%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM721^1 : 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 : n012.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 09:24:25 AM UTC 2026
% Result : Theorem 0.88s 0.88s
% Output : Refutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 31 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 254 ( 20 ~; 11 |; 0 &; 217 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 60 ( 32 ^; 28 !; 0 ?; 60 :)
% 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,
ts: nat > nat > nat ).
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f29,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f28,f22]) ).
thf(f22,plain,
( ( some @ ( diffprop @ u @ z ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ u @ z @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ u @ z @ Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( some
@ ^ [X0: nat] : ( diffprop @ u @ z @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ u @ z @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDvJfCtERu/DTF2THF_20092.p',k) ).
thf(f28,plain,
( ( some @ ( diffprop @ u @ z ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f27,f23]) ).
thf(f23,plain,
( $true
= ( some @ ( diffprop @ y @ x ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ y @ x @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ y @ x @ Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( some
@ ^ [X0: nat] : ( diffprop @ y @ x @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ y @ x @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDvJfCtERu/DTF2THF_20092.p',l) ).
thf(f27,plain,
( ( $true
!= ( some @ ( diffprop @ y @ x ) ) )
| ( ( some @ ( diffprop @ u @ z ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true != $true )
| ( $true
!= ( some @ ( diffprop @ y @ x ) ) )
| ( ( some @ ( diffprop @ u @ z ) )
!= $true ) ),
inference(superposition,[status(thm)],[f25,f24]) ).
thf(f24,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ ( ts @ X3 @ X2 ) @ ( ts @ X0 @ X1 ) ) )
= $true )
| ( ( some @ ( diffprop @ X3 @ X0 ) )
!= $true )
| ( ( some @ ( diffprop @ X2 @ X1 ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X3 @ X0 @ Y0 ) )
!= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X3 @ X2 ) @ ( ts @ X0 @ X1 ) @ Y0 ) )
= $true )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X3 @ X2 ) @ ( ts @ X0 @ X1 ) @ Y0 ) )
= $true )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X3 @ X0 @ Y0 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X3 @ X2 ) @ ( ts @ X0 @ X1 ) @ Y0 ) )
= $true )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X3 @ X0 @ Y0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X3 @ X0 @ Y0 ) )
= $true )
=> ( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) ) )
=> ( ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X3 @ X2 ) @ ( ts @ X0 @ X1 ) @ Y0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( some
@ ^ [X4: nat] : ( diffprop @ X3 @ X0 @ X4 ) )
=> ( ( some
@ ^ [X5: nat] : ( diffprop @ X2 @ X1 @ X5 ) )
=> ( some
@ ^ [X6: nat] : ( diffprop @ ( ts @ X3 @ X2 ) @ ( ts @ X0 @ X1 ) @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: nat,X4: nat,X3: nat,X1: nat] :
( ( some
@ ^ [X4: nat] : ( diffprop @ X1 @ X2 @ X4 ) )
=> ( ( some
@ ^ [X5: nat] : ( diffprop @ X3 @ X4 @ X5 ) )
=> ( some
@ ^ [X5: nat] : ( diffprop @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X4 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDvJfCtERu/DTF2THF_20092.p',satz34) ).
thf(f25,plain,
( ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Y0 ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( some
@ ^ [X0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDvJfCtERu/DTF2THF_20092.p',satz34a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM721^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue Feb 24 11:12:00 EST 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.31 ---- Original DTF file ---
% 0.06/0.31 thf(spec,logic,$$dhol).
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 % File : NUM721^1 : TPTP v9.2.1. Released v3.7.0.
% 0.06/0.31 % Domain : Number Theory
% 0.06/0.31 % Problem : Landau theorem 34a
% 0.06/0.31 % Version : Especial.
