%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM686^1 : 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 09:24:16 AM UTC 2026
% Result : Theorem 1.63s 1.34s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 239 ( 54 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 385 ( 34 ~; 21 |; 0 &; 321 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 94 ( 42 ^; 52 !; 0 ?; 94 :)
% 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,
u: nat ).
thf(func_def_5,type,
some: ( nat > $o ) > $o ).
thf(func_def_6,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_8,type,
pl: nat > nat > nat ).
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f87,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f86,f31]) ).
thf(f31,plain,
( ( some @ ( diffprop @ x @ y ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( some
@ ^ [X0: nat] : ( diffprop @ x @ y @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ x @ y @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',m) ).
thf(f86,plain,
( ( some @ ( diffprop @ x @ y ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f83,f33]) ).
thf(f33,plain,
( ( some @ ( diffprop @ z @ u ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ z @ u @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ z @ u @ Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( some
@ ^ [X0: nat] : ( diffprop @ z @ u @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( some
@ ^ [X1: nat] : ( diffprop @ z @ u @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',n) ).
thf(f83,plain,
( ( ( some @ ( diffprop @ z @ u ) )
!= $true )
| ( ( some @ ( diffprop @ x @ y ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( some @ ( diffprop @ z @ u ) )
!= $true )
| ( $true != $true )
| ( ( some @ ( diffprop @ x @ y ) )
!= $true ) ),
inference(superposition,[status(thm)],[f50,f35]) ).
thf(f35,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ ( pl @ X2 @ X1 ) @ ( pl @ X1 @ X0 ) ) )
= $true )
| ( $true
!= ( some @ ( diffprop @ X2 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f32,f24]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( pl @ X1 @ X0 )
= ( pl @ X0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( pl @ X1 @ X0 )
= ( pl @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X3: nat,X2: nat] :
( ( pl @ X2 @ X3 )
= ( pl @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',satz6) ).
thf(f32,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) )
= $true )
| ( $true
!= ( some @ ( diffprop @ X2 @ X0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) @ Y0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) )
= $true )
=> ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) @ Y0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X2 @ X0 @ X3 ) )
=> ( some
@ ^ [X4: nat] : ( diffprop @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) @ X4 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: nat,X4: nat,X2: nat] :
( ( some
@ ^ [X0: nat] : ( diffprop @ X2 @ X3 @ X0 ) )
=> ( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X4 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',satz19a) ).
thf(f50,plain,
! [X0: nat] :
( ( ( some @ ( diffprop @ ( pl @ z @ X0 ) @ ( pl @ y @ u ) ) )
!= $true )
| ( ( some @ ( diffprop @ x @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: nat] :
( ( $true != $true )
| ( ( some @ ( diffprop @ ( pl @ z @ X0 ) @ ( pl @ y @ u ) ) )
!= $true )
| ( ( some @ ( diffprop @ x @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f40,f35]) ).
thf(f40,plain,
! [X0: nat] :
( ( ( some @ ( diffprop @ ( pl @ x @ z ) @ X0 ) )
!= $true )
| ( ( some @ ( diffprop @ X0 @ ( pl @ y @ u ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: nat] :
( ( ( some @ ( diffprop @ ( pl @ x @ z ) @ X0 ) )
!= $true )
| ( ( some @ ( diffprop @ X0 @ ( pl @ y @ u ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f30,f34]) ).
thf(f34,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ X0 @ X1 ) )
= $true )
| ( ( some @ ( diffprop @ X2 @ X1 ) )
!= $true )
| ( ( some @ ( diffprop @ X0 @ X2 ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) )
= $true )
=> ( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) )
= $true )
=> ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X2 @ X1 @ X3 ) )
=> ( ( some
@ ^ [X4: nat] : ( diffprop @ X0 @ X2 @ X4 ) )
=> ( some
@ ^ [X5: nat] : ( diffprop @ X0 @ X1 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X4: nat,X2: nat,X3: nat] :
( ( some
@ ^ [X5: nat] : ( diffprop @ X3 @ X2 @ X5 ) )
=> ( ( some
@ ^ [X5: nat] : ( diffprop @ X4 @ X3 @ X5 ) )
=> ( some
@ ^ [X5: nat] : ( diffprop @ X4 @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',satz15) ).
