%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET199^5 : 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 : 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 09:31:24 AM UTC 2026
% Result : Theorem 1.60s 1.31s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 152 ( 62 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 186 ( 36 ~; 18 |; 32 &; 82 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 ^; 37 !; 18 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a ).
thf(f19,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f18,f13]) ).
thf(f13,plain,
( ( sK0 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
= ( sK1 @ X3 ) ) )
& ( $true
!= ( sK1 @ sK3 ) )
& ( $true
!= ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
= $true )
& ! [X5: a] :
( ( $true
= ( sK2 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X1 @ X3 )
= $true ) )
& ? [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
& ( ( X2 @ X4 )
!= $true )
& ( $true
= ( X0 @ X4 ) ) )
& ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
| ( ( X0 @ X5 )
!= $true ) ) )
=> ( ! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
= ( sK1 @ X3 ) ) )
& ? [X4: a] :
( ( $true
!= ( sK1 @ X4 ) )
& ( $true
!= ( sK2 @ X4 ) )
& ( $true
= ( sK0 @ X4 ) ) )
& ! [X5: a] :
( ( $true
= ( sK2 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X4: a] :
( ( $true
!= ( sK1 @ X4 ) )
& ( $true
!= ( sK2 @ X4 ) )
& ( $true
= ( sK0 @ X4 ) ) )
=> ( ( $true
!= ( sK1 @ sK3 ) )
& ( $true
!= ( sK2 @ sK3 ) )
& ( ( sK0 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X1 @ X3 )
= $true ) )
& ? [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
& ( ( X2 @ X4 )
!= $true )
& ( $true
= ( X0 @ X4 ) ) )
& ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
| ( ( X0 @ X5 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( ( X2 @ X4 )
= $true ) )
& ? [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
& ( ( X0 @ X5 )
!= $true )
& ( $true
= ( X1 @ X5 ) ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ? [X5: a] :
( ( ( X0 @ X5 )
!= $true )
& ( $true
!= ( X2 @ X5 ) )
& ( $true
= ( X1 @ X5 ) ) )
& ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
=> ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) ) )
=> ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
=> ( ( ( X0 @ X5 )
= $true )
| ( $true
= ( X2 @ X5 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) )
& ! [X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) ) )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( ( X0 @ X5 )
| ( X2 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) )
& ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) ) )
=> ! [X3: a] :
( ( X2 @ X3 )
=> ( ( X1 @ X3 )
| ( X0 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) )
& ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) ) )
=> ! [X3: a] :
( ( X2 @ X3 )
=> ( ( X1 @ X3 )
| ( X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LkJajVucA7/DTF2THF_10154.p',cBOOL_PROP_39_pme) ).
thf(f18,plain,
( ( sK0 @ sK3 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( sK0 @ sK3 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f12]) ).
thf(f12,plain,
! [X5: a] :
( ( $true
= ( sK2 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f14,plain,
( $true
!= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET199^5 : 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
% 0.16/0.34 % Computer : n007.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:54:08 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SET199^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.47 % Domain : Set Theory
% 0.29/0.47 % Problem : TPS problem BOOL-PROP-39
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English : Trybulec's 39th Boolean property of sets
% 0.29/0.47
% 0.29/0.47 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.29/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : tps_0150 [Bro09]
% 0.29/0.47 % : BOOL-PROP-39 [TPS]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.29/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.29/0.47 % Number of connectives : 13 ( 0 ~; 1 |; 1 &; 7 @)
% 0.29/0.47 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 9 ( 9 avg)
% 0.29/0.47 % Number of types : 2 ( 1 usr)
% 0.29/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.29/0.47 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.29/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.47 % : Polymorphic definitions expanded.
% 0.29/0.47 % :
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(a_type,type,
% 0.29/0.47 a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(cBOOL_PROP_39_pme,conjecture,
% 0.29/0.47 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.29/0.47 ( ( ! [Xx: a] :
% 0.29/0.47 ( ( Z @ Xx )
% 0.29/0.47 => ( X @ Xx ) )
% 0.29/0.47 & ! [Xx: a] :
% 0.29/0.47 ( ( Z @ Xx )
% 0.29/0.47 => ( Y @ Xx ) ) )
% 0.29/0.47 => ! [Xx: a] :
% 0.29/0.47 ( ( Z @ Xx )
% 0.29/0.47 => ( ( X @ Xx )
% 0.29/0.47 | ( Y @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.43/1.28 ---- Embedded in THF ---
% 1.43/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.28 %%% Generated on Tue Feb 24 11:54:09 EST 2026
% 1.43/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.28 %%% Logic specification used:
% 1.43/1.28 %%% thf(spec, logic, $$dhol).