% 0.06/0.31 % English : some (lambda v.diffprop (ts y u) (ts x z) v)
% 0.06/0.31
% 0.06/0.31 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.06/0.31 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.06/0.31 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.06/0.31 % Source : [Bro09]
% 0.06/0.31 % Names : satz34a [Lan30]
% 0.06/0.31
% 0.06/0.31 % Status : Theorem
% 0.06/0.31 % : Without extensionality : Theorem
% 0.06/0.31 % Rating : 0.00 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.2.0, 0.25 v5.1.0, 0.00 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.00 v4.0.0, 0.33 v3.7.0
% 0.06/0.31 % Syntax : Number of formulae : 12 ( 0 unt; 8 typ; 0 def)
% 0.06/0.31 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.06/0.31 % Maximal formula atoms : 6 ( 3 avg)
% 0.06/0.31 % Number of connectives : 34 ( 0 ~; 0 |; 0 &; 32 @)
% 0.06/0.31 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.06/0.31 % Maximal formula depth : 14 ( 9 avg)
% 0.06/0.31 % Number of types : 2 ( 1 usr)
% 0.06/0.31 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.06/0.31 % Number of symbols : 7 ( 7 usr; 4 con; 0-3 aty)
% 0.06/0.31 % Number of variables : 10 ( 6 ^; 4 !; 0 ?; 10 :)
% 0.06/0.31 % SPC : TH0_THM_NEQ_NAR
% 0.06/0.31
% 0.06/0.31 % Comments :
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 thf(nat_type,type,
% 0.06/0.31 nat: $tType ).
% 0.06/0.31
% 0.06/0.31 thf(x,type,
% 0.06/0.31 x: nat ).
% 0.06/0.31
% 0.06/0.31 thf(y,type,
% 0.06/0.31 y: nat ).
% 0.06/0.31
% 0.06/0.31 thf(z,type,
% 0.06/0.31 z: nat ).
% 0.06/0.31
% 0.06/0.31 thf(u,type,
% 0.06/0.31 u: nat ).
% 0.06/0.31
% 0.06/0.31 thf(some,type,
% 0.06/0.31 some: ( nat > $o ) > $o ).
% 0.06/0.31
% 0.06/0.31 thf(diffprop,type,
% 0.06/0.31 diffprop: nat > nat > nat > $o ).
% 0.06/0.31
% 0.06/0.31 thf(l,axiom,
% 0.06/0.31 ( some
% 0.06/0.31 @ ^ [Xv: nat] : ( diffprop @ y @ x @ Xv ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(k,axiom,
% 0.06/0.31 ( some
% 0.06/0.31 @ ^ [Xv: nat] : ( diffprop @ u @ z @ Xv ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(ts,type,
% 0.06/0.31 ts: nat > nat > nat ).
% 0.06/0.31
% 0.06/0.31 thf(satz34,axiom,
% 0.06/0.31 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.06/0.31 ( ( some
% 0.06/0.31 @ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
% 0.06/0.31 => ( ( some
% 0.06/0.31 @ ^ [Xu_0: nat] : ( diffprop @ Xz @ Xu @ Xu_0 ) )
% 0.06/0.31 => ( some
% 0.06/0.31 @ ^ [Xu_0: nat] : ( diffprop @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) @ Xu_0 ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(satz34a,conjecture,
% 0.06/0.31 ( some
% 0.06/0.31 @ ^ [Xv: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Xv ) ) ).
% 0.06/0.31
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 ------------------------
% 0.88/0.86 ---- Embedded in THF ---
% 0.88/0.86 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.88/0.86 %%% Generated on Tue Feb 24 11:12:01 EST 2026
% 0.88/0.86 %%% using '$$dhol' embedding, version 1.3.0.
% 0.88/0.86 %%% Logic specification used:
% 0.88/0.86 %%% thf(spec, logic, $$dhol).
% 0.88/0.86
% 0.88/0.86 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.kDvJfCtERu/DTF2DTF20092.p
% See solution above
% 0.88/0.86 ------------------------
% 0.88/0.86 ---- Cleaned THF ---
% 0.88/0.87 thf(nat_type,type,
% 0.88/0.87 nat: $tType ).