thf(f30,plain,
( ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Y0 ) )
!= $true ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Y0 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ X0 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( some
@ ^ [X1: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( some
@ ^ [X1: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',satz21) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM686^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n007.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 11:10:08 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
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : NUM686^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.45 % Domain : Number Theory
% 0.20/0.45 % Problem : Landau theorem 21
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English : some (lambda u_0.diffprop (pl x z) (pl y u) u_0)
% 0.20/0.45
% 0.20/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Bro09]
% 0.20/0.45 % Names : satz21 [Lan30]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % : Without extensionality : Theorem
% 0.20/0.45 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 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 v5.3.0, 0.80 v4.1.0, 0.67 v3.7.0
% 0.20/0.45 % Syntax : Number of formulae : 14 ( 1 unt; 8 typ; 0 def)
% 0.20/0.45 % Number of atoms : 17 ( 1 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 6 ( 2 avg)
% 0.20/0.45 % Number of connectives : 47 ( 0 ~; 0 |; 0 &; 44 @)
% 0.20/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 12 ( 8 avg)
% 0.20/0.45 % Number of types : 2 ( 1 usr)
% 0.20/0.45 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 8 ( 7 usr; 4 con; 0-3 aty)
% 0.20/0.45 % Number of variables : 16 ( 8 ^; 8 !; 0 ?; 16 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments :
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(nat_type,type,
% 0.20/0.45 nat: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(x,type,
% 0.20/0.45 x: nat ).
% 0.20/0.45
% 0.20/0.45 thf(y,type,
% 0.20/0.45 y: nat ).
% 0.20/0.45
% 0.20/0.45 thf(z,type,
% 0.20/0.45 z: nat ).
% 0.20/0.45
% 0.20/0.45 thf(u,type,
% 0.20/0.45 u: nat ).
% 0.20/0.45
% 0.20/0.45 thf(some,type,
% 0.20/0.45 some: ( nat > $o ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(diffprop,type,
% 0.20/0.45 diffprop: nat > nat > nat > $o ).
% 0.20/0.45
% 0.20/0.45 thf(m,axiom,
% 0.20/0.45 ( some
% 0.20/0.45 @ ^ [Xu: nat] : ( diffprop @ x @ y @ Xu ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(n,axiom,
% 0.20/0.45 ( some
% 0.20/0.45 @ ^ [Xu_0: nat] : ( diffprop @ z @ u @ Xu_0 ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(pl,type,
% 0.20/0.45 pl: nat > nat > nat ).
% 0.20/0.45
% 0.20/0.45 thf(satz15,axiom,
% 0.20/0.45 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.20/0.45 ( ( some
% 0.20/0.45 @ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
% 0.20/0.45 => ( ( some
% 0.20/0.45 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xy @ Xv ) )
% 0.20/0.45 => ( some
% 0.20/0.45 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(satz19a,axiom,
% 0.20/0.45 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.20/0.45 ( ( some
% 0.20/0.45 @ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
% 0.20/0.45 => ( some
% 0.20/0.45 @ ^ [Xu: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) @ Xu ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(satz6,axiom,
% 0.20/0.45 ! [Xx: nat,Xy: nat] :
% 0.20/0.45 ( ( pl @ Xx @ Xy )
% 0.20/0.45 = ( pl @ Xy @ Xx ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(satz21,conjecture,
% 0.20/0.45 ( some
% 0.20/0.45 @ ^ [Xu_0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Xu_0 ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.55/1.24 ---- Embedded in THF ---
% 1.55/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.24 %%% Generated on Tue Feb 24 11:10:09 EST 2026
% 1.55/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.24 %%% Logic specification used:
% 1.55/1.24 %%% thf(spec, logic, $$dhol).
% 1.55/1.24
% 1.55/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2DTF740.p
% See solution above
% 1.55/1.24 ------------------------
% 1.55/1.25 ---- Cleaned THF ---
% 1.55/1.25 thf(nat_type,type,
% 1.55/1.25 nat: $tType ).
% 1.55/1.25
% 1.55/1.25 thf(x,type,
% 1.55/1.25 x: nat ).
% 1.55/1.25
% 1.55/1.25 thf(y,type,
% 1.55/1.25 y: nat ).
% 1.55/1.25
% 1.55/1.25 thf(z,type,
% 1.55/1.25 z: nat ).
% 1.55/1.25
% 1.55/1.25 thf(u,type,
% 1.55/1.25 u: nat ).
% 1.55/1.25
% 1.55/1.25 thf(some,type,
% 1.55/1.25 some: ( nat > $o ) > $o ).
