%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO021^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 09:53:09 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 188 ( 77 equ)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 118 ( 51 ~; 36 |; 25 &)
% ( 4 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 163 ( 107 fml; 56 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 6 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 20 ( 10 !; 10 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(f35,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f30,f31,f33]) ).
tff(f33,plain,
spl2_1,
inference(avatar_split_clause,[status(thm)],[f19,f23]) ).
tff(f23,definition,
( spl2_1
<=> ( sK1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
tff(f19,plain,
sK1 = $true,
inference(duplicate_literal_removal,[status(thm)],[f14]) ).
tff(f14,plain,
( ( sK1 = $true )
| ( sK1 = $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
tff(f13,plain,
( ( ( sK0 != $true )
| ( sK1 != $true )
| ( sK0 != $true )
| ( sK1 != $true ) )
& ( ( ( sK0 = $true )
& ( sK1 = $true ) )
| ( ( sK0 = $true )
& ( sK1 = $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f12]) ).
tff(f12,plain,
( ? [X0: $o,X1: $o] :
( ( ( $true != (X0) )
| ( $true != (X1) )
| ( $true != (X0) )
| ( $true != (X1) ) )
& ( ( ( $true = (X0) )
& ( $true = (X1) ) )
| ( ( $true = (X0) )
& ( $true = (X1) ) ) ) )
=> ( ( ( sK0 != $true )
| ( sK1 != $true )
| ( sK0 != $true )
| ( sK1 != $true ) )
& ( ( ( sK0 = $true )
& ( sK1 = $true ) )
| ( ( sK0 = $true )
& ( sK1 = $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f11,plain,
? [X0: $o,X1: $o] :
( ( ( $true != (X0) )
| ( $true != (X1) )
| ( $true != (X0) )
| ( $true != (X1) ) )
& ( ( ( $true = (X0) )
& ( $true = (X1) ) )
| ( ( $true = (X0) )
& ( $true = (X1) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
tff(f10,plain,
? [X1: $o,X0: $o] :
( ( ( $true != (X1) )
| ( $true != (X0) )
| ( $true != (X1) )
| ( $true != (X0) ) )
& ( ( ( $true = (X1) )
& ( $true = (X0) ) )
| ( ( $true = (X1) )
& ( $true = (X0) ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
tff(f9,plain,
? [X1: $o,X0: $o] :
( ( ( $true != (X1) )
| ( $true != (X0) )
| ( $true != (X1) )
| ( $true != (X0) ) )
& ( ( ( $true = (X1) )
& ( $true = (X0) ) )
| ( ( $true = (X1) )
& ( $true = (X0) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
tff(f8,plain,
? [X1: $o,X0: $o] :
( ( ( $true = (X1) )
& ( $true = (X0) ) )
<~> ( ( $true = (X1) )
& ( $true = (X0) ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
tff(f7,plain,
~ ! [X1: $o,X0: $o] :
( ( ( $true = (X1) )
& ( $true = (X0) ) )
<=> ~ ( ( $true != (X0) )
| ( $true != (X1) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
tff(f6,plain,
~ ! [X0: $o,X1: $o] :
( ( ( $true = (X1) )
& ( $true = (X0) ) )
<=> ~ ( ( $true != (X0) )
| ( $true != (X1) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
tff(f5,plain,
~ ! [X0: $o,X1: $o] :
( (X1)
& ( (X0)
= ( ~ ( ~ (X0)
| ~ (X1) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X0: $o,X1: $o] :
( (X1)
& ( (X0)
= ( ~ ( ~ (X0)
| ~ (X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
! [X0: $o,X1: $o] :
( (X1)
& ( (X0)
= ( ~ ( ~ (X0)
| ~ (X1) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iFgQtYbUMJ/DTF2THF_26311.p',conj) ).
tff(f31,plain,
spl2_2,
inference(avatar_split_clause,[status(thm)],[f20,f27]) ).
