%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU858^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 09:37:36 AM UTC 2026
% Result : Theorem 1.46s 1.29s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 41 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 109 ( 16 ~; 15 |; 15 &; 52 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 32 ^; 25 !; 3 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
sK0: ( a > $o ) > $o ).
thf(func_def_11,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
$true != $true,
inference(superposition,[status(thm)],[f11,f12]) ).
thf(f12,plain,
( $true
= ( sK0
@ ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X1: a > $o,X2: a] :
( ( $true
!= ( sK0 @ X1 ) )
| ( $true
= ( sK0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
& ( $true
= ( sK0
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( sK0
@ ^ [Y0: a] : $false ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: ( a > $o ) > $o] :
( ! [X1: a > $o,X2: a] :
( ( $true
!= ( X0 @ X1 ) )
| ( $true
= ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
& ( $true
= ( X0
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( X0
@ ^ [Y0: a] : $false ) ) )
=> ( ! [X2: a,X1: a > $o] :
( ( $true
!= ( sK0 @ X1 ) )
| ( $true
= ( sK0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
& ( $true
= ( sK0
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( sK0
@ ^ [Y0: a] : $false ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( a > $o ) > $o] :
( ! [X1: a > $o,X2: a] :
( ( $true
!= ( X0 @ X1 ) )
| ( $true
= ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
& ( $true
= ( X0
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( X0
@ ^ [Y0: a] : $false ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( a > $o ) > $o] :
( ( $true
!= ( X0
@ ^ [Y0: a] : $false ) )
& ( $true
= ( X0
@ ^ [Y0: a] : $false ) )
& ! [X1: a > $o,X2: a] :
( ( $true
!= ( X0 @ X1 ) )
| ( $true
= ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ( $true
= ( X0
@ ^ [Y0: a] : $false ) )
& ! [X1: a > $o,X2: a] :
( ( $true
= ( X0 @ X1 ) )
=> ( $true
= ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) ) )
=> ( $true
= ( X0
@ ^ [Y0: a] : $false ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ( $true
= ( X0
@ ^ [Y0: a] : $false ) )
& ! [X2: a > $o,X3: a] :
( ( ( X0 @ X2 )
= $true )
=> ( $true
= ( X0
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) ) ) ) )
=> ( $true
= ( X0
@ ^ [Y0: a] : $false ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X2: a > $o,X3: a] :
( ( X0 @ X2 )
=> ( X0
@ ^ [X4: a] :
( ( X2 @ X4 )
| ( X3 = X4 ) ) ) ) )
=> ( X0
@ ^ [X5: a] : $false ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X2: a > $o,X1: a] :
( ( X0 @ X2 )
=> ( X0
@ ^ [X3: a] :
( ( X2 @ X3 )
| ( X1 = X3 ) ) ) ) )
=> ( X0
@ ^ [X1: a] : $false ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X2: a > $o,X1: a] :
( ( X0 @ X2 )
=> ( X0
@ ^ [X3: a] :
( ( X2 @ X3 )
| ( X1 = X3 ) ) ) ) )
=> ( X0
@ ^ [X1: a] : $false ) ),
file('/export/starexec/sandbox/tmp/tmp.NdcdhjHtbk/DTF2THF_10348.p',cTHM163_pme) ).
thf(f11,plain,
( $true
!= ( sK0
@ ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU858^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:35:39 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEU858^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.47 % Domain : Set Theory (Finite sets)
% 0.27/0.47 % Problem : TPS problem THM163
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English : A direct consequence of the definition of FINITE1.
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : tps_0136 [Bro09]
% 0.27/0.47 % : THM163 [TPS]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.27/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.27/0.47 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.27/0.47 % Number of connectives : 9 ( 0 ~; 1 |; 1 &; 5 @)
% 0.27/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 11 ( 11 avg)
% 0.27/0.47 % Number of types : 2 ( 1 usr)
% 0.27/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.27/0.47 % Number of variables : 6 ( 3 ^; 3 !; 0 ?; 6 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.47 % : Polymorphic definitions expanded.