% 0.88/0.87
% 0.88/0.87 thf(x,type,
% 0.88/0.87 x: nat ).
% 0.88/0.87
% 0.88/0.87 thf(y,type,
% 0.88/0.87 y: nat ).
% 0.88/0.87
% 0.88/0.87 thf(z,type,
% 0.88/0.87 z: nat ).
% 0.88/0.87
% 0.88/0.87 thf(u,type,
% 0.88/0.87 u: nat ).
% 0.88/0.87
% 0.88/0.87 thf(some,type,
% 0.88/0.87 some: ( nat > $o ) > $o ).
% 0.88/0.87
% 0.88/0.87 thf(diffprop,type,
% 0.88/0.87 diffprop: nat > nat > nat > $o ).
% 0.88/0.87
% 0.88/0.87 thf(l,axiom,
% 0.88/0.87 ( some
% 0.88/0.87 @ ^ [Xv: nat] : ( diffprop @ y @ x @ Xv ) ) ).
% 0.88/0.87
% 0.88/0.87 thf(k,axiom,
% 0.88/0.87 ( some
% 0.88/0.87 @ ^ [Xv: nat] : ( diffprop @ u @ z @ Xv ) ) ).
% 0.88/0.87
% 0.88/0.87 thf(ts,type,
% 0.88/0.87 ts: nat > nat > nat ).
% 0.88/0.87
% 0.88/0.87 thf(satz34,axiom,
% 0.88/0.87 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.88/0.87 ( ( some
% 0.88/0.87 @ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
% 0.88/0.87 => ( ( some
% 0.88/0.87 @ ^ [Xu_0: nat] : ( diffprop @ Xz @ Xu @ Xu_0 ) )
% 0.88/0.87 => ( some
% 0.88/0.87 @ ^ [Xu_0: nat] : ( diffprop @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) @ Xu_0 ) ) ) ) ).
% 0.88/0.87
% 0.88/0.87 thf(satz34a,conjecture,
% 0.88/0.87 ( some
% 0.88/0.87 @ ^ [Xv: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Xv ) ) ).
% 0.88/0.87 ------------------------
% 0.88/0.88 % (20295)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_20092 for (3000ds/4Mi)
% 0.88/0.88 % (20294)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20092 for (3000ds/183Mi)
% 0.88/0.88 % (20296)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_20092 for (3000ds/27Mi)
% 0.88/0.88 % (20297)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20092 for (3000ds/2Mi)
% 0.88/0.88 % (20298)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_20092 for (3000ds/2Mi)
% 0.88/0.88 % (20300)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20092 for (3000ds/18Mi)
% 0.88/0.88 % (20299)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_20092 for (3000ds/275Mi)
% 0.88/0.88 % (20297)Instruction limit reached!
% 0.88/0.88 % (20297)------------------------------
% 0.88/0.88 % (20297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.88/0.88 % (20297)Termination reason: Unknown
% 0.88/0.88 % (20297)Termination phase: Saturation
% 0.88/0.88
% 0.88/0.88 % (20297)Memory used [KB]: 5500
% 0.88/0.88 % (20297)Time elapsed: 0.002 s
% 0.88/0.88 % (20297)Instructions burned: 2 (million)
% 0.88/0.88 % (20297)------------------------------
% 0.88/0.88 % (20297)------------------------------
% 0.88/0.88 % (20298)Instruction limit reached!
% 0.88/0.88 % (20298)------------------------------
% 0.88/0.88 % (20298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.88/0.88 % (20298)Termination reason: Unknown
% 0.88/0.88 % (20298)Termination phase: Saturation
% 0.88/0.88
% 0.88/0.88 % (20298)Memory used [KB]: 5500
% 0.88/0.88 % (20298)Time elapsed: 0.002 s
% 0.88/0.88 % (20298)Instructions burned: 3 (million)
% 0.88/0.88 % (20298)------------------------------
% 0.88/0.88 % (20298)------------------------------
% 0.88/0.88 % (20299)First to succeed.