% 1.55/1.25
% 1.55/1.25 thf(diffprop,type,
% 1.55/1.25 diffprop: nat > nat > nat > $o ).
% 1.55/1.25
% 1.55/1.25 thf(m,axiom,
% 1.55/1.25 ( some
% 1.55/1.25 @ ^ [Xu: nat] : ( diffprop @ x @ y @ Xu ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(n,axiom,
% 1.55/1.25 ( some
% 1.55/1.25 @ ^ [Xu_0: nat] : ( diffprop @ z @ u @ Xu_0 ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(pl,type,
% 1.55/1.25 pl: nat > nat > nat ).
% 1.55/1.25
% 1.55/1.25 thf(satz15,axiom,
% 1.55/1.25 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.55/1.25 ( ( some
% 1.55/1.25 @ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
% 1.55/1.25 => ( ( some
% 1.55/1.25 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xy @ Xv ) )
% 1.55/1.25 => ( some
% 1.55/1.25 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(satz19a,axiom,
% 1.55/1.25 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.55/1.25 ( ( some
% 1.55/1.25 @ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
% 1.55/1.25 => ( some
% 1.55/1.25 @ ^ [Xu: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) @ Xu ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(satz6,axiom,
% 1.55/1.25 ! [Xx: nat,Xy: nat] :
% 1.55/1.25 ( ( pl @ Xx @ Xy )
% 1.55/1.25 = ( pl @ Xy @ Xx ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(satz21,conjecture,
% 1.55/1.25 ( some
% 1.55/1.25 @ ^ [Xu_0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Xu_0 ) ) ).
% 1.55/1.25 ------------------------
% 1.55/1.26 % (854)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_740 for (2999ds/4Mi)
% 1.55/1.26 % (857)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_740 for (2999ds/2Mi)
% 1.55/1.26 % (854)Instruction limit reached!
% 1.55/1.26 % (854)------------------------------
% 1.55/1.26 % (854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (854)Termination reason: Unknown
% 1.55/1.26 % (854)Termination phase: Saturation
% 1.55/1.26
% 1.55/1.26 % (854)Memory used [KB]: 5500
% 1.55/1.26 % (854)Time elapsed: 0.003 s
% 1.55/1.26 % (854)Instructions burned: 5 (million)
% 1.55/1.26 % (854)------------------------------
% 1.55/1.26 % (854)------------------------------
% 1.55/1.26 % (857)Instruction limit reached!
% 1.55/1.26 % (857)------------------------------
% 1.55/1.26 % (857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (857)Termination reason: Unknown
% 1.55/1.26 % (857)Termination phase: Saturation
% 1.55/1.26
% 1.55/1.26 % (857)Memory used [KB]: 1023
% 1.55/1.26 % (857)Time elapsed: 0.002 s
% 1.55/1.26 % (857)Instructions burned: 3 (million)
% 1.55/1.26 % (857)------------------------------
% 1.55/1.26 % (857)------------------------------
% 1.55/1.27 % (856)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/2Mi)
% 1.55/1.27 % (859)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_740 for (2999ds/275Mi)
% 1.55/1.27 % (860)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/18Mi)
% 1.55/1.27 % (856)Instruction limit reached!
% 1.55/1.27 % (856)------------------------------
% 1.55/1.27 % (856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (856)Termination reason: Unknown
% 1.55/1.27 % (856)Termination phase: Property scanning
% 1.55/1.27
% 1.55/1.27 % (856)Memory used [KB]: 895
% 1.55/1.27 % (856)Time elapsed: 0.003 s
% 1.55/1.27 % (856)Instructions burned: 2 (million)
% 1.55/1.27 % (856)------------------------------
% 1.55/1.27 % (856)------------------------------
% 1.55/1.27 % (853)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/183Mi)
% 1.55/1.27 % (855)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_740 for (2999ds/27Mi)
% 1.55/1.27 % (865)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 1.55/1.27 % (865)Instruction limit reached!
% 1.55/1.27 % (865)------------------------------
% 1.55/1.27 % (865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (866)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_740 for (2999ds/37Mi)
% 1.55/1.27 % (865)Termination reason: Unknown
% 1.55/1.27 % (865)Termination phase: Saturation
% 1.55/1.27
% 1.55/1.27 % (865)Memory used [KB]: 5500
% 1.55/1.27 % (865)Time elapsed: 0.002 s
% 1.55/1.27 % (865)Instructions burned: 3 (million)
% 1.55/1.27 % (865)------------------------------
% 1.55/1.27 % (865)------------------------------
% 1.55/1.28 % (860)Instruction limit reached!
