%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM670^1 : 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 : n007.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 09:24:12 AM UTC 2026
% Result : Theorem 1.62s 1.37s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 130 ( 13 ~; 0 |; 0 &; 116 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 29 !; 2 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
x: nat ).
thf(func_def_2,type,
y: nat ).
thf(func_def_3,type,
z: nat ).
thf(func_def_4,type,
pl: nat > nat > nat ).
thf(func_def_8,type,
sK0: nat ).
thf(f45,plain,
$false,
inference(equality_resolution,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: nat] :
( ( pl @ y @ ( pl @ z @ sK0 ) )
!= ( pl @ y @ ( pl @ z @ X0 ) ) ),
inference(superposition,[status(thm)],[f28,f20]) ).
thf(f20,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( pl @ ( pl @ X1 @ X0 ) @ X2 )
= ( pl @ X1 @ ( pl @ X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( pl @ ( pl @ X1 @ X0 ) @ X2 )
= ( pl @ X1 @ ( pl @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( pl @ X2 @ ( pl @ X1 @ X0 ) )
= ( pl @ ( pl @ X2 @ X1 ) @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X4: nat,X3: nat,X2: nat] :
( ( pl @ ( pl @ X2 @ X3 ) @ X4 )
= ( pl @ X2 @ ( pl @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RigGXqeYS0/DTF2THF_30679.p',satz5) ).
thf(f28,plain,
! [X0: nat] :
( ( pl @ ( pl @ y @ z ) @ X0 )
!= ( pl @ y @ ( pl @ z @ sK0 ) ) ),
inference(backward_demodulation,[status(thm)],[f27,f22]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X3: nat,X2: nat] :
( ( pl @ X2 @ X3 )
= ( pl @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.RigGXqeYS0/DTF2THF_30679.p',satz6) ).
thf(f27,plain,
! [X0: nat] :
( ( pl @ ( pl @ y @ z ) @ X0 )
!= ( pl @ y @ ( pl @ sK0 @ z ) ) ),
inference(backward_demodulation,[status(thm)],[f25,f20]) ).
thf(f25,plain,
! [X0: nat] :
( ( pl @ ( pl @ y @ z ) @ X0 )
!= ( pl @ ( pl @ y @ sK0 ) @ z ) ),
inference(definition_unfolding,[status(thm)],[f21,f23]) ).
thf(f23,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( x
= ( pl @ y @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f18]) ).
thf(f18,plain,
( ? [X0: nat] :
( x
= ( pl @ y @ X0 ) )
=> ( x
= ( pl @ y @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: nat] :
( x
= ( pl @ y @ X0 ) ),
inference(ennf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ! [X0: nat] :
( x
!= ( pl @ y @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.RigGXqeYS0/DTF2THF_30679.p',m) ).
thf(f21,plain,
! [X0: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X0 ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ~ ! [X0: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
~ ! [X0: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.RigGXqeYS0/DTF2THF_30679.p',satz19a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM670^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n007.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:09:38 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 : NUM670^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Number Theory
% 0.29/0.46 % Problem : Landau theorem 19a
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : ~(forall x_0:nat.~(pl x z = pl (pl y z) x_0))
% 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 : satz19a [Lan30]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % : Without extensionality : Theorem
% 0.29/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.00 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 10 ( 4 unt; 5 typ; 0 def)
% 0.29/0.46 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 0 avg)
% 0.29/0.46 % Number of connectives : 27 ( 6 ~; 0 |; 0 &; 20 @)
% 0.29/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 5 ( 4 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_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(z,type,
% 0.29/0.46 z: nat ).
