%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO299^5 : 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 : 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 09:53:53 AM UTC 2026
% Result : Theorem 1.49s 1.27s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 146 ( 67 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 115 ( 38 ~; 35 |; 19 &)
% ( 17 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 152 ( 63 fml; 89 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 7 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 45 ( 26 !; 19 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
tff(f51,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f36,f50]) ).
tff(f50,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f49]) ).
tff(f49,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f41,f39]) ).
tff(f39,plain,
( ! [X0: $o,X1: $o] : ( (X0) = (X1) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f24,f24]) ).
tff(f24,plain,
( ! [X3: $o] : ( sK1 = (X3) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
tff(f23,definition,
( spl3_2
<=> ! [X3: $o] : ( sK1 = (X3) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
tff(f41,plain,
( ! [X0: $o] : ( $true != (X0) )
| spl3_1
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f20,f39]) ).
tff(f20,plain,
( ( $true != sK0 )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
tff(f19,definition,
( spl3_1
<=> ( $true = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
tff(f36,plain,
~ spl3_1,
inference(avatar_split_clause,[status(thm)],[f17,f19]) ).
tff(f17,plain,
$true != sK0,
inference(equality_resolution,[status(thm)],[f16]) ).
tff(f16,plain,
! [X3: $o] :
( ( $true != sK0 )
| ( sK1 != (X3) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
tff(f12,plain,
! [X3: $o] :
( ( ( $true != sK0 )
| ( sK1 != (X3) ) )
& ( ( $true = sK0 )
| ( sK1 = (X3) ) )
& ( ( sK1 = sK0 )
| ( sK2 != $true ) )
& ( ( sK2 = $true )
| ( sK1 != sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11]) ).
tff(f11,plain,
( ? [X0: $o,X1: $o,X2: $o] :
! [X3: $o] :
( ( ( $true != (X0) )
| ( (X1) != (X3) ) )
& ( ( $true = (X0) )
| ( (X1) = (X3) ) )
& ( ( (X0) = (X1) )
| ( $true != (X2) ) )
& ( ( $true = (X2) )
| ( (X0) != (X1) ) ) )
=> ! [X3: $o] :
( ( ( $true != sK0 )
| ( sK1 != (X3) ) )
& ( ( $true = sK0 )
| ( sK1 = (X3) ) )
& ( ( sK1 = sK0 )
| ( sK2 != $true ) )
& ( ( sK2 = $true )
| ( sK1 != sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f10,plain,
? [X0: $o,X1: $o,X2: $o] :
! [X3: $o] :
( ( ( $true != (X0) )
| ( (X1) != (X3) ) )
& ( ( $true = (X0) )
| ( (X1) = (X3) ) )
& ( ( (X0) = (X1) )
| ( $true != (X2) ) )
& ( ( $true = (X2) )
| ( (X0) != (X1) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
tff(f9,plain,
? [X2: $o,X0: $o,X1: $o] :
! [X3: $o] :
( ( ( $true != (X2) )
| ( (X0) != (X3) ) )
& ( ( $true = (X2) )
| ( (X0) = (X3) ) )
& ( ( (X0) = (X2) )
| ( $true != (X1) ) )
& ( ( $true = (X1) )
| ( (X0) != (X2) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
tff(f8,plain,
? [X2: $o,X0: $o,X1: $o] :
! [X3: $o] :
( ( ( $true != (X2) )
| ( (X0) != (X3) ) )
& ( ( $true = (X2) )
| ( (X0) = (X3) ) )
& ( ( (X0) = (X2) )
| ( $true != (X1) ) )
& ( ( $true = (X1) )
| ( (X0) != (X2) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
tff(f7,plain,
? [X2: $o,X0: $o,X1: $o] :
! [X3: $o] :
( ( ( (X0) = (X3) )
<~> ( $true = (X2) ) )
& ( ( (X0) = (X2) )
<=> ( $true = (X1) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
tff(f6,plain,
~ ! [X0: $o,X2: $o,X1: $o] :
? [X3: $o] :
( ( ( (X0) = (X2) )
<=> ( $true = (X1) ) )
=> ( ( (X0) = (X3) )
<=> ( $true = (X2) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
tff(f5,plain,
~ ! [X0: $o,X1: $o,X2: $o] :
? [X3: $o] :
( ( ( (X0)
<=> (X2) )
<=> (X1) )
=> ( ( (X0)
<=> (X3) )
<=> (X2) ) ),
inference(rectify,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X1: $o,X2: $o,X0: $o] :
? [X3: $o] :
( ( ( (X1)
<=> (X0) )
<=> (X2) )
=> ( ( (X1)
<=> (X3) )
<=> (X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
! [X1: $o,X2: $o,X0: $o] :
? [X3: $o] :
( ( ( (X1)
<=> (X0) )
<=> (X2) )
=> ( ( (X1)
<=> (X3) )
<=> (X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YRy8ceTJXt/DTF2THF_24547.p',cTHM51) ).