% 0.88/0.88 % (20295)Instruction limit reached!
% 0.88/0.88 % (20295)------------------------------
% 0.88/0.88 % (20295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.88/0.88 % (20295)Termination reason: Unknown
% 0.88/0.88 % (20295)Termination phase: Saturation
% 0.88/0.88
% 0.88/0.88 % (20295)Memory used [KB]: 5500
% 0.88/0.88 % (20295)Time elapsed: 0.003 s
% 0.88/0.88 % (20295)Instructions burned: 5 (million)
% 0.88/0.88 % (20295)------------------------------
% 0.88/0.88 % (20295)------------------------------
% 0.88/0.88 % (20296)Also succeeded, but the first one will report.
% 0.88/0.88 % (20299)Refutation found. Thanks to Tanya!
% 0.88/0.88 % SZS status Theorem for DTF2THF_20092
% 0.88/0.88 % SZS output start Proof for DTF2THF_20092
% 0.88/0.88 thf(type_def_5, type, nat: $tType).
% 0.88/0.88 thf(func_def_0, type, nat: $tType).
% 0.88/0.88 thf(func_def_1, type, x: nat).
% 0.88/0.88 thf(func_def_2, type, y: nat).
% 0.88/0.88 thf(func_def_3, type, z: nat).
% 0.88/0.88 thf(func_def_4, type, u: nat).
% 0.88/0.88 thf(func_def_5, type, some: (nat > $o) > $o).
% 0.88/0.88 thf(func_def_6, type, diffprop: nat > nat > nat > $o).
% 0.88/0.88 thf(func_def_8, type, ts: nat > nat > nat).
% 0.88/0.88 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 0.88/0.88 thf(f29,plain,(
% 0.88/0.88 $false),
% 0.88/0.88 inference(subsumption_resolution,[status(thm)],[f28,f22])).
% 0.88/0.88 thf(f22,plain,(
% 0.88/0.88 ((some @ (diffprop @ u @ z)) = $true)),
% 0.88/0.88 inference(beta_eta_normalization,[status(thm)],[f20])).
% 0.88/0.88 thf(f20,plain,(
% 0.88/0.88 ((some @ (^[Y0 : nat]: (diffprop @ u @ z @ Y0))) = $true)),
% 0.88/0.88 inference(cnf_transformation,[status(thm)],[f10])).
% 0.88/0.88 thf(f10,plain,(
% 0.88/0.88 ((some @ (^[Y0 : nat]: (diffprop @ u @ z @ Y0))) = $true)),
% 0.88/0.88 inference(fool_elimination,[status(thm)],[f9])).
% 0.88/0.88 thf(f9,plain,(
% 0.88/0.88 (some @ (^[X0 : nat] : (diffprop @ u @ z @ X0)))),
% 0.88/0.88 inference(rectify,[status(thm)],[f2])).
% 0.88/0.88 thf(f2,axiom,(
% 0.88/0.88 (some @ (^[X0 : nat] : (diffprop @ u @ z @ X0)))),
% 0.88/0.88 file('/export/starexec/sandbox2/tmp/tmp.kDvJfCtERu/DTF2THF_20092.p',k)).
% 0.88/0.88 thf(f28,plain,(
% 0.88/0.88 ((some @ (diffprop @ u @ z)) != $true)),
% 0.88/0.88 inference(subsumption_resolution,[status(thm)],[f27,f23])).
% 0.88/0.88 thf(f23,plain,(
% 0.88/0.88 ($true = (some @ (diffprop @ y @ x)))),
% 0.88/0.88 inference(beta_eta_normalization,[status(thm)],[f18])).