% 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(m,axiom,
% 0.29/0.46 ~ ! [Xx_0: nat] :
% 0.29/0.46 ( x
% 0.29/0.46 != ( pl @ y @ Xx_0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(et,axiom,
% 0.29/0.46 ! [Xa: $o] :
% 0.29/0.46 ( ~ ~ Xa
% 0.29/0.46 => Xa ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz6,axiom,
% 0.29/0.46 ! [Xx: nat,Xy: nat] :
% 0.29/0.46 ( ( pl @ Xx @ Xy )
% 0.29/0.46 = ( pl @ Xy @ Xx ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz5,axiom,
% 0.29/0.46 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.29/0.46 ( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
% 0.29/0.46 = ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz19a,conjecture,
% 0.29/0.46 ~ ! [Xx_0: nat] :
% 0.29/0.46 ( ( pl @ x @ z )
% 0.29/0.46 != ( pl @ ( pl @ y @ z ) @ Xx_0 ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.62/1.33 ---- Embedded in THF ---
% 1.62/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.33 %%% Generated on Tue Feb 24 11:09:39 EST 2026
% 1.62/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.33 %%% Logic specification used:
% 1.62/1.33 %%% thf(spec, logic, $$dhol).
% 1.62/1.33
% 1.62/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.RigGXqeYS0/DTF2DTF30679.p
% See solution above
% 1.62/1.33 ------------------------
% 1.62/1.34 ---- Cleaned THF ---
% 1.62/1.34 thf(nat_type,type,
% 1.62/1.34 nat: $tType ).
% 1.62/1.34
% 1.62/1.34 thf(x,type,
% 1.62/1.34 x: nat ).
% 1.62/1.34
% 1.62/1.34 thf(y,type,
% 1.62/1.34 y: nat ).
% 1.62/1.34
% 1.62/1.34 thf(z,type,
% 1.62/1.34 z: nat ).
% 1.62/1.34
% 1.62/1.34 thf(pl,type,
% 1.62/1.34 pl: nat > nat > nat ).
% 1.62/1.34
% 1.62/1.34 thf(m,axiom,
% 1.62/1.34 ~ ! [Xx_0: nat] :
% 1.62/1.34 ( x
% 1.62/1.34 != ( pl @ y @ Xx_0 ) ) ).
% 1.62/1.34
% 1.62/1.34 thf(et,axiom,
% 1.62/1.34 ! [Xa: $o] :
% 1.62/1.34 ( ~ ~ Xa
% 1.62/1.34 => Xa ) ).
% 1.62/1.34
% 1.62/1.34 thf(satz6,axiom,
% 1.62/1.34 ! [Xx: nat,Xy: nat] :
% 1.62/1.34 ( ( pl @ Xx @ Xy )
% 1.62/1.34 = ( pl @ Xy @ Xx ) ) ).
% 1.62/1.34
% 1.62/1.34 thf(satz5,axiom,
% 1.62/1.34 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.62/1.34 ( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
% 1.62/1.34 = ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) ).
% 1.62/1.34
% 1.62/1.34 thf(satz19a,conjecture,
% 1.62/1.34 ~ ! [Xx_0: nat] :
% 1.62/1.34 ( ( pl @ x @ z )
% 1.62/1.34 != ( pl @ ( pl @ y @ z ) @ Xx_0 ) ) ).
% 1.62/1.34 ------------------------
% 1.62/1.36 % (30965)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_30679 for (2999ds/275Mi)
% 1.62/1.36 % (30960)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30679 for (2999ds/183Mi)
% 1.62/1.36 % (30961)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_30679 for (2999ds/4Mi)
% 1.62/1.36 % (30962)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_30679 for (2999ds/27Mi)
% 1.62/1.36 % (30963)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30679 for (2999ds/2Mi)
% 1.62/1.36 % (30964)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_30679 for (2999ds/2Mi)
% 1.62/1.36 % (30966)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30679 for (2999ds/18Mi)
% 1.62/1.37 % (30964)Instruction limit reached!
% 1.62/1.37 % (30964)------------------------------
% 1.62/1.37 % (30964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (30964)Termination reason: Unknown
% 1.62/1.37 % (30964)Termination phase: Property scanning
% 1.62/1.37
% 1.62/1.37 % (30964)Memory used [KB]: 895
% 1.62/1.37 % (30964)Time elapsed: 0.003 s
% 1.62/1.37 % (30964)Instructions burned: 2 (million)
% 1.62/1.37 % (30964)------------------------------
% 1.62/1.37 % (30964)------------------------------
% 1.62/1.37 % (30963)Instruction limit reached!