tff(f25,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f23,f19]) ).
tff(f15,plain,
! [X3: $o] :
( ( sK1 = (X3) )
| ( $true = sK0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO299^5 : 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
% 0.15/0.34 % Computer : n026.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 14:27:55 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYO299^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : TPS problem from BASIC-HO-THMS
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0762 [Bro09]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.28/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.28/0.46 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 0 @)
% 0.28/0.46 % ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.28/0.46 % Number of types : 1 ( 0 usr)
% 0.28/0.46 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.28/0.46 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(cTHM51,conjecture,
% 0.28/0.46 ! [P: $o,Q: $o,R: $o] :
% 0.28/0.46 ? [S: $o] :
% 0.28/0.46 ( ( ( P
% 0.28/0.46 <=> Q )
% 0.28/0.46 <=> R )
% 0.28/0.46 => ( P
% 0.28/0.46 <=> ( Q
% 0.28/0.46 <=> S ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.24 %%% Generated on Tue Feb 24 14:27:56 EST 2026
% 1.49/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.24 %%% Logic specification used:
% 1.49/1.24 %%% thf(spec, logic, $$dhol).
% 1.49/1.24
% 1.49/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YRy8ceTJXt/DTF2DTF24547.p
% See solution above
% 1.49/1.24 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(cTHM51,conjecture,
% 1.49/1.25 ! [P: $o,Q: $o,R: $o] :
% 1.49/1.25 ? [S: $o] :
% 1.49/1.25 ( ( ( P
% 1.49/1.25 <=> Q )
% 1.49/1.25 <=> R )
% 1.49/1.25 => ( P
% 1.49/1.25 <=> ( Q
% 1.49/1.25 <=> S ) ) ) ).
% 1.49/1.25 ------------------------
% 1.49/1.27 % (24764)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_24547 for (3000ds/275Mi)
% 1.49/1.27 % (24761)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_24547 for (3000ds/27Mi)
% 1.49/1.27 % (24764)First to succeed.
% 1.49/1.27 % (24761)Also succeeded, but the first one will report.
% 1.49/1.27 % (24764)Refutation found. Thanks to Tanya!
% 1.49/1.27 % SZS status Theorem for DTF2THF_24547
% 1.49/1.27 % SZS output start Proof for DTF2THF_24547
% 1.49/1.27 tff(f51,plain,(
% 1.49/1.27 $false),
% 1.49/1.27 inference(avatar_sat_refutation,[status(thm)],[f25,f36,f50])).
% 1.49/1.27 tff(f50,plain,(
% 1.49/1.27 spl3_1 | ~spl3_2),
% 1.49/1.27 inference(avatar_contradiction_clause,[status(thm)],[f49])).
% 1.49/1.27 tff(f49,plain,(
% 1.49/1.27 $false | (spl3_1 | ~spl3_2)),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f41,f39])).
% 1.49/1.27 tff(f39,plain,(
% 1.49/1.27 ( ! [X0 : $o,X1 : $o] : ((X0 = X1)) ) | ~spl3_2),
% 1.49/1.27 inference(superposition,[status(thm)],[f24,f24])).
% 1.49/1.27 tff(f24,plain,(
% 1.49/1.27 ( ! [X3 : $o] : ((sK1 = X3)) ) | ~spl3_2),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.49/1.27 tff(f23,definition,(
% 1.49/1.27 spl3_2 <=> ! [X3 : $o] : (sK1 = X3)),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.49/1.27 tff(f41,plain,(
% 1.49/1.27 ( ! [X0 : $o] : (($true != X0)) ) | (spl3_1 | ~spl3_2)),
% 1.49/1.27 inference(superposition,[status(thm)],[f20,f39])).
% 1.49/1.27 tff(f20,plain,(
% 1.49/1.27 ($true != sK0) | spl3_1),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.49/1.27 tff(f19,definition,(
% 1.49/1.27 spl3_1 <=> ($true = sK0)),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.49/1.27 tff(f36,plain,(
% 1.49/1.27 ~spl3_1),
% 1.49/1.27 inference(avatar_split_clause,[status(thm)],[f17,f19])).
% 1.49/1.27 tff(f17,plain,(
% 1.49/1.27 ($true != sK0)),
% 1.49/1.27 inference(equality_resolution,[status(thm)],[f16])).
% 1.49/1.27 tff(f16,plain,(
% 1.49/1.27 ( ! [X3 : $o] : (($true != sK0) | (sK1 != X3)) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.27 tff(f12,plain,(
% 1.49/1.27 ! [X3 : $o] : ((($true != sK0) | (sK1 != X3)) & (($true = sK0) | (sK1 = X3)) & ((sK1 = sK0) | (sK2 != $true)) & ((sK2 = $true) | (sK1 != sK0)))),
% 1.49/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11])).
