%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET599^5 : 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 : n002.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 09:31:52 AM UTC 2026
% Result : Theorem 1.60s 1.30s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 47 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 154 ( 37 ~; 16 |; 30 &; 65 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 15 !; 9 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(f16,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f15,f11]) ).
thf(f11,plain,
( $true
= ( sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( sK2 @ sK0 )
= $true )
| ( $true
!= ( sK1 @ sK0 ) ) )
& ( ( sK2 @ sK0 )
!= $true )
& ( ( ( sK2 @ sK0 )
!= $true )
| ( $true
= ( sK1 @ sK0 ) ) )
& ( $true
= ( sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a,X1: a > $o,X2: a > $o] :
( ( ( ( X2 @ X0 )
= $true )
| ( ( X1 @ X0 )
!= $true ) )
& ( ( X2 @ X0 )
!= $true )
& ( ( ( X2 @ X0 )
!= $true )
| ( ( X1 @ X0 )
= $true ) )
& ( ( X1 @ X0 )
= $true ) )
=> ( ( ( ( sK2 @ sK0 )
= $true )
| ( $true
!= ( sK1 @ sK0 ) ) )
& ( ( sK2 @ sK0 )
!= $true )
& ( ( ( sK2 @ sK0 )
!= $true )
| ( $true
= ( sK1 @ sK0 ) ) )
& ( $true
= ( sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a,X1: a > $o,X2: a > $o] :
( ( ( ( X2 @ X0 )
= $true )
| ( ( X1 @ X0 )
!= $true ) )
& ( ( X2 @ X0 )
!= $true )
& ( ( ( X2 @ X0 )
!= $true )
| ( ( X1 @ X0 )
= $true ) )
& ( ( X1 @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > $o,X2: a > $o,X0: a] :
( ( ( ( X2 @ X0 )
!= $true )
| ( ( X1 @ X0 )
= $true ) )
& ( ( ( X2 @ X0 )
= $true )
| ( ( X1 @ X0 )
!= $true ) )
& ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X1: a > $o,X2: a > $o,X0: a] :
( ( ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) )
=> ( ( ( ( X1 @ X0 )
!= $true )
& ( ( X2 @ X0 )
= $true ) )
| ( ( ( X2 @ X0 )
!= $true )
& ( ( X1 @ X0 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a,X1: a > $o,X2: a > $o] :
( ( ( ( X2 @ X0 )
!= $true )
& ( ( X1 @ X0 )
= $true ) )
=> ( ( ( ( X2 @ X0 )
= $true )
& ( ( X1 @ X0 )
!= $true ) )
| ( ( ( X2 @ X0 )
!= $true )
& ( ( X1 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > $o,X2: a > $o] :
( ( ~ ( X2 @ X0 )
& ( X1 @ X0 ) )
=> ( ( ( X2 @ X0 )
& ~ ( X1 @ X0 ) )
| ( ~ ( X2 @ X0 )
& ( X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X0: a > $o,X1: a > $o] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
=> ( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a,X0: a > $o,X1: a > $o] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
=> ( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zb3TrzJEWM/DTF2THF_30182.p',cBOOL_PROP_58_pme) ).
thf(f15,plain,
( $true
!= ( sK1 @ sK0 ) ),
inference(subsumption_resolution,[status(thm)],[f14,f13]) ).
thf(f13,plain,
( ( sK2 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f14,plain,
( ( ( sK2 @ sK0 )
= $true )
| ( $true
!= ( sK1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET599^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n002.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:00:18 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.22/0.45 ---- Original DTF file ---
% 0.22/0.45 thf(spec,logic,$$dhol).
% 0.22/0.45 %------------------------------------------------------------------------------
% 0.22/0.45 % File : SET599^5 : TPTP v9.2.1. Released v4.0.0.
% 0.22/0.45 % Domain : Set Theory
% 0.22/0.45 % Problem : TPS problem BOOL-PROP-58
% 0.22/0.45 % Version : Especial.
% 0.22/0.45 % English : Trybulec's 58th Boolean property of sets
% 0.22/0.45
% 0.22/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.22/0.45 % : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.22/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.45 % Source : [Bro09]
% 0.22/0.45 % Names : tps_0130 [Bro09]
% 0.22/0.45 % : 45 [Bar92]
% 0.22/0.45 % : GAZING-THM45 [TPS]
% 0.22/0.45 % : BOOL-PROP-58 [TPS]
% 0.22/0.45
% 0.22/0.45 % Status : Theorem
% 0.22/0.45 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.22/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.22/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.22/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.22/0.45 % Number of connectives : 14 ( 3 ~; 1 |; 3 &; 6 @)
% 0.22/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.22/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.22/0.45 % Number of types : 2 ( 1 usr)
% 0.22/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.22/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.22/0.45 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.22/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.22/0.45
% 0.22/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.45 % : Polymorphic definitions expanded.
