%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV240^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.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 09:40:38 AM UTC 2026
% Result : Theorem 1.49s 1.26s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 33 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 96 ( 20 ~; 8 |; 14 &; 44 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 15 !; 10 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cA: ( a > $o ) > $o ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f15,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f14,f11]) ).
thf(f11,plain,
( ( sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( $true
= ( cA @ sK0 ) )
& ( ( sK0 @ sK1 )
= $true )
& ! [X2: a > $o] :
( ( $true
!= ( X2 @ sK1 ) )
| ( ( cA @ X2 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X0: a > $o] :
( ( ( cA @ X0 )
= $true )
& ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: a > $o] :
( ( ( X2 @ X1 )
!= $true )
| ( ( cA @ X2 )
!= $true ) ) ) )
=> ( ( $true
= ( cA @ sK0 ) )
& ? [X1: a] :
( ( $true
= ( sK0 @ X1 ) )
& ! [X2: a > $o] :
( ( ( X2 @ X1 )
!= $true )
| ( ( cA @ X2 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X1: a] :
( ( $true
= ( sK0 @ X1 ) )
& ! [X2: a > $o] :
( ( ( X2 @ X1 )
!= $true )
| ( ( cA @ X2 )
!= $true ) ) )
=> ( ( ( sK0 @ sK1 )
= $true )
& ! [X2: a > $o] :
( ( $true
!= ( X2 @ sK1 ) )
| ( ( cA @ X2 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o] :
( ( ( cA @ X0 )
= $true )
& ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: a > $o] :
( ( ( X2 @ X1 )
!= $true )
| ( ( cA @ X2 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o] :
( ( ( cA @ X0 )
= $true )
=> ! [X1: a] :
( ( ( X0 @ X1 )
= $true )
=> ? [X2: a > $o] :
( ( ( X2 @ X1 )
= $true )
& ( ( cA @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ( cA @ X0 )
=> ! [X1: a] :
( ( X0 @ X1 )
=> ? [X2: a > $o] :
( ( cA @ X2 )
& ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ( cA @ X0 )
=> ! [X1: a] :
( ( X0 @ X1 )
=> ? [X2: a > $o] :
( ( cA @ X2 )
& ( X2 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o] :
( ( cA @ X0 )
=> ! [X1: a] :
( ( X0 @ X1 )
=> ? [X2: a > $o] :
( ( cA @ X2 )
& ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOeMbcbN7V/DTF2THF_1513.p',cDOMTHM1_pme) ).
thf(f14,plain,
( ( sK0 @ sK1 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true != $true )
| ( ( sK0 @ sK1 )
!= $true ) ),
inference(superposition,[status(thm)],[f10,f12]) ).
thf(f12,plain,
( $true
= ( cA @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f10,plain,
! [X2: a > $o] :
( ( ( cA @ X2 )
!= $true )
| ( $true
!= ( X2 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV240^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n031.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 12:43:33 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SEV240^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.46 % Domain : Set Theory (Sets of sets)
% 0.27/0.46 % Problem : TPS problem from SETS-OF-SETS-THMS
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Bro09]
% 0.27/0.46 % Names : tps_0748 [Bro09]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.27/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.27/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.27/0.46 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 4 @)
% 0.27/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.27/0.46 % Number of types : 2 ( 1 usr)
% 0.27/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.27/0.46 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.27/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(a_type,type,
% 0.27/0.46 a: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(cA,type,
% 0.27/0.46 cA: ( a > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(cDOMTHM1_pme,conjecture,
% 0.27/0.46 ! [Xx: a > $o] :
% 0.27/0.46 ( ( cA @ Xx )
% 0.27/0.46 => ! [Xx0: a] :
% 0.27/0.46 ( ( Xx @ Xx0 )
% 0.27/0.46 => ? [S: a > $o] :
% 0.27/0.46 ( ( cA @ S )
% 0.27/0.46 & ( S @ Xx0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.24 %%% Generated on Tue Feb 24 12:43:34 EST 2026
% 1.49/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.24 %%% Logic specification used:
% 1.49/1.24 %%% thf(spec, logic, $$dhol).
% 1.49/1.24
% 1.49/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.VOeMbcbN7V/DTF2DTF1513.p
% See solution above
% 1.49/1.24 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(a_type,type,
% 1.49/1.25 a: $tType ).
% 1.49/1.25
% 1.49/1.25 thf(cA,type,
% 1.49/1.25 cA: ( a > $o ) > $o ).
% 1.49/1.25
% 1.49/1.25 thf(cDOMTHM1_pme,conjecture,
% 1.49/1.25 ! [Xx: a > $o] :
% 1.49/1.25 ( ( cA @ Xx )
% 1.49/1.25 => ! [Xx0: a] :
% 1.49/1.25 ( ( Xx @ Xx0 )
% 1.49/1.25 => ? [S: a > $o] :
% 1.49/1.25 ( ( cA @ S )
% 1.49/1.25 & ( S @ Xx0 ) ) ) ) ).
% 1.49/1.25 ------------------------
% 1.49/1.26 % (1783)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1513 for (2999ds/2Mi)
% 1.49/1.26 % (1781)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_1513 for (2999ds/4Mi)
% 1.49/1.26 % (1783)First to succeed.
% 1.49/1.26 % (1781)Also succeeded, but the first one will report.