% 1.55/1.28 % (860)------------------------------
% 1.55/1.28 % (860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (860)Termination reason: Unknown
% 1.55/1.28 % (860)Termination phase: Saturation
% 1.55/1.28
% 1.55/1.28 % (860)Memory used [KB]: 5628
% 1.55/1.28 % (860)Time elapsed: 0.014 s
% 1.55/1.28 % (860)Instructions burned: 18 (million)
% 1.55/1.28 % (860)------------------------------
% 1.55/1.28 % (860)------------------------------
% 1.55/1.28 % (868)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 1.55/1.28 % (868)Instruction limit reached!
% 1.55/1.28 % (868)------------------------------
% 1.55/1.28 % (868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (868)Termination reason: Unknown
% 1.55/1.28 % (868)Termination phase: Saturation
% 1.55/1.28
% 1.55/1.28 % (868)Memory used [KB]: 5500
% 1.55/1.28 % (868)Time elapsed: 0.002 s
% 1.55/1.28 % (868)Instructions burned: 3 (million)
% 1.55/1.28 % (868)------------------------------
% 1.55/1.28 % (868)------------------------------
% 1.55/1.29 % (866)Instruction limit reached!
% 1.55/1.29 % (866)------------------------------
% 1.55/1.29 % (866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.29 % (866)Termination reason: Unknown
% 1.55/1.29 % (866)Termination phase: Saturation
% 1.55/1.29
% 1.55/1.29 % (866)Memory used [KB]: 5756
% 1.55/1.29 % (866)Time elapsed: 0.015 s
% 1.55/1.29 % (866)Instructions burned: 38 (million)
% 1.55/1.29 % (866)------------------------------
% 1.55/1.29 % (866)------------------------------
% 1.55/1.29 % (855)Instruction limit reached!
% 1.55/1.29 % (855)------------------------------
% 1.55/1.29 % (855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.29 % (855)Termination reason: Unknown
% 1.55/1.29 % (855)Termination phase: Saturation
% 1.55/1.29
% 1.55/1.29 % (855)Memory used [KB]: 5628
% 1.55/1.29 % (855)Time elapsed: 0.019 s
% 1.55/1.29 % (855)Instructions burned: 28 (million)
% 1.55/1.29 % (855)------------------------------
% 1.55/1.29 % (855)------------------------------
% 1.55/1.29 % (867)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/15Mi)
% 1.55/1.29 % (870)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/7Mi)
% 1.55/1.30 % (870)Instruction limit reached!
% 1.55/1.30 % (870)------------------------------
% 1.55/1.30 % (870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (870)Termination reason: Unknown
% 1.55/1.30 % (870)Termination phase: Saturation
% 1.55/1.30
% 1.55/1.30 % (870)Memory used [KB]: 1023
% 1.55/1.30 % (870)Time elapsed: 0.004 s
% 1.55/1.30 % (870)Instructions burned: 9 (million)
% 1.55/1.30 % (870)------------------------------
% 1.55/1.30 % (870)------------------------------
% 1.55/1.30 % (867)Instruction limit reached!
% 1.55/1.30 % (867)------------------------------
% 1.55/1.30 % (867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (871)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/16Mi)
% 1.63/1.30 % (867)Termination reason: Unknown
% 1.63/1.30 % (867)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (867)Memory used [KB]: 5628
% 1.63/1.30 % (867)Time elapsed: 0.011 s
% 1.63/1.30 % (867)Instructions burned: 15 (million)
% 1.63/1.30 % (867)------------------------------
% 1.63/1.30 % (867)------------------------------
% 1.63/1.30 % (869)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/1041Mi)
% 1.63/1.30 % (871)Instruction limit reached!
% 1.63/1.30 % (871)------------------------------
% 1.63/1.30 % (871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (871)Termination reason: Unknown
% 1.63/1.30 % (871)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (871)Memory used [KB]: 5628
% 1.63/1.30 % (871)Time elapsed: 0.008 s
% 1.63/1.30 % (871)Instructions burned: 16 (million)
% 1.63/1.30 % (871)------------------------------
% 1.63/1.30 % (871)------------------------------
% 1.63/1.30 % (872)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 1.63/1.31 % (873)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 1.63/1.31 % (873)Instruction limit reached!
