%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV161^5 : 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 : n004.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 09:40:26 AM UTC 2026
% Result : Theorem 1.51s 1.21s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 7 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 53 ( 9 ~; 0 |; 0 &; 40 @)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 12 !; 9 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_6,type,
sK2: a > a > $o ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
thf(f10,plain,
( ( sK2 @ sK0 @ sK1 )
!= ( sK2 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( sK2 @ sK0 @ sK1 )
!= ( sK2 @ sK0 @ sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: a,X1: a,X2: a > a > $o] :
( ( X2 @ X0 @ X1 )
!= ( X2 @ X0 @ X1 ) )
=> ( ( sK2 @ sK0 @ sK1 )
!= ( sK2 @ sK0 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a,X1: a,X2: a > a > $o] :
( ( X2 @ X0 @ X1 )
!= ( X2 @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X2: a,X0: a,X1: a > a > $o] :
( ( X1 @ X2 @ X0 )
!= ( X1 @ X2 @ X0 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X2: a,X1: a > a > $o,X0: a] :
( ( X1 @ X2 @ X0 )
= ( X1 @ X2 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a] :
( ( X1 @ X2 @ X0 )
<=> ( X1 @ X2 @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X0: a > a > $o,X1: a] :
( ( X0 @ X1 @ X2 )
<=> ( X0 @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a,X0: a > a > $o,X1: a] :
( ( X0 @ X1 @ X2 )
<=> ( X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.DCgaru4zMd/DTF2THF_12146.p',cTHM183_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV161^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n004.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 12:40:56 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.41 ---- Original DTF file ---
% 0.18/0.41 thf(spec,logic,$$dhol).
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 % File : SEV161^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.41 % Domain : Set Theory
% 0.18/0.41 % Problem : TPS problem THM183
% 0.18/0.41 % Version : Especial.
% 0.18/0.41 % English : Basic theorem about pairing.
% 0.18/0.41
% 0.18/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.41 % Source : [Bro09]
% 0.18/0.41 % Names : tps_0071 [Bro09]
% 0.18/0.41 % : THM183 [TPS]
% 0.18/0.41
% 0.18/0.41 % Status : Theorem
% 0.18/0.41 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.18/0.41 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.41 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.18/0.41 % Maximal formula atoms : 0 ( 0 avg)
% 0.18/0.41 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% 0.18/0.41 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.41 % Maximal formula depth : 7 ( 7 avg)
% 0.18/0.41 % Number of types : 2 ( 1 usr)
% 0.18/0.41 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.18/0.41 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.18/0.41 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.18/0.41 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.41
% 0.18/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.41 % : Polymorphic definitions expanded.
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 thf(a_type,type,
% 0.18/0.41 a: $tType ).
% 0.18/0.41
% 0.18/0.41 thf(cTHM183_pme,conjecture,
% 0.18/0.41 ! [Xr: a > a > $o,Xx: a,Xy: a] :
% 0.18/0.41 ( ( Xr @ Xx @ Xy )
% 0.18/0.41 <=> ( Xr @ Xx @ Xy ) ) ).
% 0.18/0.41
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 ------------------------
% 1.38/1.19 ---- Embedded in THF ---
% 1.38/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.19 %%% Generated on Tue Feb 24 12:40:57 EST 2026
% 1.38/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.19 %%% Logic specification used:
% 1.38/1.19 %%% thf(spec, logic, $$dhol).
% 1.38/1.19
% 1.38/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.DCgaru4zMd/DTF2DTF12146.p
% See solution above
% 1.38/1.19 ------------------------
% 1.51/1.20 ---- Cleaned THF ---
% 1.51/1.20 thf(a_type,type,
% 1.51/1.20 a: $tType ).
% 1.51/1.20
% 1.51/1.20 thf(cTHM183_pme,conjecture,
% 1.51/1.20 ! [Xr: a > a > $o,Xx: a,Xy: a] :
% 1.51/1.20 ( ( Xr @ Xx @ Xy )
% 1.51/1.20 <=> ( Xr @ Xx @ Xy ) ) ).
% 1.51/1.20 ------------------------
% 1.51/1.21 % (12429)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_12146 for (2999ds/2Mi)
% 1.51/1.21 % (12426)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_12146 for (2999ds/4Mi)
% 1.51/1.21 % (12429)Instruction limit reached!
