%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET618^5 : 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 : n016.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 09:31:56 AM UTC 2026
% Result : Theorem 1.62s 1.33s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 17 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 84 ( 20 ~; 6 |; 12 &; 39 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 2 usr; 3 con; 0-2 aty)
% ( 7 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 27 ( 24 ^; 3 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_13,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK2: a > $o ).
thf(f14,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > $o] : $true
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) ),
inference(not_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) ) ),
inference(boolean_simplification,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ^ [Y1: a] : $false )
= ( ^ [Y1: a] : $false ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ^ [Y1: a] : $false )
= ( ^ [Y1: a] :
( ~ ( Y0 @ Y1 )
& ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f7]) ).
thf(f7,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ^ [Y1: a] : $false )
= ( ^ [Y1: a] :
( ( ~ ( Y0 @ Y1 )
& ( Y0 @ Y1 ) )
| $false ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ^ [Y1: a] : $false )
= ( ^ [Y1: a] :
( ( ~ ( Y0 @ Y1 )
& ( Y0 @ Y1 ) )
| ( ( Y0 @ Y1 )
& ~ ( Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ^ [Y1: a] : $false )
= ( ^ [Y1: a] :
( ( ~ ( Y0 @ Y1 )
& ( Y0 @ Y1 ) )
| ( ( Y0 @ Y1 )
& ~ ( Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ( ^ [X1: a] : $false )
= ( ^ [X2: a] :
( ( ~ ( X0 @ X2 )
& ( X0 @ X2 ) )
| ( ( X0 @ X2 )
& ~ ( X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ( ^ [X2: a] : $false )
= ( ^ [X1: a] :
( ( ~ ( X0 @ X1 )
& ( X0 @ X1 ) )
| ( ( X0 @ X1 )
& ~ ( X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o] :
( ( ^ [X2: a] : $false )
= ( ^ [X1: a] :
( ( ~ ( X0 @ X1 )
& ( X0 @ X1 ) )
| ( ( X0 @ X1 )
& ~ ( X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.62ctPnHWVJ/DTF2THF_29028.p',cBOOL_PROP_93_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET618^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n016.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:01:06 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SET618^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : TPS problem BOOL-PROP-93
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : Trybulec's 93th Boolean property of sets
% 0.19/0.45
% 0.19/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0201 [Bro09]
% 0.19/0.45 % : BOOL-PROP-93 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 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
% 0.19/0.45 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.45 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 1 ( 2 avg)
% 0.19/0.45 % Number of connectives : 9 ( 2 ~; 1 |; 2 &; 4 @)
% 0.19/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 2 ( 2 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 % : Polymorphic definitions expanded.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(cBOOL_PROP_93_pme,conjecture,
% 0.19/0.45 ! [X: a > $o] :
% 0.19/0.45 ( ( ^ [Xz: a] :
% 0.19/0.45 ( ( ( X @ Xz )
% 0.19/0.45 & ~ ( X @ Xz ) )
% 0.19/0.45 | ( ( X @ Xz )
% 0.19/0.45 & ~ ( X @ Xz ) ) ) )
% 0.19/0.45 = ( ^ [Xx: a] : $false ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.62/1.30 ---- Embedded in THF ---
% 1.62/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.31 %%% Generated on Tue Feb 24 12:01:07 EST 2026
% 1.62/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.31 %%% Logic specification used:
% 1.62/1.31 %%% thf(spec, logic, $$dhol).
% 1.62/1.31
% 1.62/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.62ctPnHWVJ/DTF2DTF29028.p
% See solution above
% 1.62/1.31 ------------------------
% 1.62/1.31 ---- Cleaned THF ---
% 1.62/1.31 thf(a_type,type,
% 1.62/1.31 a: $tType ).
% 1.62/1.31
% 1.62/1.31 thf(cBOOL_PROP_93_pme,conjecture,
% 1.62/1.31 ! [X: a > $o] :
% 1.62/1.31 ( ( ^ [Xz: a] :
% 1.62/1.31 ( ( ( X @ Xz )
% 1.62/1.31 & ~ ( X @ Xz ) )
% 1.62/1.31 | ( ( X @ Xz )
% 1.62/1.31 & ~ ( X @ Xz ) ) ) )
% 1.62/1.31 = ( ^ [Xx: a] : $false ) ) ).
% 1.62/1.31 ------------------------
% 1.62/1.33 % (29190)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_29028 for (3000ds/2Mi)
% 1.62/1.33 % (29190)First to succeed.
% 1.62/1.33 % (29190)Refutation found. Thanks to Tanya!
% 1.62/1.33 % SZS status Theorem for DTF2THF_29028
% 1.62/1.33 % SZS output start Proof for DTF2THF_29028
% 1.62/1.33 thf(type_def_5, type, a: $tType).