% 1.63/1.31 % (873)------------------------------
% 1.63/1.31 % (873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (873)Termination reason: Unknown
% 1.63/1.31 % (873)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (873)Memory used [KB]: 1023
% 1.63/1.31 % (873)Time elapsed: 0.002 s
% 1.63/1.31 % (873)Instructions burned: 3 (million)
% 1.63/1.31 % (873)------------------------------
% 1.63/1.31 % (873)------------------------------
% 1.63/1.31 % (872)Instruction limit reached!
% 1.63/1.31 % (872)------------------------------
% 1.63/1.31 % (872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (872)Termination reason: Unknown
% 1.63/1.31 % (872)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (872)Memory used [KB]: 5500
% 1.63/1.31 % (872)Time elapsed: 0.004 s
% 1.63/1.31 % (872)Instructions burned: 3 (million)
% 1.63/1.31 % (872)------------------------------
% 1.63/1.31 % (872)------------------------------
% 1.63/1.31 % (875)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 1.63/1.31 % (875)Instruction limit reached!
% 1.63/1.31 % (875)------------------------------
% 1.63/1.31 % (875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (875)Termination reason: Unknown
% 1.63/1.31 % (875)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (875)Memory used [KB]: 5500
% 1.63/1.31 % (875)Time elapsed: 0.003 s
% 1.63/1.31 % (875)Instructions burned: 3 (million)
% 1.63/1.31 % (875)------------------------------
% 1.63/1.31 % (875)------------------------------
% 1.63/1.32 % (876)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/4Mi)
% 1.63/1.32 % (876)Instruction limit reached!
% 1.63/1.32 % (876)------------------------------
% 1.63/1.32 % (876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (876)Termination reason: Unknown
% 1.63/1.32 % (876)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (876)Memory used [KB]: 5500
% 1.63/1.32 % (876)Time elapsed: 0.003 s
% 1.63/1.32 % (876)Instructions burned: 6 (million)
% 1.63/1.32 % (876)------------------------------
% 1.63/1.32 % (876)------------------------------
% 1.63/1.32 % (877)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/18Mi)
% 1.63/1.32 % (878)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/710Mi)
% 1.63/1.32 % (874)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/7Mi)
% 1.63/1.33 % (879)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/6Mi)
% 1.63/1.33 % (874)Refutation not found, incomplete strategy
% 1.63/1.33 % (874)------------------------------
% 1.63/1.33 % (874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (874)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.33
% 1.63/1.33
% 1.63/1.33 % (874)Memory used [KB]: 5500
% 1.63/1.33 % (874)Time elapsed: 0.004 s
% 1.63/1.33 % (874)Instructions burned: 3 (million)
% 1.63/1.33 % (874)------------------------------
% 1.63/1.33 % (874)------------------------------
% 1.63/1.33 % (879)Instruction limit reached!
% 1.63/1.33 % (879)------------------------------
% 1.63/1.33 % (879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (879)Termination reason: Unknown
% 1.63/1.33 % (879)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (879)Memory used [KB]: 5500
% 1.63/1.33 % (879)Time elapsed: 0.003 s
% 1.63/1.33 % (879)Instructions burned: 6 (million)
% 1.63/1.33 % (879)------------------------------
% 1.63/1.33 % (879)------------------------------
% 1.63/1.33 % (877)First to succeed.
% 1.63/1.34 % (877)Refutation found. Thanks to Tanya!
% 1.63/1.34 % SZS status Theorem for DTF2THF_740
% 1.63/1.34 % SZS output start Proof for DTF2THF_740
% 1.63/1.34 thf(type_def_5, type, nat: $tType).
% 1.63/1.34 thf(func_def_0, type, nat: $tType).
% 1.63/1.34 thf(func_def_1, type, x: nat).
% 1.63/1.34 thf(func_def_2, type, y: nat).
% 1.63/1.34 thf(func_def_3, type, z: nat).
% 1.63/1.34 thf(func_def_4, type, u: nat).
% 1.63/1.34 thf(func_def_5, type, some: (nat > $o) > $o).
% 1.63/1.34 thf(func_def_6, type, diffprop: nat > nat > nat > $o).
% 1.63/1.34 thf(func_def_8, type, pl: nat > nat > nat).
% 1.63/1.34 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 1.63/1.34 thf(f87,plain,(
% 1.63/1.34 $false),
% 1.63/1.34 inference(subsumption_resolution,[status(thm)],[f86,f31])).