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(a_type,type,
% 0.27/0.47 a: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(cTHM163_pme,conjecture,
% 0.27/0.47 ! [Xw: ( a > $o ) > $o] :
% 0.27/0.47 ( ( ( Xw
% 0.27/0.47 @ ^ [Xx: a] : $false )
% 0.27/0.47 & ! [Xr: a > $o,Xx: a] :
% 0.27/0.47 ( ( Xw @ Xr )
% 0.27/0.47 => ( Xw
% 0.27/0.47 @ ^ [Xt: a] :
% 0.27/0.47 ( ( Xr @ Xt )
% 0.27/0.47 | ( Xt = Xx ) ) ) ) )
% 0.27/0.47 => ( Xw
% 0.27/0.47 @ ^ [Xx: a] : $false ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 12:35:39 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.NdcdhjHtbk/DTF2DTF10348.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(a_type,type,
% 1.46/1.27 a: $tType ).
% 1.46/1.27
% 1.46/1.27 thf(cTHM163_pme,conjecture,
% 1.46/1.27 ! [Xw: ( a > $o ) > $o] :
% 1.46/1.27 ( ( ( Xw
% 1.46/1.27 @ ^ [Xx: a] : $false )
% 1.46/1.27 & ! [Xr: a > $o,Xx: a] :
% 1.46/1.27 ( ( Xw @ Xr )
% 1.46/1.27 => ( Xw
% 1.46/1.27 @ ^ [Xt: a] :
% 1.46/1.27 ( ( Xr @ Xt )
% 1.46/1.27 | ( Xt = Xx ) ) ) ) )
% 1.46/1.27 => ( Xw
% 1.46/1.27 @ ^ [Xx: a] : $false ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.29 % (10504)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_10348 for (2999ds/27Mi)
% 1.46/1.29 % (10503)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_10348 for (2999ds/4Mi)
% 1.46/1.29 % (10504)First to succeed.
% 1.46/1.29 % (10503)Also succeeded, but the first one will report.
% 1.46/1.29 % (10504)Refutation found. Thanks to Tanya!
% 1.46/1.29 % SZS status Theorem for DTF2THF_10348
% 1.46/1.29 % SZS output start Proof for DTF2THF_10348
% 1.46/1.29 thf(type_def_5, type, a: $tType).
% 1.46/1.29 thf(func_def_0, type, a: $tType).
% 1.46/1.29 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.46/1.29 thf(func_def_9, type, sK0: (a > $o) > $o).
% 1.46/1.29 thf(func_def_11, type, ph2: !>[X0: $tType]:(X0)).
% 1.46/1.29 thf(f16,plain,(
% 1.46/1.29 $false),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.46/1.29 thf(f15,plain,(
% 1.46/1.29 ($true != $true)),
% 1.46/1.29 inference(superposition,[status(thm)],[f11,f12])).
% 1.46/1.29 thf(f12,plain,(
% 1.46/1.29 ($true = (sK0 @ (^[Y0 : a]: ($false))))),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.29 thf(f10,plain,(
% 1.46/1.29 ! [X1 : a > $o,X2 : a] : (($true != (sK0 @ X1)) | ($true = (sK0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))) & ($true = (sK0 @ (^[Y0 : a]: ($false)))) & ($true != (sK0 @ (^[Y0 : a]: ($false))))),
% 1.46/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.46/1.29 thf(f9,plain,(
% 1.46/1.29 ? [X0 : (a > $o) > $o] : (! [X1 : a > $o,X2 : a] : (($true != (X0 @ X1)) | ($true = (X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))) & ($true = (X0 @ (^[Y0 : a]: ($false)))) & ($true != (X0 @ (^[Y0 : a]: ($false))))) => (! [X2 : a,X1 : a > $o] : (($true != (sK0 @ X1)) | ($true = (sK0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))) & ($true = (sK0 @ (^[Y0 : a]: ($false)))) & ($true != (sK0 @ (^[Y0 : a]: ($false)))))),
% 1.46/1.29 introduced(definition,[],[choice_axiom])).