% 1.43/1.28
% 1.43/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LkJajVucA7/DTF2DTF10154.p
% See solution above
% 1.43/1.28 ------------------------
% 1.43/1.29 ---- Cleaned THF ---
% 1.43/1.30 thf(a_type,type,
% 1.43/1.30 a: $tType ).
% 1.43/1.30
% 1.43/1.30 thf(cBOOL_PROP_39_pme,conjecture,
% 1.43/1.30 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.43/1.30 ( ( ! [Xx: a] :
% 1.43/1.30 ( ( Z @ Xx )
% 1.43/1.30 => ( X @ Xx ) )
% 1.43/1.30 & ! [Xx: a] :
% 1.43/1.30 ( ( Z @ Xx )
% 1.43/1.30 => ( Y @ Xx ) ) )
% 1.43/1.30 => ! [Xx: a] :
% 1.43/1.30 ( ( Z @ Xx )
% 1.43/1.30 => ( ( X @ Xx )
% 1.43/1.30 | ( Y @ Xx ) ) ) ) ).
% 1.43/1.30 ------------------------
% 1.60/1.31 % (10426)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10154 for (3000ds/183Mi)
% 1.60/1.31 % (10426)First to succeed.
% 1.60/1.31 % (10426)Refutation found. Thanks to Tanya!
% 1.60/1.31 % SZS status Theorem for DTF2THF_10154
% 1.60/1.31 % SZS output start Proof for DTF2THF_10154
% 1.60/1.31 thf(type_def_5, type, a: $tType).
% 1.60/1.31 thf(func_def_0, type, a: $tType).
% 1.60/1.31 thf(func_def_4, type, sK0: a > $o).
% 1.60/1.31 thf(func_def_5, type, sK1: a > $o).
% 1.60/1.31 thf(func_def_6, type, sK2: a > $o).
% 1.60/1.31 thf(func_def_7, type, sK3: a).
% 1.60/1.31 thf(f19,plain,(
% 1.60/1.31 $false),
% 1.60/1.31 inference(subsumption_resolution,[status(thm)],[f18,f13])).
% 1.60/1.31 thf(f13,plain,(
% 1.60/1.31 ((sK0 @ sK3) = $true)),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.31 thf(f11,plain,(
% 1.60/1.31 ! [X3 : a] : (($true != (sK0 @ X3)) | ($true = (sK1 @ X3))) & (($true != (sK1 @ sK3)) & ($true != (sK2 @ sK3)) & ((sK0 @ sK3) = $true)) & ! [X5 : a] : (($true = (sK2 @ X5)) | ($true != (sK0 @ X5)))),
% 1.60/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.60/1.31 thf(f9,plain,(
% 1.60/1.31 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) != $true) | ((X1 @ X3) = $true)) & ? [X4 : a] : (($true != (X1 @ X4)) & ((X2 @ X4) != $true) & ($true = (X0 @ X4))) & ! [X5 : a] : (($true = (X2 @ X5)) | ((X0 @ X5) != $true))) => (! [X3 : a] : (($true != (sK0 @ X3)) | ($true = (sK1 @ X3))) & ? [X4 : a] : (($true != (sK1 @ X4)) & ($true != (sK2 @ X4)) & ($true = (sK0 @ X4))) & ! [X5 : a] : (($true = (sK2 @ X5)) | ($true != (sK0 @ X5))))),
% 1.60/1.31 introduced(definition,[],[choice_axiom])).
% 1.60/1.31 thf(f10,plain,(
% 1.60/1.31 ? [X4 : a] : (($true != (sK1 @ X4)) & ($true != (sK2 @ X4)) & ($true = (sK0 @ X4))) => (($true != (sK1 @ sK3)) & ($true != (sK2 @ sK3)) & ((sK0 @ sK3) = $true))),
% 1.60/1.31 introduced(definition,[],[choice_axiom])).