% 1.62/1.37 % (30963)------------------------------
% 1.62/1.37 % (30963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (30963)Termination reason: Unknown
% 1.62/1.37 % (30963)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (30963)Memory used [KB]: 5500
% 1.62/1.37 % (30963)Time elapsed: 0.004 s
% 1.62/1.37 % (30963)Instructions burned: 2 (million)
% 1.62/1.37 % (30963)------------------------------
% 1.62/1.37 % (30963)------------------------------
% 1.62/1.37 % (30961)Instruction limit reached!
% 1.62/1.37 % (30961)------------------------------
% 1.62/1.37 % (30961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (30961)Termination reason: Unknown
% 1.62/1.37 % (30961)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (30961)Memory used [KB]: 5500
% 1.62/1.37 % (30961)Time elapsed: 0.005 s
% 1.62/1.37 % (30961)Instructions burned: 4 (million)
% 1.62/1.37 % (30961)------------------------------
% 1.62/1.37 % (30961)------------------------------
% 1.62/1.37 % (30966)First to succeed.
% 1.62/1.37 % (30966)Refutation found. Thanks to Tanya!
% 1.62/1.37 % SZS status Theorem for DTF2THF_30679
% 1.62/1.37 % SZS output start Proof for DTF2THF_30679
% 1.62/1.37 thf(type_def_5, type, nat: $tType).
% 1.62/1.37 thf(func_def_0, type, nat: $tType).
% 1.62/1.37 thf(func_def_1, type, x: nat).
% 1.62/1.37 thf(func_def_2, type, y: nat).
% 1.62/1.37 thf(func_def_3, type, z: nat).
% 1.62/1.37 thf(func_def_4, type, pl: nat > nat > nat).
% 1.62/1.37 thf(func_def_8, type, sK0: nat).
% 1.62/1.37 thf(f45,plain,(
% 1.62/1.37 $false),
% 1.62/1.37 inference(equality_resolution,[status(thm)],[f36])).
% 1.62/1.37 thf(f36,plain,(
% 1.62/1.37 ( ! [X0 : nat] : (((pl @ y @ (pl @ z @ sK0)) != (pl @ y @ (pl @ z @ X0)))) )),
% 1.62/1.37 inference(superposition,[status(thm)],[f28,f20])).
% 1.62/1.37 thf(f20,plain,(
% 1.62/1.37 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((pl @ (pl @ X1 @ X0) @ X2) = (pl @ X1 @ (pl @ X0 @ X2)))) )),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f16])).
% 1.62/1.37 thf(f16,plain,(
% 1.62/1.37 ! [X0 : nat,X1 : nat,X2 : nat] : ((pl @ (pl @ X1 @ X0) @ X2) = (pl @ X1 @ (pl @ X0 @ X2)))),
% 1.62/1.37 inference(rectify,[status(thm)],[f12])).
% 1.62/1.37 thf(f12,plain,(
% 1.62/1.37 ! [X1 : nat,X2 : nat,X0 : nat] : ((pl @ X2 @ (pl @ X1 @ X0)) = (pl @ (pl @ X2 @ X1) @ X0))),
% 1.62/1.37 inference(rectify,[status(thm)],[f4])).
% 1.62/1.37 thf(f4,axiom,(
% 1.62/1.37 ! [X4 : nat,X3 : nat,X2 : nat] : ((pl @ (pl @ X2 @ X3) @ X4) = (pl @ X2 @ (pl @ X3 @ X4)))),
% 1.62/1.37 file('/export/starexec/sandbox2/tmp/tmp.RigGXqeYS0/DTF2THF_30679.p',satz5)).
% 1.62/1.37 thf(f28,plain,(
% 1.62/1.37 ( ! [X0 : nat] : (((pl @ (pl @ y @ z) @ X0) != (pl @ y @ (pl @ z @ sK0)))) )),
% 1.62/1.37 inference(backward_demodulation,[status(thm)],[f27,f22])).
% 1.62/1.37 thf(f22,plain,(
% 1.62/1.37 ( ! [X0 : nat,X1 : nat] : (((pl @ X0 @ X1) = (pl @ X1 @ X0))) )),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f17])).
% 1.62/1.37 thf(f17,plain,(
% 1.62/1.37 ! [X0 : nat,X1 : nat] : ((pl @ X0 @ X1) = (pl @ X1 @ X0))),
% 1.62/1.37 inference(rectify,[status(thm)],[f11])).