% 1.63/1.34 thf(f31,plain,(
% 1.63/1.34 ((some @ (diffprop @ x @ y)) = $true)),
% 1.63/1.34 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.63/1.34 thf(f28,plain,(
% 1.63/1.34 ($true = (some @ (^[Y0 : nat]: (diffprop @ x @ y @ Y0))))),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.34 thf(f10,plain,(
% 1.63/1.34 ($true = (some @ (^[Y0 : nat]: (diffprop @ x @ y @ Y0))))),
% 1.63/1.34 inference(fool_elimination,[status(thm)],[f9])).
% 1.63/1.34 thf(f9,plain,(
% 1.63/1.34 (some @ (^[X0 : nat] : (diffprop @ x @ y @ X0)))),
% 1.63/1.34 inference(rectify,[status(thm)],[f1])).
% 1.63/1.34 thf(f1,axiom,(
% 1.63/1.34 (some @ (^[X0 : nat] : (diffprop @ x @ y @ X0)))),
% 1.63/1.34 file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',m)).
% 1.63/1.34 thf(f86,plain,(
% 1.63/1.34 ((some @ (diffprop @ x @ y)) != $true)),
% 1.63/1.34 inference(subsumption_resolution,[status(thm)],[f83,f33])).
% 1.63/1.34 thf(f33,plain,(
% 1.63/1.34 ((some @ (diffprop @ z @ u)) = $true)),
% 1.63/1.34 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.63/1.34 thf(f27,plain,(
% 1.63/1.34 ((some @ (^[Y0 : nat]: (diffprop @ z @ u @ Y0))) = $true)),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.34 thf(f14,plain,(
% 1.63/1.34 ((some @ (^[Y0 : nat]: (diffprop @ z @ u @ Y0))) = $true)),
% 1.63/1.34 inference(fool_elimination,[status(thm)],[f13])).
% 1.63/1.34 thf(f13,plain,(
% 1.63/1.34 (some @ (^[X0 : nat] : (diffprop @ z @ u @ X0)))),
% 1.63/1.34 inference(rectify,[status(thm)],[f2])).
% 1.63/1.34 thf(f2,axiom,(
% 1.63/1.34 (some @ (^[X1 : nat] : (diffprop @ z @ u @ X1)))),
% 1.63/1.34 file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',n)).
% 1.63/1.34 thf(f83,plain,(
% 1.63/1.34 ((some @ (diffprop @ z @ u)) != $true) | ((some @ (diffprop @ x @ y)) != $true)),
% 1.63/1.34 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.63/1.34 thf(f80,plain,(
% 1.63/1.34 ((some @ (diffprop @ z @ u)) != $true) | ($true != $true) | ((some @ (diffprop @ x @ y)) != $true)),
% 1.63/1.34 inference(superposition,[status(thm)],[f50,f35])).
% 1.63/1.34 thf(f35,plain,(
% 1.63/1.34 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((some @ (diffprop @ (pl @ X2 @ X1) @ (pl @ X1 @ X0))) = $true) | ($true != (some @ (diffprop @ X2 @ X0)))) )),
% 1.63/1.34 inference(superposition,[status(thm)],[f32,f24])).
% 1.63/1.34 thf(f24,plain,(
% 1.63/1.34 ( ! [X0 : nat,X1 : nat] : (((pl @ X1 @ X0) = (pl @ X0 @ X1))) )),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f19])).
% 1.63/1.34 thf(f19,plain,(
% 1.63/1.34 ! [X0 : nat,X1 : nat] : ((pl @ X1 @ X0) = (pl @ X0 @ X1))),
% 1.63/1.34 inference(rectify,[status(thm)],[f5])).
% 1.63/1.34 thf(f5,axiom,(
% 1.63/1.34 ! [X3 : nat,X2 : nat] : ((pl @ X2 @ X3) = (pl @ X3 @ X2))),
% 1.63/1.34 file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',satz6)).
% 1.63/1.34 thf(f32,plain,(
% 1.63/1.34 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((some @ (diffprop @ (pl @ X2 @ X1) @ (pl @ X0 @ X1))) = $true) | ($true != (some @ (diffprop @ X2 @ X0)))) )),
% 1.63/1.34 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.63/1.34 thf(f29,plain,(
% 1.63/1.34 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X2 @ X0 @ Y0))) != $true) | ((some @ (^[Y0 : nat]: (diffprop @ (pl @ X2 @ X1) @ (pl @ X0 @ X1) @ Y0))) = $true)) )),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f21])).
