%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV388^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 09:41:09 AM UTC 2026
% Result : Theorem 1.80s 1.54s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 42 ( 8 ~; 0 |; 6 &; 19 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 4 !; 2 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: $i > $o ).
thf(func_def_1,type,
cR: $i > $o ).
thf(f13,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f10,f12]) ).
thf(f12,plain,
( ( cS @ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f11,f9]) ).
thf(f9,plain,
cR = cS,
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( $true
= ( cR @ sK0 ) )
& ( ( cS @ sK0 )
!= $true )
& ( cR = cS ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: $i] :
( ( ( cR @ X0 )
= $true )
& ( ( cS @ X0 )
!= $true ) )
=> ( ( $true
= ( cR @ sK0 ) )
& ( ( cS @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ? [X0: $i] :
( ( ( cR @ X0 )
= $true )
& ( ( cS @ X0 )
!= $true ) )
& ( cR = cS ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( cR = cS )
=> ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cS @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( cR = cS )
=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( cR = cS )
=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( cR = cS )
=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8nzg9VEcYw/DTF2THF_26618.p',cTHM36_pme) ).
thf(f11,plain,
( $true
= ( cR @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f10,plain,
( ( cS @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV388^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n006.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:45:45 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEV388^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.44 % Domain : Set Theory
% 0.17/0.44 % Problem : TPS problem THM36
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Bro09]
% 0.17/0.44 % Names : tps_0043 [Bro09]
% 0.17/0.44 % : THM36 [TPS]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.17/0.44 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.17/0.44 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 3 ( 5 avg)
% 0.17/0.44 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 2 @)
% 0.17/0.44 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 5 ( 5 avg)
% 0.17/0.44 % Number of types : 2 ( 0 usr)
% 0.17/0.44 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.17/0.44 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.17/0.44 % SPC : TH0_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.44 % : Polymorphic definitions expanded.
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(cS,type,
% 0.17/0.44 cS: $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(cR,type,
% 0.17/0.44 cR: $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(cTHM36_pme,conjecture,
% 0.17/0.44 ( ( cR = cS )
% 0.17/0.44 => ! [Xx: $i] :
% 0.17/0.44 ( ( cR @ Xx )
% 0.17/0.44 => ( cS @ Xx ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.80/1.50 ---- Embedded in THF ---
% 1.80/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.80/1.50 %%% Generated on Tue Feb 24 12:45:46 EST 2026
% 1.80/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 1.80/1.50 %%% Logic specification used:
% 1.80/1.50 %%% thf(spec, logic, $$dhol).
% 1.80/1.50
% 1.80/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8nzg9VEcYw/DTF2DTF26618.p
% See solution above
% 1.80/1.50 ------------------------
% 1.80/1.51 ---- Cleaned THF ---
% 1.80/1.52 thf(cS,type,
% 1.80/1.52 cS: $i > $o ).
% 1.80/1.52
% 1.80/1.52 thf(cR,type,
% 1.80/1.52 cR: $i > $o ).
% 1.80/1.52
% 1.80/1.52 thf(cTHM36_pme,conjecture,
% 1.80/1.52 ( ( cR = cS )
% 1.80/1.52 => ! [Xx: $i] :
% 1.80/1.52 ( ( cR @ Xx )
% 1.80/1.52 => ( cS @ Xx ) ) ) ).
% 1.80/1.52 ------------------------
% 1.80/1.54 % (26722)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26618 for (2999ds/18Mi)
% 1.80/1.54 % (26718)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_26618 for (2999ds/27Mi)
% 1.80/1.54 % (26721)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_26618 for (2999ds/275Mi)
% 1.80/1.54 % (26721)First to succeed.
% 1.80/1.54 % (26722)Also succeeded, but the first one will report.
% 1.80/1.54 % (26718)Also succeeded, but the first one will report.
% 1.80/1.54 % (26721)Refutation found. Thanks to Tanya!