% 1.62/1.33 thf(func_def_0, type, a: $tType).
% 1.62/1.33 thf(func_def_13, type, ph1: !>[X0: $tType]:(X0)).
% 1.62/1.33 thf(func_def_14, type, sK2: a > $o).
% 1.62/1.33 thf(f14,plain,(
% 1.62/1.33 $false),
% 1.62/1.33 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.62/1.33 thf(f13,plain,(
% 1.62/1.33 ($true = $false)),
% 1.62/1.33 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.62/1.33 thf(f12,plain,(
% 1.62/1.33 ($false = ((^[Y0 : a > $o]: ($true)) @ sK2))),
% 1.62/1.33 inference(sigma_clausification,[status(thm)],[f11])).
% 1.62/1.33 thf(f11,plain,(
% 1.62/1.33 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: ($true))))),
% 1.62/1.33 inference(not_proxy_clausification,[status(thm)],[f10])).
% 1.62/1.33 thf(f10,plain,(
% 1.62/1.33 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: ($true)))))),
% 1.62/1.33 inference(boolean_simplification,[status(thm)],[f9])).
% 1.62/1.33 thf(f9,plain,(
% 1.62/1.33 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: ((^[Y1 : a]: ($false)) = (^[Y1 : a]: ($false)))))))),
% 1.62/1.33 inference(boolean_simplification,[status(thm)],[f8])).
% 1.62/1.33 thf(f8,plain,(
% 1.62/1.33 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: ((^[Y1 : a]: ($false)) = (^[Y1 : a]: ((~ (Y0 @ Y1)) & (Y0 @ Y1))))))))),
% 1.62/1.33 inference(boolean_simplification,[status(thm)],[f7])).
% 1.62/1.33 thf(f7,plain,(
% 1.62/1.33 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: ((^[Y1 : a]: ($false)) = (^[Y1 : a]: (((~ (Y0 @ Y1)) & (Y0 @ Y1)) | $false)))))))),
% 1.62/1.33 inference(boolean_simplification,[status(thm)],[f6])).
% 1.62/1.33 thf(f6,plain,(
% 1.62/1.33 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: ((^[Y1 : a]: ($false)) = (^[Y1 : a]: (((~ (Y0 @ Y1)) & (Y0 @ Y1)) | ((Y0 @ Y1) & (~ (Y0 @ Y1))))))))))),
% 1.62/1.33 inference(cnf_transformation,[status(thm)],[f5])).
% 1.62/1.33 thf(f5,plain,(
% 1.62/1.33 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: ((^[Y1 : a]: ($false)) = (^[Y1 : a]: (((~ (Y0 @ Y1)) & (Y0 @ Y1)) | ((Y0 @ Y1) & (~ (Y0 @ Y1))))))))))),
% 1.62/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.33 thf(f4,plain,(
% 1.62/1.33 ~! [X0 : a > $o] : ((^[X1 : a] : ($false)) = (^[X2 : a] : ((~(X0 @ X2) & (X0 @ X2)) | ((X0 @ X2) & ~(X0 @ X2)))))),
% 1.62/1.33 inference(rectify,[status(thm)],[f2])).
% 1.62/1.33 thf(f2,negated_conjecture,(
% 1.62/1.33 ~! [X0 : a > $o] : ((^[X2 : a] : ($false)) = (^[X1 : a] : ((~(X0 @ X1) & (X0 @ X1)) | ((X0 @ X1) & ~(X0 @ X1)))))),
% 1.62/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.33 thf(f1,conjecture,(
% 1.62/1.33 ! [X0 : a > $o] : ((^[X2 : a] : ($false)) = (^[X1 : a] : ((~(X0 @ X1) & (X0 @ X1)) | ((X0 @ X1) & ~(X0 @ X1)))))),
% 1.62/1.33 file('/export/starexec/sandbox2/tmp/tmp.62ctPnHWVJ/DTF2THF_29028.p',cBOOL_PROP_93_pme)).
% 1.62/1.33 % SZS output end Proof for DTF2THF_29028
% 1.62/1.33 % (29190)------------------------------
% 1.62/1.33 % (29190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (29190)Termination reason: Refutation
% 1.62/1.33
% 1.62/1.33 % (29190)Memory used [KB]: 5500
% 1.62/1.33 % (29190)Time elapsed: 0.003 s
% 1.62/1.33 % (29190)Instructions burned: 1 (million)
% 1.62/1.33 % (29190)------------------------------
% 1.62/1.33 % (29190)------------------------------
% 1.62/1.33 % (29185)Success in time 0.012 s
%------------------------------------------------------------------------------