% 1.63/1.34 thf(f21,plain,(
% 1.63/1.34 ! [X0 : nat,X1 : nat,X2 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ (pl @ X2 @ X1) @ (pl @ X0 @ X1) @ Y0))) = $true) | ((some @ (^[Y0 : nat]: (diffprop @ X2 @ X0 @ Y0))) != $true))),
% 1.63/1.34 inference(ennf_transformation,[status(thm)],[f18])).
% 1.63/1.34 thf(f18,plain,(
% 1.63/1.34 ! [X0 : nat,X1 : nat,X2 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X2 @ X0 @ Y0))) = $true) => ((some @ (^[Y0 : nat]: (diffprop @ (pl @ X2 @ X1) @ (pl @ X0 @ X1) @ Y0))) = $true))),
% 1.63/1.34 inference(fool_elimination,[status(thm)],[f17])).
% 1.63/1.34 thf(f17,plain,(
% 1.63/1.34 ! [X0 : nat,X1 : nat,X2 : nat] : ((some @ (^[X3 : nat] : (diffprop @ X2 @ X0 @ X3))) => (some @ (^[X4 : nat] : (diffprop @ (pl @ X2 @ X1) @ (pl @ X0 @ X1) @ X4))))),
% 1.63/1.34 inference(rectify,[status(thm)],[f4])).
% 1.63/1.34 thf(f4,axiom,(
% 1.63/1.34 ! [X3 : nat,X4 : nat,X2 : nat] : ((some @ (^[X0 : nat] : (diffprop @ X2 @ X3 @ X0))) => (some @ (^[X0 : nat] : (diffprop @ (pl @ X2 @ X4) @ (pl @ X3 @ X4) @ X0))))),
% 1.63/1.34 file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',satz19a)).
% 1.63/1.34 thf(f50,plain,(
% 1.63/1.34 ( ! [X0 : nat] : (((some @ (diffprop @ (pl @ z @ X0) @ (pl @ y @ u))) != $true) | ((some @ (diffprop @ x @ X0)) != $true)) )),
% 1.63/1.34 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.63/1.34 thf(f49,plain,(
% 1.63/1.34 ( ! [X0 : nat] : (($true != $true) | ((some @ (diffprop @ (pl @ z @ X0) @ (pl @ y @ u))) != $true) | ((some @ (diffprop @ x @ X0)) != $true)) )),
% 1.63/1.34 inference(superposition,[status(thm)],[f40,f35])).
% 1.63/1.34 thf(f40,plain,(
% 1.63/1.34 ( ! [X0 : nat] : (((some @ (diffprop @ (pl @ x @ z) @ X0)) != $true) | ((some @ (diffprop @ X0 @ (pl @ y @ u))) != $true)) )),
% 1.63/1.34 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.63/1.34 thf(f39,plain,(
% 1.63/1.34 ( ! [X0 : nat] : (((some @ (diffprop @ (pl @ x @ z) @ X0)) != $true) | ((some @ (diffprop @ X0 @ (pl @ y @ u))) != $true) | ($true != $true)) )),
% 1.63/1.34 inference(superposition,[status(thm)],[f30,f34])).
% 1.63/1.34 thf(f34,plain,(
% 1.63/1.34 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((some @ (diffprop @ X0 @ X1)) = $true) | ((some @ (diffprop @ X2 @ X1)) != $true) | ((some @ (diffprop @ X0 @ X2)) != $true)) )),
% 1.63/1.34 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.63/1.34 thf(f25,plain,(
% 1.63/1.34 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X0 @ X2 @ Y0))) != $true) | ((some @ (^[Y0 : nat]: (diffprop @ X0 @ X1 @ Y0))) = $true) | ((some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))) != $true)) )),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.63/1.34 thf(f23,plain,(
% 1.63/1.34 ! [X0 : nat,X1 : nat,X2 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X0 @ X2 @ Y0))) != $true) | ((some @ (^[Y0 : nat]: (diffprop @ X0 @ X1 @ Y0))) = $true) | ((some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))) != $true))),
% 1.63/1.34 inference(flattening,[status(thm)],[f22])).