% 1.80/1.54 % SZS status Theorem for DTF2THF_26618
% 1.80/1.54 % SZS output start Proof for DTF2THF_26618
% 1.80/1.54 thf(func_def_0, type, cS: $i > $o).
% 1.80/1.54 thf(func_def_1, type, cR: $i > $o).
% 1.80/1.54 thf(f13,plain,(
% 1.80/1.54 $false),
% 1.80/1.54 inference(subsumption_resolution,[status(thm)],[f10,f12])).
% 1.80/1.54 thf(f12,plain,(
% 1.80/1.54 ((cS @ sK0) = $true)),
% 1.80/1.54 inference(definition_unfolding,[status(thm)],[f11,f9])).
% 1.80/1.54 thf(f9,plain,(
% 1.80/1.54 (cR = cS)),
% 1.80/1.54 inference(cnf_transformation,[status(thm)],[f8])).
% 1.80/1.54 thf(f8,plain,(
% 1.80/1.54 (($true = (cR @ sK0)) & ((cS @ sK0) != $true)) & (cR = cS)),
% 1.80/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.80/1.54 thf(f7,plain,(
% 1.80/1.54 ? [X0 : $i] : (((cR @ X0) = $true) & ((cS @ X0) != $true)) => (($true = (cR @ sK0)) & ((cS @ sK0) != $true))),
% 1.80/1.54 introduced(definition,[],[choice_axiom])).
% 1.80/1.54 thf(f6,plain,(
% 1.80/1.54 ? [X0 : $i] : (((cR @ X0) = $true) & ((cS @ X0) != $true)) & (cR = cS)),
% 1.80/1.54 inference(ennf_transformation,[status(thm)],[f5])).
% 1.80/1.54 thf(f5,plain,(
% 1.80/1.54 ~((cR = cS) => ! [X0 : $i] : (((cR @ X0) = $true) => ((cS @ X0) = $true)))),
% 1.80/1.54 inference(fool_elimination,[status(thm)],[f4])).
% 1.80/1.54 thf(f4,plain,(
% 1.80/1.54 ~((cR = cS) => ! [X0 : $i] : ((cR @ X0) => (cS @ X0)))),
% 1.80/1.54 inference(rectify,[status(thm)],[f2])).
% 1.80/1.54 thf(f2,negated_conjecture,(
% 1.80/1.54 ~((cR = cS) => ! [X0 : $i] : ((cR @ X0) => (cS @ X0)))),
% 1.80/1.54 inference(negated_conjecture,[status(cth)],[f1])).
% 1.80/1.54 thf(f1,conjecture,(
% 1.80/1.54 (cR = cS) => ! [X0 : $i] : ((cR @ X0) => (cS @ X0))),
% 1.80/1.54 file('/export/starexec/sandbox/tmp/tmp.8nzg9VEcYw/DTF2THF_26618.p',cTHM36_pme)).
% 1.80/1.54 thf(f11,plain,(
% 1.80/1.54 ($true = (cR @ sK0))),
% 1.80/1.54 inference(cnf_transformation,[status(thm)],[f8])).
% 1.80/1.54 thf(f10,plain,(
% 1.80/1.54 ((cS @ sK0) != $true)),
% 1.80/1.54 inference(cnf_transformation,[status(thm)],[f8])).
% 1.80/1.54 % SZS output end Proof for DTF2THF_26618
% 1.80/1.54 % (26721)------------------------------
% 1.80/1.54 % (26721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.54 % (26721)Termination reason: Refutation
% 1.80/1.54
% 1.80/1.54 % (26721)Memory used [KB]: 5373
% 1.80/1.54 % (26721)Time elapsed: 0.002 s
% 1.80/1.54 % (26721)Instructions burned: 1 (million)
% 1.80/1.54 % (26721)------------------------------
% 1.80/1.54 % (26721)------------------------------
% 1.80/1.54 % (26715)Success in time 0.019 s
%------------------------------------------------------------------------------