.64/1.31 % (10080)Instructions burned: 17 (million)
% 1.64/1.31 % (10080)------------------------------
% 1.64/1.31 % (10080)------------------------------
% 1.64/1.31 % (10079)Success in time 0.027 s
%------------------------------------------------------------------------------