% 1.63/1.34 thf(f22,plain,(
% 1.63/1.34 ! [X0 : nat,X1 : nat,X2 : nat] : ((((some @ (^[Y0 : nat]: (diffprop @ X0 @ X1 @ Y0))) = $true) | ((some @ (^[Y0 : nat]: (diffprop @ X0 @ X2 @ Y0))) != $true)) | ((some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))) != $true))),
% 1.63/1.34 inference(ennf_transformation,[status(thm)],[f16])).
% 1.63/1.34 thf(f16,plain,(
% 1.63/1.34 ! [X0 : nat,X1 : nat,X2 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))) = $true) => (((some @ (^[Y0 : nat]: (diffprop @ X0 @ X2 @ Y0))) = $true) => ((some @ (^[Y0 : nat]: (diffprop @ X0 @ X1 @ Y0))) = $true)))),
% 1.63/1.34 inference(fool_elimination,[status(thm)],[f15])).
% 1.63/1.34 thf(f15,plain,(
% 1.63/1.34 ! [X0 : nat,X1 : nat,X2 : nat] : ((some @ (^[X3 : nat] : (diffprop @ X2 @ X1 @ X3))) => ((some @ (^[X4 : nat] : (diffprop @ X0 @ X2 @ X4))) => (some @ (^[X5 : nat] : (diffprop @ X0 @ X1 @ X5)))))),
% 1.63/1.34 inference(rectify,[status(thm)],[f3])).
% 1.63/1.34 thf(f3,axiom,(
% 1.63/1.34 ! [X4 : nat,X2 : nat,X3 : nat] : ((some @ (^[X5 : nat] : (diffprop @ X3 @ X2 @ X5))) => ((some @ (^[X5 : nat] : (diffprop @ X4 @ X3 @ X5))) => (some @ (^[X5 : nat] : (diffprop @ X4 @ X2 @ X5)))))),
% 1.63/1.34 file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',satz15)).
% 1.63/1.34 thf(f30,plain,(
% 1.63/1.34 ((some @ (diffprop @ (pl @ x @ z) @ (pl @ y @ u))) != $true)),
% 1.63/1.34 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.63/1.34 thf(f26,plain,(
% 1.63/1.34 ((some @ (^[Y0 : nat]: (diffprop @ (pl @ x @ z) @ (pl @ y @ u) @ Y0))) != $true)),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 1.63/1.34 thf(f20,plain,(
% 1.63/1.34 ((some @ (^[Y0 : nat]: (diffprop @ (pl @ x @ z) @ (pl @ y @ u) @ Y0))) != $true)),
% 1.63/1.34 inference(flattening,[status(thm)],[f12])).
% 1.63/1.34 thf(f12,plain,(
% 1.63/1.34 ~((some @ (^[Y0 : nat]: (diffprop @ (pl @ x @ z) @ (pl @ y @ u) @ Y0))) = $true)),
% 1.63/1.34 inference(fool_elimination,[status(thm)],[f11])).
% 1.63/1.34 thf(f11,plain,(
% 1.63/1.34 ~(some @ (^[X0 : nat] : (diffprop @ (pl @ x @ z) @ (pl @ y @ u) @ X0)))),
% 1.63/1.34 inference(rectify,[status(thm)],[f7])).
% 1.63/1.34 thf(f7,negated_conjecture,(
% 1.63/1.34 ~(some @ (^[X1 : nat] : (diffprop @ (pl @ x @ z) @ (pl @ y @ u) @ X1)))),
% 1.63/1.34 inference(negated_conjecture,[status(cth)],[f6])).
% 1.63/1.34 thf(f6,conjecture,(
% 1.63/1.34 (some @ (^[X1 : nat] : (diffprop @ (pl @ x @ z) @ (pl @ y @ u) @ X1)))),
% 1.63/1.34 file('/export/starexec/sandbox2/tmp/tmp.EStopkkSNx/DTF2THF_740.p',satz21)).
% 1.63/1.34 % SZS output end Proof for DTF2THF_740
% 1.63/1.34 % (877)------------------------------
% 1.63/1.34 % (877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (877)Termination reason: Refutation
% 1.63/1.34
% 1.63/1.34 % (877)Memory used [KB]: 5628
% 1.63/1.34 % (877)Time elapsed: 0.014 s
% 1.63/1.34 % (877)Instructions burned: 16 (million)
% 1.63/1.34 % (877)------------------------------
% 1.63/1.34 % (877)------------------------------
% 1.63/1.34 % (847)Success in time 0.076 s
%------------------------------------------------------------------------------