%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO019^1 : 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 : n026.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 1.27s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 73 equ)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 117 ( 50 ~; 35 |; 25 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 158 ( 102 fml; 56 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 4 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 20 ( 10 !; 10 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(f23,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f19,f22]) ).
tff(f22,plain,
$true != sK1,
inference(subsumption_resolution,[status(thm)],[f20,f21]) ).
tff(f21,plain,
$true = sK0,
inference(duplicate_literal_removal,[status(thm)],[f17]) ).
tff(f17,plain,
( ( $true = sK0 )
| ( $true = sK0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
tff(f13,plain,
( ( ( $true != sK0 )
| ( $true != sK1 )
| ( $true != sK0 )
| ( $true != sK1 ) )
& ( ( ( $true = sK0 )
& ( $true = sK1 ) )
| ( ( $true = sK0 )
& ( $true = sK1 ) ) ) ),
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) ) ) ) )
=> ( ( ( $true != sK0 )
| ( $true != sK1 )
| ( $true != sK0 )
| ( $true != sK1 ) )
& ( ( ( $true = sK0 )
& ( $true = sK1 ) )
| ( ( $true = sK0 )
& ( $true = sK1 ) ) ) ) ),
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 = (X1) )
& ( $true = (X0) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
tff(f5,plain,
~ ! [X0: $o,X1: $o] :
( ~ ( ~ (X1)
| ~ (X0) )
<=> ( (X1)
& (X0) ) ),
inference(rectify,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X0: $o,X1: $o] :
( ~ ( ~ (X1)
| ~ (X0) )
<=> ( (X1)
& (X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
! [X0: $o,X1: $o] :
( ~ ( ~ (X1)
| ~ (X0) )
<=> ( (X1)
& (X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3W0e7x277T/DTF2THF_2969.p',conj) ).
tff(f20,plain,
( ( $true != sK1 )
| ( $true != sK0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
tff(f18,plain,
( ( $true != sK1 )
| ( $true != sK0 )
| ( $true != sK1 )
| ( $true != sK0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
tff(f19,plain,
$true = sK1,
inference(duplicate_literal_removal,[status(thm)],[f14]) ).
tff(f14,plain,
( ( $true = sK1 )
| ( $true = sK1 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO019^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n026.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 14:21:40 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO019^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : De Morgan by equivalance
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.30/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Ben09]
% 0.30/0.46 % Names : Example 20a [BB05]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.30/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.30/0.46 % Number of connectives : 6 ( 3 ~; 1 |; 1 &; 0 @)
% 0.30/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.30/0.46 % Number of types : 1 ( 0 usr)
% 0.30/0.46 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.30/0.46 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(conj,conjecture,
% 0.30/0.46 ! [X: $o,Y: $o] :
% 0.30/0.46 ( ( X
% 0.30/0.46 & Y )
% 0.30/0.46 <=> ~ ( ~ X
% 0.30/0.46 | ~ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 14:21:41 EST 2026
% 1.48/1.25 %%% using '$$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.3W0e7x277T/DTF2DTF2969.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 ------------------------
% 1.48/1.27 % (3181)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_2969 for (3000ds/275Mi)
% 1.48/1.27 % (3181)First to succeed.
% 1.48/1.27 % (3181)Refutation found. Thanks to Tanya!
% 1.48/1.27 % SZS status Theorem for DTF2THF_2969
% 1.48/1.27 % SZS output start Proof for DTF2THF_2969
% 1.48/1.27 tff(f23,plain,(
% 1.48/1.27 $false),
% 1.48/1.27 inference(subsumption_resolution,[status(thm)],[f19,f22])).
% 1.48/1.27 tff(f22,plain,(
% 1.48/1.27 ($true != sK1)),
% 1.48/1.27 inference(subsumption_resolution,[status(thm)],[f20,f21])).
% 1.48/1.27 tff(f21,plain,(
% 1.48/1.27 ($true = sK0)),
% 1.48/1.27 inference(duplicate_literal_removal,[status(thm)],[f17])).
% 1.48/1.27 tff(f17,plain,(
% 1.48/1.27 ($true = sK0) | ($true = sK0)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.27 tff(f13,plain,(
% 1.48/1.27 (($true != sK0) | ($true != sK1) | ($true != sK0) | ($true != sK1)) & ((($true = sK0) & ($true = sK1)) | (($true = sK0) & ($true = sK1)))),
% 1.48/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f12])).