% 1.46/1.29 thf(f8,plain,(
% 1.46/1.29 ? [X0 : (a > $o) > $o] : (! [X1 : a > $o,X2 : a] : (($true != (X0 @ X1)) | ($true = (X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))) & ($true = (X0 @ (^[Y0 : a]: ($false)))) & ($true != (X0 @ (^[Y0 : a]: ($false)))))),
% 1.46/1.29 inference(flattening,[status(thm)],[f7])).
% 1.46/1.29 thf(f7,plain,(
% 1.46/1.29 ? [X0 : (a > $o) > $o] : (($true != (X0 @ (^[Y0 : a]: ($false)))) & (($true = (X0 @ (^[Y0 : a]: ($false)))) & ! [X1 : a > $o,X2 : a] : (($true != (X0 @ X1)) | ($true = (X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0))))))))),
% 1.46/1.29 inference(ennf_transformation,[status(thm)],[f6])).
% 1.46/1.29 thf(f6,plain,(
% 1.46/1.29 ~! [X0 : (a > $o) > $o] : ((($true = (X0 @ (^[Y0 : a]: ($false)))) & ! [X1 : a > $o,X2 : a] : (($true = (X0 @ X1)) => ($true = (X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0))))))) => ($true = (X0 @ (^[Y0 : a]: ($false)))))),
% 1.46/1.29 inference(rectify,[status(thm)],[f5])).
% 1.46/1.29 thf(f5,plain,(
% 1.46/1.29 ~! [X0 : (a > $o) > $o] : ((($true = (X0 @ (^[Y0 : a]: ($false)))) & ! [X2 : a > $o,X3 : a] : (((X0 @ X2) = $true) => ($true = (X0 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))))) => ($true = (X0 @ (^[Y0 : a]: ($false)))))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.29 thf(f4,plain,(
% 1.46/1.29 ~! [X0 : (a > $o) > $o] : (((X0 @ (^[X1 : a] : ($false))) & ! [X2 : a > $o,X3 : a] : ((X0 @ X2) => (X0 @ (^[X4 : a] : ((X2 @ X4) | (X3 = X4)))))) => (X0 @ (^[X5 : a] : ($false))))),
% 1.46/1.29 inference(rectify,[status(thm)],[f2])).
% 1.46/1.29 thf(f2,negated_conjecture,(
% 1.46/1.29 ~! [X0 : (a > $o) > $o] : (((X0 @ (^[X1 : a] : ($false))) & ! [X2 : a > $o,X1 : a] : ((X0 @ X2) => (X0 @ (^[X3 : a] : ((X2 @ X3) | (X1 = X3)))))) => (X0 @ (^[X1 : a] : ($false))))),
% 1.46/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.29 thf(f1,conjecture,(
% 1.46/1.29 ! [X0 : (a > $o) > $o] : (((X0 @ (^[X1 : a] : ($false))) & ! [X2 : a > $o,X1 : a] : ((X0 @ X2) => (X0 @ (^[X3 : a] : ((X2 @ X3) | (X1 = X3)))))) => (X0 @ (^[X1 : a] : ($false))))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.NdcdhjHtbk/DTF2THF_10348.p',cTHM163_pme)).
% 1.46/1.29 thf(f11,plain,(
% 1.46/1.29 ($true != (sK0 @ (^[Y0 : a]: ($false))))),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.29 % SZS output end Proof for DTF2THF_10348
% 1.46/1.29 % (10504)------------------------------
% 1.46/1.29 % (10504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (10504)Termination reason: Refutation
% 1.46/1.29
% 1.46/1.29 % (10504)Memory used [KB]: 5500
% 1.46/1.29 % (10504)Time elapsed: 0.002 s
% 1.46/1.29 % (10504)Instructions burned: 1 (million)
% 1.46/1.29 % (10504)------------------------------
% 1.46/1.29 % (10504)------------------------------
% 1.46/1.29 % (10501)Success in time 0.012 s
%------------------------------------------------------------------------------