% 1.49/1.26 % (1783)Refutation found. Thanks to Tanya!
% 1.49/1.26 % SZS status Theorem for DTF2THF_1513
% 1.49/1.26 % SZS output start Proof for DTF2THF_1513
% 1.49/1.26 thf(type_def_5, type, a: $tType).
% 1.49/1.26 thf(func_def_0, type, a: $tType).
% 1.49/1.26 thf(func_def_1, type, cA: (a > $o) > $o).
% 1.49/1.26 thf(func_def_5, type, sK0: a > $o).
% 1.49/1.26 thf(func_def_6, type, sK1: a).
% 1.49/1.26 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.49/1.26 thf(f15,plain,(
% 1.49/1.26 $false),
% 1.49/1.26 inference(subsumption_resolution,[status(thm)],[f14,f11])).
% 1.49/1.26 thf(f11,plain,(
% 1.49/1.26 ((sK0 @ sK1) = $true)),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.26 thf(f9,plain,(
% 1.49/1.26 ($true = (cA @ sK0)) & (((sK0 @ sK1) = $true) & ! [X2 : a > $o] : (($true != (X2 @ sK1)) | ((cA @ X2) != $true)))),
% 1.49/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.49/1.26 thf(f7,plain,(
% 1.49/1.26 ? [X0 : a > $o] : (((cA @ X0) = $true) & ? [X1 : a] : (((X0 @ X1) = $true) & ! [X2 : a > $o] : (((X2 @ X1) != $true) | ((cA @ X2) != $true)))) => (($true = (cA @ sK0)) & ? [X1 : a] : (($true = (sK0 @ X1)) & ! [X2 : a > $o] : (((X2 @ X1) != $true) | ((cA @ X2) != $true))))),
% 1.49/1.26 introduced(definition,[],[choice_axiom])).
% 1.49/1.26 thf(f8,plain,(
% 1.49/1.26 ? [X1 : a] : (($true = (sK0 @ X1)) & ! [X2 : a > $o] : (((X2 @ X1) != $true) | ((cA @ X2) != $true))) => (((sK0 @ sK1) = $true) & ! [X2 : a > $o] : (($true != (X2 @ sK1)) | ((cA @ X2) != $true)))),
% 1.49/1.26 introduced(definition,[],[choice_axiom])).
% 1.49/1.26 thf(f6,plain,(
% 1.49/1.26 ? [X0 : a > $o] : (((cA @ X0) = $true) & ? [X1 : a] : (((X0 @ X1) = $true) & ! [X2 : a > $o] : (((X2 @ X1) != $true) | ((cA @ X2) != $true))))),
% 1.49/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.26 thf(f5,plain,(
% 1.49/1.26 ~! [X0 : a > $o] : (((cA @ X0) = $true) => ! [X1 : a] : (((X0 @ X1) = $true) => ? [X2 : a > $o] : (((X2 @ X1) = $true) & ((cA @ X2) = $true))))),
% 1.49/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.26 thf(f4,plain,(
% 1.49/1.26 ~! [X0 : a > $o] : ((cA @ X0) => ! [X1 : a] : ((X0 @ X1) => ? [X2 : a > $o] : ((cA @ X2) & (X2 @ X1))))),
% 1.49/1.26 inference(rectify,[status(thm)],[f2])).
% 1.49/1.26 thf(f2,negated_conjecture,(
% 1.49/1.26 ~! [X0 : a > $o] : ((cA @ X0) => ! [X1 : a] : ((X0 @ X1) => ? [X2 : a > $o] : ((cA @ X2) & (X2 @ X1))))),
% 1.49/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.26 thf(f1,conjecture,(
% 1.49/1.26 ! [X0 : a > $o] : ((cA @ X0) => ! [X1 : a] : ((X0 @ X1) => ? [X2 : a > $o] : ((cA @ X2) & (X2 @ X1))))),
% 1.49/1.26 file('/export/starexec/sandbox2/tmp/tmp.VOeMbcbN7V/DTF2THF_1513.p',cDOMTHM1_pme)).
% 1.49/1.26 thf(f14,plain,(
% 1.49/1.26 ((sK0 @ sK1) != $true)),
% 1.49/1.26 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.49/1.26 thf(f13,plain,(
% 1.49/1.26 ($true != $true) | ((sK0 @ sK1) != $true)),
% 1.49/1.26 inference(superposition,[status(thm)],[f10,f12])).
% 1.49/1.26 thf(f12,plain,(
% 1.49/1.26 ($true = (cA @ sK0))),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.26 thf(f10,plain,(
% 1.49/1.26 ( ! [X2 : a > $o] : (((cA @ X2) != $true) | ($true != (X2 @ sK1))) )),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.26 % SZS output end Proof for DTF2THF_1513
% 1.49/1.26 % (1783)------------------------------
% 1.49/1.26 % (1783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (1783)Termination reason: Refutation
% 1.49/1.26
% 1.49/1.26 % (1783)Memory used [KB]: 5500
% 1.49/1.26 % (1783)Time elapsed: 0.002 s
% 1.49/1.26 % (1783)Instructions burned: 1 (million)
% 1.49/1.26 % (1783)------------------------------
% 1.49/1.26 % (1783)------------------------------
% 1.49/1.26 % (1778)Success in time 0.012 s
%------------------------------------------------------------------------------