% 1.60/1.31 thf(f8,plain,(
% 1.60/1.31 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) != $true) | ((X1 @ X3) = $true)) & ? [X4 : a] : (($true != (X1 @ X4)) & ((X2 @ X4) != $true) & ($true = (X0 @ X4))) & ! [X5 : a] : (($true = (X2 @ X5)) | ((X0 @ X5) != $true)))),
% 1.60/1.31 inference(rectify,[status(thm)],[f7])).
% 1.60/1.31 thf(f7,plain,(
% 1.60/1.31 ? [X1 : a > $o,X2 : a > $o,X0 : a > $o] : (! [X4 : a] : (($true != (X1 @ X4)) | ((X2 @ X4) = $true)) & ? [X5 : a] : (($true != (X2 @ X5)) & ((X0 @ X5) != $true) & ($true = (X1 @ X5))) & ! [X3 : a] : (((X0 @ X3) = $true) | ((X1 @ X3) != $true)))),
% 1.60/1.31 inference(flattening,[status(thm)],[f6])).
% 1.60/1.31 thf(f6,plain,(
% 1.60/1.31 ? [X0 : a > $o,X2 : a > $o,X1 : a > $o] : (? [X5 : a] : ((((X0 @ X5) != $true) & ($true != (X2 @ X5))) & ($true = (X1 @ X5))) & (! [X4 : a] : (($true != (X1 @ X4)) | ((X2 @ X4) = $true)) & ! [X3 : a] : (((X0 @ X3) = $true) | ((X1 @ X3) != $true))))),
% 1.60/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.60/1.31 thf(f5,plain,(
% 1.60/1.31 ~! [X0 : a > $o,X2 : a > $o,X1 : a > $o] : ((! [X4 : a] : (($true = (X1 @ X4)) => ((X2 @ X4) = $true)) & ! [X3 : a] : (((X1 @ X3) = $true) => ((X0 @ X3) = $true))) => ! [X5 : a] : (($true = (X1 @ X5)) => (((X0 @ X5) = $true) | ($true = (X2 @ X5)))))),
% 1.60/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.31 thf(f4,plain,(
% 1.60/1.31 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X0 @ X3)) & ! [X4 : a] : ((X1 @ X4) => (X2 @ X4))) => ! [X5 : a] : ((X1 @ X5) => ((X0 @ X5) | (X2 @ X5))))),
% 1.60/1.31 inference(rectify,[status(thm)],[f2])).
% 1.60/1.31 thf(f2,negated_conjecture,(
% 1.60/1.31 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X2 @ X3) => (X1 @ X3)) & ! [X3 : a] : ((X2 @ X3) => (X0 @ X3))) => ! [X3 : a] : ((X2 @ X3) => ((X1 @ X3) | (X0 @ X3))))),
% 1.60/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.31 thf(f1,conjecture,(
% 1.60/1.31 ! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X2 @ X3) => (X1 @ X3)) & ! [X3 : a] : ((X2 @ X3) => (X0 @ X3))) => ! [X3 : a] : ((X2 @ X3) => ((X1 @ X3) | (X0 @ X3))))),
% 1.60/1.31 file('/export/starexec/sandbox2/tmp/tmp.LkJajVucA7/DTF2THF_10154.p',cBOOL_PROP_39_pme)).
% 1.60/1.31 thf(f18,plain,(
% 1.60/1.31 ((sK0 @ sK3) != $true)),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.60/1.31 thf(f17,plain,(
% 1.60/1.31 ((sK0 @ sK3) != $true) | ($true != $true)),
% 1.60/1.31 inference(superposition,[status(thm)],[f14,f12])).
% 1.60/1.31 thf(f12,plain,(
% 1.60/1.31 ( ! [X5 : a] : (($true = (sK2 @ X5)) | ($true != (sK0 @ X5))) )),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.31 thf(f14,plain,(
% 1.60/1.31 ($true != (sK2 @ sK3))),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.31 % SZS output end Proof for DTF2THF_10154
% 1.60/1.31 % (10426)------------------------------
% 1.60/1.31 % (10426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (10426)Termination reason: Refutation
% 1.60/1.31
% 1.60/1.31 % (10426)Memory used [KB]: 5500
% 1.60/1.31 % (10426)Time elapsed: 0.002 s
% 1.60/1.31 % (10426)Instructions burned: 2 (million)
% 1.60/1.31 % (10426)------------------------------
% 1.60/1.31 % (10426)------------------------------
% 1.60/1.31 % (10425)Success in time 0.012 s
%------------------------------------------------------------------------------