tff(f27,definition,
( spl2_2
<=> ( sK0 = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
tff(f20,plain,
sK0 = $true,
inference(duplicate_literal_removal,[status(thm)],[f17]) ).
tff(f17,plain,
( ( sK0 = $true )
| ( sK0 = $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
tff(f30,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f27,f23]) ).
tff(f21,plain,
( ( sK1 != $true )
| ( sK0 != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
tff(f18,plain,
( ( sK1 != $true )
| ( sK0 != $true )
| ( sK0 != $true )
| ( sK1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO021^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:22:20 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SYO021^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.45 % Domain : Syntactic
% 0.29/0.45 % Problem : De Morgan by equality
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.29/0.45 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Ben09]
% 0.29/0.45 % Names : Example 20b [BB05]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % : Without Boolean extensionality : CounterSatisfiable
% 0.29/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 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 v4.1.0, 0.00 v3.7.0
% 0.29/0.45 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.29/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.45 % Number of connectives : 5 ( 3 ~; 1 |; 1 &; 0 @)
% 0.29/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 3 ( 3 avg)
% 0.29/0.45 % Number of types : 1 ( 0 usr)
% 0.29/0.45 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.45 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments :
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(conj,conjecture,
% 0.29/0.45 ! [X: $o,Y: $o] :
% 0.29/0.45 ( ( X
% 0.29/0.45 & Y )
% 0.29/0.45 = ( ~ ( ~ X
% 0.29/0.45 | ~ Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 14:22:21 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.iFgQtYbUMJ/DTF2DTF26311.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(conj,conjecture,
% 1.48/1.26 ! [X: $o,Y: $o] :
% 1.48/1.26 ( ( X
% 1.48/1.26 & Y )
% 1.48/1.26 = ( ~ ( ~ X
% 1.48/1.26 | ~ Y ) ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.28 % (26534)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26311 for (3000ds/183Mi)
% 1.48/1.28 % (26534)First to succeed.
% 1.48/1.28 % (26534)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_26311
% 1.48/1.28 % SZS output start Proof for DTF2THF_26311
% 1.48/1.28 tff(f35,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(avatar_sat_refutation,[status(thm)],[f30,f31,f33])).
% 1.48/1.28 tff(f33,plain,(
% 1.48/1.28 spl2_1),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f19,f23])).
% 1.48/1.28 tff(f23,definition,(
% 1.48/1.28 spl2_1 <=> (sK1 = $true)),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.48/1.28 tff(f19,plain,(
% 1.48/1.28 (sK1 = $true)),
% 1.48/1.28 inference(duplicate_literal_removal,[status(thm)],[f14])).
% 1.48/1.28 tff(f14,plain,(
% 1.48/1.28 (sK1 = $true) | (sK1 = $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.28 tff(f13,plain,(
% 1.48/1.28 ((sK0 != $true) | (sK1 != $true) | (sK0 != $true) | (sK1 != $true)) & (((sK0 = $true) & (sK1 = $true)) | ((sK0 = $true) & (sK1 = $true)))),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f12])).
% 1.48/1.28 tff(f12,plain,(
% 1.48/1.28 ? [X0 : $o,X1 : $o] : ((($true != X0) | ($true != X1) | ($true != X0) | ($true != X1)) & ((($true = X0) & ($true = X1)) | (($true = X0) & ($true = X1)))) => (((sK0 != $true) | (sK1 != $true) | (sK0 != $true) | (sK1 != $true)) & (((sK0 = $true) & (sK1 = $true)) | ((sK0 = $true) & (sK1 = $true))))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 tff(f11,plain,(
% 1.48/1.28 ? [X0 : $o,X1 : $o] : ((($true != X0) | ($true != X1) | ($true != X0) | ($true != X1)) & ((($true = X0) & ($true = X1)) | (($true = X0) & ($true = X1))))),
% 1.48/1.28 inference(rectify,[status(thm)],[f10])).