% 1.51/1.21 % (12429)------------------------------
% 1.51/1.21 % (12429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.21 % (12429)Termination reason: Unknown
% 1.51/1.21 % (12429)Termination phase: Saturation
% 1.51/1.21
% 1.51/1.21 % (12429)Memory used [KB]: 5500
% 1.51/1.21 % (12429)Time elapsed: 0.002 s
% 1.51/1.21 % (12429)Instructions burned: 2 (million)
% 1.51/1.21 % (12429)------------------------------
% 1.51/1.21 % (12429)------------------------------
% 1.51/1.21 % (12426)First to succeed.
% 1.51/1.21 % (12426)Refutation found. Thanks to Tanya!
% 1.51/1.21 % SZS status Theorem for DTF2THF_12146
% 1.51/1.21 % SZS output start Proof for DTF2THF_12146
% 1.51/1.21 thf(type_def_5, type, a: $tType).
% 1.51/1.21 thf(func_def_0, type, a: $tType).
% 1.51/1.21 thf(func_def_4, type, sK0: a).
% 1.51/1.21 thf(func_def_5, type, sK1: a).
% 1.51/1.21 thf(func_def_6, type, sK2: a > a > $o).
% 1.51/1.21 thf(f11,plain,(
% 1.51/1.21 $false),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 1.51/1.21 thf(f10,plain,(
% 1.51/1.21 ((sK2 @ sK0 @ sK1) != (sK2 @ sK0 @ sK1))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.21 thf(f9,plain,(
% 1.51/1.21 ((sK2 @ sK0 @ sK1) != (sK2 @ sK0 @ sK1))),
% 1.51/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f8])).
% 1.51/1.21 thf(f8,plain,(
% 1.51/1.21 ? [X0 : a,X1 : a,X2 : a > a > $o] : ((X2 @ X0 @ X1) != (X2 @ X0 @ X1)) => ((sK2 @ sK0 @ sK1) != (sK2 @ sK0 @ sK1))),
% 1.51/1.21 introduced(definition,[],[choice_axiom])).
% 1.51/1.21 thf(f7,plain,(
% 1.51/1.21 ? [X0 : a,X1 : a,X2 : a > a > $o] : ((X2 @ X0 @ X1) != (X2 @ X0 @ X1))),
% 1.51/1.21 inference(rectify,[status(thm)],[f6])).
% 1.51/1.21 thf(f6,plain,(
% 1.51/1.21 ? [X2 : a,X0 : a,X1 : a > a > $o] : ((X1 @ X2 @ X0) != (X1 @ X2 @ X0))),
% 1.51/1.21 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.21 thf(f5,plain,(
% 1.51/1.21 ~! [X2 : a,X1 : a > a > $o,X0 : a] : ((X1 @ X2 @ X0) = (X1 @ X2 @ X0))),
% 1.51/1.21 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.21 thf(f4,plain,(
% 1.51/1.21 ~! [X0 : a,X1 : a > a > $o,X2 : a] : ((X1 @ X2 @ X0) <=> (X1 @ X2 @ X0))),
% 1.51/1.21 inference(rectify,[status(thm)],[f2])).
% 1.51/1.21 thf(f2,negated_conjecture,(
% 1.51/1.21 ~! [X2 : a,X0 : a > a > $o,X1 : a] : ((X0 @ X1 @ X2) <=> (X0 @ X1 @ X2))),
% 1.51/1.21 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.21 thf(f1,conjecture,(
% 1.51/1.21 ! [X2 : a,X0 : a > a > $o,X1 : a] : ((X0 @ X1 @ X2) <=> (X0 @ X1 @ X2))),
% 1.51/1.21 file('/export/starexec/sandbox/tmp/tmp.DCgaru4zMd/DTF2THF_12146.p',cTHM183_pme)).
% 1.51/1.21 % SZS output end Proof for DTF2THF_12146
% 1.51/1.21 % (12426)------------------------------
% 1.51/1.21 % (12426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.21 % (12426)Termination reason: Refutation
% 1.51/1.21
% 1.51/1.21 % (12426)Memory used [KB]: 5373
% 1.51/1.21 % (12426)Time elapsed: 0.001 s
% 1.51/1.21 % (12426)Instructions burned: 1 (million)
% 1.51/1.21 % (12426)------------------------------
% 1.51/1.21 % (12426)------------------------------
% 1.51/1.21 % (12424)Success in time 0.011 s
%------------------------------------------------------------------------------