% 1.62/1.37 thf(f11,plain,(
% 1.62/1.37 ! [X1 : nat,X0 : nat] : ((pl @ X0 @ X1) = (pl @ X1 @ X0))),
% 1.62/1.37 inference(rectify,[status(thm)],[f3])).
% 1.62/1.37 thf(f3,axiom,(
% 1.62/1.37 ! [X3 : nat,X2 : nat] : ((pl @ X2 @ X3) = (pl @ X3 @ X2))),
% 1.62/1.37 file('/export/starexec/sandbox2/tmp/tmp.RigGXqeYS0/DTF2THF_30679.p',satz6)).
% 1.62/1.37 thf(f27,plain,(
% 1.62/1.37 ( ! [X0 : nat] : (((pl @ (pl @ y @ z) @ X0) != (pl @ y @ (pl @ sK0 @ z)))) )),
% 1.62/1.37 inference(backward_demodulation,[status(thm)],[f25,f20])).
% 1.62/1.37 thf(f25,plain,(
% 1.62/1.37 ( ! [X0 : nat] : (((pl @ (pl @ y @ z) @ X0) != (pl @ (pl @ y @ sK0) @ z))) )),
% 1.62/1.37 inference(definition_unfolding,[status(thm)],[f21,f23])).
% 1.62/1.37 thf(f23,plain,(
% 1.62/1.37 (x = (pl @ y @ sK0))),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f19])).
% 1.62/1.37 thf(f19,plain,(
% 1.62/1.37 (x = (pl @ y @ sK0))),
% 1.62/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f18])).
% 1.62/1.37 thf(f18,plain,(
% 1.62/1.37 ? [X0 : nat] : (x = (pl @ y @ X0)) => (x = (pl @ y @ sK0))),
% 1.62/1.37 introduced(definition,[],[choice_axiom])).
% 1.62/1.37 thf(f15,plain,(
% 1.62/1.37 ? [X0 : nat] : (x = (pl @ y @ X0))),
% 1.62/1.37 inference(ennf_transformation,[status(thm)],[f1])).
% 1.62/1.37 thf(f1,axiom,(
% 1.62/1.37 ~! [X0 : nat] : (x != (pl @ y @ X0))),
% 1.62/1.37 file('/export/starexec/sandbox2/tmp/tmp.RigGXqeYS0/DTF2THF_30679.p',m)).
% 1.62/1.37 thf(f21,plain,(
% 1.62/1.37 ( ! [X0 : nat] : (((pl @ x @ z) != (pl @ (pl @ y @ z) @ X0))) )),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f10])).
% 1.62/1.37 thf(f10,plain,(
% 1.62/1.37 ! [X0 : nat] : ((pl @ x @ z) != (pl @ (pl @ y @ z) @ X0))),
% 1.62/1.37 inference(flattening,[status(thm)],[f6])).
% 1.62/1.37 thf(f6,negated_conjecture,(
% 1.62/1.37 ~~! [X0 : nat] : ((pl @ x @ z) != (pl @ (pl @ y @ z) @ X0))),
% 1.62/1.37 inference(negated_conjecture,[status(cth)],[f5])).
% 1.62/1.37 thf(f5,conjecture,(
% 1.62/1.37 ~! [X0 : nat] : ((pl @ x @ z) != (pl @ (pl @ y @ z) @ X0))),
% 1.62/1.37 file('/export/starexec/sandbox2/tmp/tmp.RigGXqeYS0/DTF2THF_30679.p',satz19a)).
% 1.62/1.37 % SZS output end Proof for DTF2THF_30679
% 1.62/1.37 % (30966)------------------------------
% 1.62/1.37 % (30966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (30966)Termination reason: Refutation
% 1.62/1.37
% 1.62/1.37 % (30966)Memory used [KB]: 5500
% 1.62/1.37 % (30966)Time elapsed: 0.009 s
% 1.62/1.37 % (30966)Instructions burned: 9 (million)
% 1.62/1.37 % (30966)------------------------------
% 1.62/1.37 % (30966)------------------------------
% 1.62/1.37 % (30959)Success in time 0.024 s
%------------------------------------------------------------------------------