% 0.88/0.88 thf(f18,plain,(
% 0.88/0.88 ((some @ (^[Y0 : nat]: (diffprop @ y @ x @ Y0))) = $true)),
% 0.88/0.88 inference(cnf_transformation,[status(thm)],[f12])).
% 0.88/0.88 thf(f12,plain,(
% 0.88/0.88 ((some @ (^[Y0 : nat]: (diffprop @ y @ x @ Y0))) = $true)),
% 0.88/0.88 inference(fool_elimination,[status(thm)],[f11])).
% 0.88/0.88 thf(f11,plain,(
% 0.88/0.88 (some @ (^[X0 : nat] : (diffprop @ y @ x @ X0)))),
% 0.88/0.88 inference(rectify,[status(thm)],[f1])).
% 0.88/0.88 thf(f1,axiom,(
% 0.88/0.88 (some @ (^[X0 : nat] : (diffprop @ y @ x @ X0)))),
% 0.88/0.88 file('/export/starexec/sandbox2/tmp/tmp.kDvJfCtERu/DTF2THF_20092.p',l)).
% 0.88/0.88 thf(f27,plain,(
% 0.88/0.88 ($true != (some @ (diffprop @ y @ x))) | ((some @ (diffprop @ u @ z)) != $true)),
% 0.88/0.88 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 0.88/0.88 thf(f26,plain,(
% 0.88/0.88 ($true != $true) | ($true != (some @ (diffprop @ y @ x))) | ((some @ (diffprop @ u @ z)) != $true)),
% 0.88/0.88 inference(superposition,[status(thm)],[f25,f24])).
% 0.88/0.88 thf(f24,plain,(
% 0.88/0.88 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (((some @ (diffprop @ (ts @ X3 @ X2) @ (ts @ X0 @ X1))) = $true) | ((some @ (diffprop @ X3 @ X0)) != $true) | ((some @ (diffprop @ X2 @ X1)) != $true)) )),
% 0.88/0.88 inference(beta_eta_normalization,[status(thm)],[f21])).
% 0.88/0.88 thf(f21,plain,(
% 0.88/0.88 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X3 @ X0 @ Y0))) != $true) | ((some @ (^[Y0 : nat]: (diffprop @ (ts @ X3 @ X2) @ (ts @ X0 @ X1) @ Y0))) = $true) | ($true != (some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))))) )),
% 0.88/0.88 inference(cnf_transformation,[status(thm)],[f17])).
% 0.88/0.88 thf(f17,plain,(
% 0.88/0.88 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ (ts @ X3 @ X2) @ (ts @ X0 @ X1) @ Y0))) = $true) | ($true != (some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0)))) | ((some @ (^[Y0 : nat]: (diffprop @ X3 @ X0 @ Y0))) != $true))),
% 0.88/0.88 inference(flattening,[status(thm)],[f16])).
% 0.88/0.88 thf(f16,plain,(
% 0.88/0.88 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((((some @ (^[Y0 : nat]: (diffprop @ (ts @ X3 @ X2) @ (ts @ X0 @ X1) @ Y0))) = $true) | ($true != (some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0))))) | ((some @ (^[Y0 : nat]: (diffprop @ X3 @ X0 @ Y0))) != $true))),
% 0.88/0.88 inference(ennf_transformation,[status(thm)],[f14])).
% 0.88/0.88 thf(f14,plain,(
% 0.88/0.88 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X3 @ X0 @ Y0))) = $true) => (($true = (some @ (^[Y0 : nat]: (diffprop @ X2 @ X1 @ Y0)))) => ((some @ (^[Y0 : nat]: (diffprop @ (ts @ X3 @ X2) @ (ts @ X0 @ X1) @ Y0))) = $true)))),
% 0.88/0.88 inference(fool_elimination,[status(thm)],[f13])).