% 1.48/1.28 tff(f10,plain,(
% 1.48/1.28 ? [X1 : $o,X0 : $o] : ((($true != X1) | ($true != X0) | ($true != X1) | ($true != X0)) & ((($true = X1) & ($true = X0)) | (($true = X1) & ($true = X0))))),
% 1.48/1.28 inference(flattening,[status(thm)],[f9])).
% 1.48/1.28 tff(f9,plain,(
% 1.48/1.28 ? [X1 : $o,X0 : $o] : (((($true != X1) | ($true != X0)) | (($true != X1) | ($true != X0))) & ((($true = X1) & ($true = X0)) | (($true = X1) & ($true = X0))))),
% 1.48/1.28 inference(nnf_transformation,[status(thm)],[f8])).
% 1.48/1.28 tff(f8,plain,(
% 1.48/1.28 ? [X1 : $o,X0 : $o] : ((($true = X1) & ($true = X0)) <~> (($true = X1) & ($true = X0)))),
% 1.48/1.28 inference(ennf_transformation,[status(thm)],[f7])).
% 1.48/1.28 tff(f7,plain,(
% 1.48/1.28 ~! [X1 : $o,X0 : $o] : ((($true = X1) & ($true = X0)) <=> ~(($true != X0) | ($true != X1)))),
% 1.48/1.28 inference(flattening,[status(thm)],[f6])).
% 1.48/1.28 tff(f6,plain,(
% 1.48/1.28 ~! [X0 : $o,X1 : $o] : ((($true = X1) & ($true = X0)) <=> ~(~($true = X0) | ~($true = X1)))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f5])).
% 1.48/1.28 tff(f5,plain,(
% 1.48/1.28 ~! [X0 : $o,X1 : $o] : (X1 & X0 = ~(~X0 | ~X1))),
% 1.48/1.28 inference(rectify,[status(thm)],[f2])).
% 1.48/1.28 tff(f2,negated_conjecture,(
% 1.48/1.28 ~! [X0 : $o,X1 : $o] : (X1 & X0 = ~(~X0 | ~X1))),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.28 tff(f1,conjecture,(
% 1.48/1.28 ! [X0 : $o,X1 : $o] : (X1 & X0 = ~(~X0 | ~X1))),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.iFgQtYbUMJ/DTF2THF_26311.p',conj)).
% 1.48/1.28 tff(f31,plain,(
% 1.48/1.28 spl2_2),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f20,f27])).
% 1.48/1.28 tff(f27,definition,(
% 1.48/1.28 spl2_2 <=> (sK0 = $true)),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.48/1.28 tff(f20,plain,(
% 1.48/1.28 (sK0 = $true)),
% 1.48/1.28 inference(duplicate_literal_removal,[status(thm)],[f17])).
% 1.48/1.28 tff(f17,plain,(
% 1.48/1.28 (sK0 = $true) | (sK0 = $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.28 tff(f30,plain,(
% 1.48/1.28 ~spl2_1 | ~spl2_2),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f21,f27,f23])).
% 1.48/1.28 tff(f21,plain,(
% 1.48/1.28 (sK1 != $true) | (sK0 != $true)),
% 1.48/1.28 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 1.48/1.28 tff(f18,plain,(
% 1.48/1.28 (sK1 != $true) | (sK0 != $true) | (sK0 != $true) | (sK1 != $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.28 % SZS output end Proof for DTF2THF_26311
% 1.48/1.28 % (26534)------------------------------
% 1.48/1.28 % (26534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (26534)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (26534)Memory used [KB]: 5500
% 1.48/1.28 % (26534)Time elapsed: 0.002 s
% 1.48/1.28 % (26534)------------------------------
% 1.48/1.28 % (26534)------------------------------
% 1.48/1.28 % (26533)Success in time 0.01 s
%------------------------------------------------------------------------------