%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO368^5 : 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 : n015.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 09:54:03 AM UTC 2026
% Result : Theorem 1.48s 1.26s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 14 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 37 ( 7 ~; 0 |; 8 &; 15 @)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cP: $o > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_8,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f13,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
$true != $true,
inference(superposition,[status(thm)],[f9,f11]) ).
thf(f11,plain,
( ( cP @ b )
= $true ),
inference(definition_unfolding,[status(thm)],[f10,f8]) ).
thf(f8,plain,
a = b,
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cP @ a )
= $true )
& ( ( cP @ b )
!= $true )
& ( a = b ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cP @ b )
!= $true )
& ( a = b )
& ( ( cP @ a )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( a = b )
& ( ( cP @ a )
= $true ) )
=> ( ( cP @ b )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cP @ a )
& ( a
<=> b ) )
=> ( cP @ b ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cP @ a )
& ( a
<=> b ) )
=> ( cP @ b ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cP @ a )
& ( a
<=> b ) )
=> ( cP @ b ) ),
file('/export/starexec/sandbox2/tmp/tmp.OfNV1DZT46/DTF2THF_1495.p',cTRIVEXT1) ).
thf(f10,plain,
( ( cP @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f9,plain,
( ( cP @ b )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO368^5 : 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
% 0.17/0.34 % Computer : n015.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 14:29:01 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO368^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : TPS problem from EXTENSIONALITY
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0630 [Bro09]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 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 v5.3.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.46 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 6 ( 6 avg)
% 0.29/0.46 % Number of connectives : 5 ( 0 ~; 0 |; 1 &; 2 @)
% 0.29/0.46 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 4 ( 4 avg)
% 0.29/0.46 % Number of types : 1 ( 0 usr)
% 0.29/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 3 ( 3 usr; 2 con; 0-1 aty)
% 0.29/0.46 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(b,type,
% 0.29/0.46 b: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cP,type,
% 0.29/0.46 cP: $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(a,type,
% 0.29/0.46 a: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cTRIVEXT1,conjecture,
% 0.29/0.46 ( ( ( a
% 0.29/0.46 <=> b )
% 0.29/0.46 & ( cP @ a ) )
% 0.29/0.46 => ( cP @ b ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.48/1.23 ---- Embedded in THF ---
% 1.48/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.23 %%% Generated on Tue Feb 24 14:29:02 EST 2026
% 1.48/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.23 %%% Logic specification used:
% 1.48/1.23 %%% thf(spec, logic, $$dhol).
% 1.48/1.23
% 1.48/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.OfNV1DZT46/DTF2DTF1495.p
% See solution above
% 1.48/1.23 ------------------------
% 1.48/1.24 ---- Cleaned THF ---
% 1.48/1.24 thf(b,type,
% 1.48/1.24 b: $o ).
% 1.48/1.24
% 1.48/1.24 thf(cP,type,
% 1.48/1.24 cP: $o > $o ).
% 1.48/1.24
% 1.48/1.24 thf(a,type,
% 1.48/1.24 a: $o ).
% 1.48/1.24
% 1.48/1.24 thf(cTRIVEXT1,conjecture,
% 1.48/1.24 ( ( ( a
% 1.48/1.24 <=> b )
% 1.48/1.24 & ( cP @ a ) )
% 1.48/1.24 => ( cP @ b ) ) ).
% 1.48/1.24 ------------------------
% 1.48/1.25 % (1716)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_1495 for (2999ds/27Mi)
% 1.48/1.25 % (1713)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1495 for (2999ds/183Mi)
% 1.48/1.25 % (1716)First to succeed.
% 1.48/1.25 % (1713)Also succeeded, but the first one will report.
% 1.48/1.26 % (1716)Refutation found. Thanks to Tanya!
% 1.48/1.26 % SZS status Theorem for DTF2THF_1495
% 1.48/1.26 % SZS output start Proof for DTF2THF_1495
% 1.48/1.26 thf(func_def_1, type, cP: $o > $o).
% 1.48/1.26 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.48/1.26 thf(func_def_8, type, ph1: !>[X0: $tType]:(X0)).
% 1.48/1.26 thf(f13,plain,(
% 1.48/1.26 $false),
% 1.48/1.26 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.48/1.26 thf(f12,plain,(
% 1.48/1.26 ($true != $true)),
% 1.48/1.26 inference(superposition,[status(thm)],[f9,f11])).
% 1.48/1.26 thf(f11,plain,(
% 1.48/1.26 ((cP @ b) = $true)),
% 1.48/1.26 inference(definition_unfolding,[status(thm)],[f10,f8])).
% 1.48/1.26 thf(f8,plain,(
% 1.48/1.26 (a = b)),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.48/1.26 thf(f7,plain,(
% 1.48/1.26 ((cP @ a) = $true) & ((cP @ b) != $true) & (a = b)),
% 1.48/1.26 inference(flattening,[status(thm)],[f6])).
% 1.48/1.26 thf(f6,plain,(
% 1.48/1.26 ((cP @ b) != $true) & ((a = b) & ((cP @ a) = $true))),
% 1.48/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.26 thf(f5,plain,(
% 1.48/1.26 ~(((a = b) & ((cP @ a) = $true)) => ((cP @ b) = $true))),
% 1.48/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.26 thf(f4,plain,(
% 1.48/1.26 ~(((cP @ a) & (a <=> b)) => (cP @ b))),
% 1.48/1.26 inference(rectify,[status(thm)],[f2])).
% 1.48/1.26 thf(f2,negated_conjecture,(
% 1.48/1.26 ~(((cP @ a) & (a <=> b)) => (cP @ b))),
% 1.48/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.26 thf(f1,conjecture,(
% 1.48/1.26 ((cP @ a) & (a <=> b)) => (cP @ b)),
% 1.48/1.26 file('/export/starexec/sandbox2/tmp/tmp.OfNV1DZT46/DTF2THF_1495.p',cTRIVEXT1)).
% 1.48/1.26 thf(f10,plain,(
% 1.48/1.26 ((cP @ a) = $true)),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.48/1.26 thf(f9,plain,(
% 1.48/1.26 ((cP @ b) != $true)),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.48/1.26 % SZS output end Proof for DTF2THF_1495
% 1.48/1.26 % (1716)------------------------------
% 1.48/1.26 % (1716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (1716)Termination reason: Refutation
% 1.48/1.26
% 1.48/1.26 % (1716)Memory used [KB]: 5500
% 1.48/1.26 % (1716)Time elapsed: 0.002 s
% 1.48/1.26 % (1716)Instructions burned: 1 (million)
% 1.48/1.26 % (1716)------------------------------
% 1.48/1.26 % (1716)------------------------------
% 1.48/1.26 % (1712)Success in time 0.012 s
%------------------------------------------------------------------------------