% 1.48/1.27 tff(f12,plain,(
% 1.48/1.27 ? [X0 : $o,X1 : $o] : ((($true != X0) | ($true != X1) | ($true != X0) | ($true != X1)) & ((($true = X0) & ($true = X1)) | (($true = X0) & ($true = X1)))) => ((($true != sK0) | ($true != sK1) | ($true != sK0) | ($true != sK1)) & ((($true = sK0) & ($true = sK1)) | (($true = sK0) & ($true = sK1))))),
% 1.48/1.27 introduced(definition,[],[choice_axiom])).
% 1.48/1.27 tff(f11,plain,(
% 1.48/1.27 ? [X0 : $o,X1 : $o] : ((($true != X0) | ($true != X1) | ($true != X0) | ($true != X1)) & ((($true = X0) & ($true = X1)) | (($true = X0) & ($true = X1))))),
% 1.48/1.27 inference(rectify,[status(thm)],[f10])).
% 1.48/1.27 tff(f10,plain,(
% 1.48/1.27 ? [X1 : $o,X0 : $o] : ((($true != X1) | ($true != X0) | ($true != X1) | ($true != X0)) & ((($true = X1) & ($true = X0)) | (($true = X1) & ($true = X0))))),
% 1.48/1.27 inference(flattening,[status(thm)],[f9])).
% 1.48/1.27 tff(f9,plain,(
% 1.48/1.27 ? [X1 : $o,X0 : $o] : (((($true != X1) | ($true != X0)) | (($true != X1) | ($true != X0))) & ((($true = X1) & ($true = X0)) | (($true = X1) & ($true = X0))))),
% 1.48/1.27 inference(nnf_transformation,[status(thm)],[f8])).
% 1.48/1.27 tff(f8,plain,(
% 1.48/1.27 ? [X1 : $o,X0 : $o] : ((($true = X1) & ($true = X0)) <~> (($true = X1) & ($true = X0)))),
% 1.48/1.27 inference(ennf_transformation,[status(thm)],[f7])).
% 1.48/1.27 tff(f7,plain,(
% 1.48/1.27 ~! [X1 : $o,X0 : $o] : ((($true = X1) & ($true = X0)) <=> ~(($true != X0) | ($true != X1)))),
% 1.48/1.27 inference(flattening,[status(thm)],[f6])).
% 1.48/1.27 tff(f6,plain,(
% 1.48/1.27 ~! [X0 : $o,X1 : $o] : (~(~($true = X1) | ~($true = X0)) <=> (($true = X1) & ($true = X0)))),
% 1.48/1.27 inference(fool_elimination,[status(thm)],[f5])).
% 1.48/1.27 tff(f5,plain,(
% 1.48/1.27 ~! [X0 : $o,X1 : $o] : (~(~X1 | ~X0) <=> (X1 & X0))),
% 1.48/1.27 inference(rectify,[status(thm)],[f2])).
% 1.48/1.27 tff(f2,negated_conjecture,(
% 1.48/1.27 ~! [X0 : $o,X1 : $o] : (~(~X1 | ~X0) <=> (X1 & X0))),
% 1.48/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.27 tff(f1,conjecture,(
% 1.48/1.27 ! [X0 : $o,X1 : $o] : (~(~X1 | ~X0) <=> (X1 & X0))),
% 1.48/1.27 file('/export/starexec/sandbox2/tmp/tmp.3W0e7x277T/DTF2THF_2969.p',conj)).
% 1.48/1.27 tff(f20,plain,(
% 1.48/1.27 ($true != sK1) | ($true != sK0)),
% 1.48/1.27 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 1.48/1.27 tff(f18,plain,(
% 1.48/1.27 ($true != sK1) | ($true != sK0) | ($true != sK1) | ($true != sK0)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.27 tff(f19,plain,(
% 1.48/1.27 ($true = sK1)),
% 1.48/1.27 inference(duplicate_literal_removal,[status(thm)],[f14])).
% 1.48/1.27 tff(f14,plain,(
% 1.48/1.27 ($true = sK1) | ($true = sK1)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.27 % SZS output end Proof for DTF2THF_2969
% 1.48/1.27 % (3181)------------------------------
% 1.48/1.27 % (3181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (3181)Termination reason: Refutation
% 1.48/1.27
% 1.48/1.27 % (3181)Memory used [KB]: 5373
% 1.48/1.27 % (3181)Time elapsed: 0.002 s
% 1.48/1.27 % (3181)Instructions burned: 1 (million)
% 1.48/1.27 % (3181)------------------------------
% 1.48/1.27 % (3181)------------------------------
% 1.48/1.27 % (3175)Success in time 0.011 s
%------------------------------------------------------------------------------