% 0.88/0.88 thf(f13,plain,(
% 0.88/0.88 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((some @ (^[X4 : nat] : (diffprop @ X3 @ X0 @ X4))) => ((some @ (^[X5 : nat] : (diffprop @ X2 @ X1 @ X5))) => (some @ (^[X6 : nat] : (diffprop @ (ts @ X3 @ X2) @ (ts @ X0 @ X1) @ X6)))))),
% 0.88/0.88 inference(rectify,[status(thm)],[f3])).
% 0.88/0.88 thf(f3,axiom,(
% 0.88/0.88 ! [X2 : nat,X4 : nat,X3 : nat,X1 : nat] : ((some @ (^[X4 : nat] : (diffprop @ X1 @ X2 @ X4))) => ((some @ (^[X5 : nat] : (diffprop @ X3 @ X4 @ X5))) => (some @ (^[X5 : nat] : (diffprop @ (ts @ X1 @ X3) @ (ts @ X2 @ X4) @ X5)))))),
% 0.88/0.88 file('/export/starexec/sandbox2/tmp/tmp.kDvJfCtERu/DTF2THF_20092.p',satz34)).
% 0.88/0.88 thf(f25,plain,(
% 0.88/0.88 ((some @ (diffprop @ (ts @ y @ u) @ (ts @ x @ z))) != $true)),
% 0.88/0.88 inference(beta_eta_normalization,[status(thm)],[f19])).
% 0.88/0.88 thf(f19,plain,(
% 0.88/0.88 ($true != (some @ (^[Y0 : nat]: (diffprop @ (ts @ y @ u) @ (ts @ x @ z) @ Y0))))),
% 0.88/0.88 inference(cnf_transformation,[status(thm)],[f15])).
% 0.88/0.88 thf(f15,plain,(
% 0.88/0.88 ($true != (some @ (^[Y0 : nat]: (diffprop @ (ts @ y @ u) @ (ts @ x @ z) @ Y0))))),
% 0.88/0.88 inference(flattening,[status(thm)],[f8])).
% 0.88/0.88 thf(f8,plain,(
% 0.88/0.88 ~($true = (some @ (^[Y0 : nat]: (diffprop @ (ts @ y @ u) @ (ts @ x @ z) @ Y0))))),
% 0.88/0.88 inference(fool_elimination,[status(thm)],[f7])).
% 0.88/0.88 thf(f7,plain,(
% 0.88/0.88 ~(some @ (^[X0 : nat] : (diffprop @ (ts @ y @ u) @ (ts @ x @ z) @ X0)))),
% 0.88/0.88 inference(rectify,[status(thm)],[f5])).
% 0.88/0.88 thf(f5,negated_conjecture,(
% 0.88/0.88 ~(some @ (^[X0 : nat] : (diffprop @ (ts @ y @ u) @ (ts @ x @ z) @ X0)))),
% 0.88/0.88 inference(negated_conjecture,[status(cth)],[f4])).
% 0.88/0.88 thf(f4,conjecture,(
% 0.88/0.88 (some @ (^[X0 : nat] : (diffprop @ (ts @ y @ u) @ (ts @ x @ z) @ X0)))),
% 0.88/0.88 file('/export/starexec/sandbox2/tmp/tmp.kDvJfCtERu/DTF2THF_20092.p',satz34a)).
% 0.88/0.88 % SZS output end Proof for DTF2THF_20092
% 0.88/0.88 % (20299)------------------------------
% 0.88/0.88 % (20299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.88/0.88 % (20299)Termination reason: Refutation
% 0.88/0.88
% 0.88/0.88 % (20299)Memory used [KB]: 5500
% 0.88/0.88 % (20299)Time elapsed: 0.002 s
% 0.88/0.88 % (20299)Instructions burned: 2 (million)
% 0.88/0.88 % (20299)------------------------------
% 0.88/0.88 % (20299)------------------------------
% 0.88/0.88 % (20293)Success in time 0.01 s
%------------------------------------------------------------------------------