% 1.49/1.27 tff(f11,plain,(
% 1.49/1.27 ? [X0 : $o,X1 : $o,X2 : $o] : ! [X3 : $o] : ((($true != X0) | (X1 != X3)) & (($true = X0) | (X1 = X3)) & ((X0 = X1) | ($true != X2)) & (($true = X2) | (X0 != X1))) => ! [X3 : $o] : ((($true != sK0) | (sK1 != X3)) & (($true = sK0) | (sK1 = X3)) & ((sK1 = sK0) | (sK2 != $true)) & ((sK2 = $true) | (sK1 != sK0)))),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 tff(f10,plain,(
% 1.49/1.27 ? [X0 : $o,X1 : $o,X2 : $o] : ! [X3 : $o] : ((($true != X0) | (X1 != X3)) & (($true = X0) | (X1 = X3)) & ((X0 = X1) | ($true != X2)) & (($true = X2) | (X0 != X1)))),
% 1.49/1.27 inference(rectify,[status(thm)],[f9])).
% 1.49/1.27 tff(f9,plain,(
% 1.49/1.27 ? [X2 : $o,X0 : $o,X1 : $o] : ! [X3 : $o] : ((($true != X2) | (X0 != X3)) & (($true = X2) | (X0 = X3)) & ((X0 = X2) | ($true != X1)) & (($true = X1) | (X0 != X2)))),
% 1.49/1.27 inference(flattening,[status(thm)],[f8])).
% 1.49/1.27 tff(f8,plain,(
% 1.49/1.27 ? [X2 : $o,X0 : $o,X1 : $o] : ! [X3 : $o] : (((($true != X2) | (X0 != X3)) & (($true = X2) | (X0 = X3))) & (((X0 = X2) | ($true != X1)) & (($true = X1) | (X0 != X2))))),
% 1.49/1.27 inference(nnf_transformation,[status(thm)],[f7])).
% 1.49/1.27 tff(f7,plain,(
% 1.49/1.27 ? [X2 : $o,X0 : $o,X1 : $o] : ! [X3 : $o] : (((X0 = X3) <~> ($true = X2)) & ((X0 = X2) <=> ($true = X1)))),
% 1.49/1.27 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.27 tff(f6,plain,(
% 1.49/1.27 ~! [X0 : $o,X2 : $o,X1 : $o] : ? [X3 : $o] : (((X0 = X2) <=> ($true = X1)) => ((X0 = X3) <=> ($true = X2)))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f5])).
% 1.49/1.27 tff(f5,plain,(
% 1.49/1.27 ~! [X0 : $o,X1 : $o,X2 : $o] : ? [X3 : $o] : (((X0 <=> X2) <=> X1) => ((X0 <=> X3) <=> X2))),
% 1.49/1.27 inference(rectify,[status(thm)],[f2])).
% 1.49/1.27 tff(f2,negated_conjecture,(
% 1.49/1.27 ~! [X1 : $o,X2 : $o,X0 : $o] : ? [X3 : $o] : (((X1 <=> X0) <=> X2) => ((X1 <=> X3) <=> X0))),
% 1.49/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.27 tff(f1,conjecture,(
% 1.49/1.27 ! [X1 : $o,X2 : $o,X0 : $o] : ? [X3 : $o] : (((X1 <=> X0) <=> X2) => ((X1 <=> X3) <=> X0))),
% 1.49/1.27 file('/export/starexec/sandbox2/tmp/tmp.YRy8ceTJXt/DTF2THF_24547.p',cTHM51)).
% 1.49/1.27 tff(f25,plain,(
% 1.49/1.27 spl3_1 | spl3_2),
% 1.49/1.27 inference(avatar_split_clause,[status(thm)],[f15,f23,f19])).
% 1.49/1.27 tff(f15,plain,(
% 1.49/1.27 ( ! [X3 : $o] : ((sK1 = X3) | ($true = sK0)) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.27 % SZS output end Proof for DTF2THF_24547
% 1.49/1.27 % (24764)------------------------------
% 1.49/1.27 % (24764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (24764)Termination reason: Refutation
% 1.49/1.27
% 1.49/1.27 % (24764)Memory used [KB]: 5500
% 1.49/1.27 % (24764)Time elapsed: 0.002 s
% 1.49/1.27 % (24764)Instructions burned: 1 (million)
% 1.49/1.27 % (24764)------------------------------
% 1.49/1.27 % (24764)------------------------------
% 1.49/1.27 % (24758)Success in time 0.011 s
%------------------------------------------------------------------------------