% 0.22/0.45 %------------------------------------------------------------------------------
% 0.22/0.45 thf(a_type,type,
% 0.22/0.45 a: $tType ).
% 0.22/0.45
% 0.22/0.45 thf(cBOOL_PROP_58_pme,conjecture,
% 0.22/0.45 ! [X: a > $o,Y: a > $o,Xx: a] :
% 0.22/0.45 ( ( ( X @ Xx )
% 0.22/0.45 & ~ ( Y @ Xx ) )
% 0.22/0.45 => ( ( ( X @ Xx )
% 0.22/0.45 & ~ ( Y @ Xx ) )
% 0.22/0.45 | ( ( Y @ Xx )
% 0.22/0.45 & ~ ( X @ Xx ) ) ) ) ).
% 0.22/0.45
% 0.22/0.45 %------------------------------------------------------------------------------
% 0.22/0.45 ------------------------
% 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 12:00:19 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/sandbox2/tmp/tmp.zb3TrzJEWM/DTF2DTF30182.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(cBOOL_PROP_58_pme,conjecture,
% 1.46/1.27 ! [X: a > $o,Y: a > $o,Xx: a] :
% 1.46/1.27 ( ( ( X @ Xx )
% 1.46/1.27 & ~ ( Y @ Xx ) )
% 1.46/1.27 => ( ( ( X @ Xx )
% 1.46/1.27 & ~ ( Y @ Xx ) )
% 1.46/1.27 | ( ( Y @ Xx )
% 1.46/1.27 & ~ ( X @ Xx ) ) ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.29 % (30301)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_30182 for (2999ds/2Mi)
% 1.46/1.29 % (30301)Instruction limit reached!
% 1.46/1.29 % (30301)------------------------------
% 1.46/1.29 % (30301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (30301)Termination reason: Unknown
% 1.46/1.29 % (30301)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (30301)Memory used [KB]: 5500
% 1.46/1.29 % (30301)Time elapsed: 0.002 s
% 1.46/1.29 % (30301)Instructions burned: 2 (million)
% 1.46/1.29 % (30301)------------------------------
% 1.46/1.29 % (30301)------------------------------
% 1.46/1.29 % (30297)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/183Mi)
% 1.46/1.29 % (30298)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_30182 for (2999ds/4Mi)
% 1.46/1.29 % (30300)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/2Mi)
% 1.46/1.29 % (30299)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_30182 for (2999ds/27Mi)
% 1.46/1.29 % (30302)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_30182 for (2999ds/275Mi)
% 1.46/1.29 % (30303)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/18Mi)
% 1.46/1.30 % (30297)First to succeed.
% 1.60/1.30 % (30300)Also succeeded, but the first one will report.
% 1.60/1.30 % (30297)Refutation found. Thanks to Tanya!
% 1.60/1.30 % SZS status Theorem for DTF2THF_30182
% 1.60/1.30 % SZS output start Proof for DTF2THF_30182
% 1.60/1.30 thf(type_def_5, type, a: $tType).
% 1.60/1.30 thf(func_def_0, type, a: $tType).
% 1.60/1.30 thf(func_def_4, type, sK0: a).
% 1.60/1.30 thf(func_def_5, type, sK1: a > $o).
% 1.60/1.30 thf(func_def_6, type, sK2: a > $o).
% 1.60/1.30 thf(f16,plain,(
% 1.60/1.30 $false),
% 1.60/1.30 inference(subsumption_resolution,[status(thm)],[f15,f11])).
% 1.60/1.30 thf(f11,plain,(
% 1.60/1.30 ($true = (sK1 @ sK0))),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.60/1.30 thf(f10,plain,(
% 1.60/1.30 (((sK2 @ sK0) = $true) | ($true != (sK1 @ sK0))) & ((sK2 @ sK0) != $true) & (((sK2 @ sK0) != $true) | ($true = (sK1 @ sK0))) & ($true = (sK1 @ sK0))),
% 1.60/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.60/1.30 thf(f9,plain,(
% 1.60/1.30 ? [X0 : a,X1 : a > $o,X2 : a > $o] : ((((X2 @ X0) = $true) | ((X1 @ X0) != $true)) & ((X2 @ X0) != $true) & (((X2 @ X0) != $true) | ((X1 @ X0) = $true)) & ((X1 @ X0) = $true)) => ((((sK2 @ sK0) = $true) | ($true != (sK1 @ sK0))) & ((sK2 @ sK0) != $true) & (((sK2 @ sK0) != $true) | ($true = (sK1 @ sK0))) & ($true = (sK1 @ sK0)))),
% 1.60/1.30 introduced(definition,[],[choice_axiom])).
% 1.60/1.30 thf(f8,plain,(
% 1.60/1.30 ? [X0 : a,X1 : a > $o,X2 : a > $o] : ((((X2 @ X0) = $true) | ((X1 @ X0) != $true)) & ((X2 @ X0) != $true) & (((X2 @ X0) != $true) | ((X1 @ X0) = $true)) & ((X1 @ X0) = $true))),
% 1.60/1.30 inference(flattening,[status(thm)],[f7])).
% 1.60/1.30 thf(f7,plain,(
% 1.60/1.30 ? [X1 : a > $o,X2 : a > $o,X0 : a] : (((((X2 @ X0) != $true) | ((X1 @ X0) = $true)) & (((X2 @ X0) = $true) | ((X1 @ X0) != $true))) & (((X1 @ X0) = $true) & ((X2 @ X0) != $true)))),
% 1.60/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.60/1.30 thf(f6,plain,(
% 1.60/1.30 ~! [X1 : a > $o,X2 : a > $o,X0 : a] : ((((X1 @ X0) = $true) & ((X2 @ X0) != $true)) => ((((X1 @ X0) != $true) & ((X2 @ X0) = $true)) | (((X2 @ X0) != $true) & ((X1 @ X0) = $true))))),
% 1.60/1.30 inference(flattening,[status(thm)],[f5])).
% 1.60/1.30 thf(f5,plain,(
% 1.60/1.30 ~! [X0 : a,X1 : a > $o,X2 : a > $o] : ((~((X2 @ X0) = $true) & ((X1 @ X0) = $true)) => ((((X2 @ X0) = $true) & ~((X1 @ X0) = $true)) | (~((X2 @ X0) = $true) & ((X1 @ X0) = $true))))),
% 1.60/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.30 thf(f4,plain,(
% 1.60/1.30 ~! [X0 : a,X1 : a > $o,X2 : a > $o] : ((~(X2 @ X0) & (X1 @ X0)) => (((X2 @ X0) & ~(X1 @ X0)) | (~(X2 @ X0) & (X1 @ X0))))),
% 1.60/1.30 inference(rectify,[status(thm)],[f2])).
% 1.60/1.30 thf(f2,negated_conjecture,(
% 1.60/1.30 ~! [X2 : a,X0 : a > $o,X1 : a > $o] : ((~(X1 @ X2) & (X0 @ X2)) => (((X1 @ X2) & ~(X0 @ X2)) | (~(X1 @ X2) & (X0 @ X2))))),
% 1.60/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.30 thf(f1,conjecture,(
% 1.60/1.30 ! [X2 : a,X0 : a > $o,X1 : a > $o] : ((~(X1 @ X2) & (X0 @ X2)) => (((X1 @ X2) & ~(X0 @ X2)) | (~(X1 @ X2) & (X0 @ X2))))),
% 1.60/1.30 file('/export/starexec/sandbox2/tmp/tmp.zb3TrzJEWM/DTF2THF_30182.p',cBOOL_PROP_58_pme)).
% 1.60/1.30 thf(f15,plain,(
% 1.60/1.30 ($true != (sK1 @ sK0))),
% 1.60/1.30 inference(subsumption_resolution,[status(thm)],[f14,f13])).
% 1.60/1.30 thf(f13,plain,(
% 1.60/1.30 ((sK2 @ sK0) != $true)),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.60/1.30 thf(f14,plain,(
% 1.60/1.30 ((sK2 @ sK0) = $true) | ($true != (sK1 @ sK0))),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.60/1.30 % SZS output end Proof for DTF2THF_30182
% 1.60/1.30 % (30297)------------------------------
% 1.60/1.30 % (30297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (30297)Termination reason: Refutation
% 1.60/1.30
% 1.60/1.30 % (30297)Memory used [KB]: 5500
% 1.60/1.30 % (30297)Time elapsed: 0.004 s
% 1.60/1.30 % (30297)Instructions burned: 1 (million)
% 1.60/1.30 % (30297)------------------------------
% 1.60/1.30 % (30297)------------------------------
% 1.60/1.30 % (30296)Success in time 0.006 s
%------------------------------------------------------------------------------